Talk:Wavelength/Archive 3

Recent revisions
I hope you will re-read the mess you have made of this, try to connect the thought fragments, and fix the formatting. Brews ohare (talk) 05:05, 1 July 2009 (UTC)


 * Are you trying to set a good example of following your advice to be specific? It's not working.  Dicklyon (talk) 06:59, 1 July 2009 (UTC)

Fortunately, Srleffler has some notion of coherence. Brews ohare (talk) 13:18, 1 July 2009 (UTC)


 * Indeed, he does; very good work there. Dicklyon (talk) 15:01, 1 July 2009 (UTC)

WKB method
Brews, you added a thing that said how the amplitude scales with wavelength, but that's very problem dependent. It depends on what's making the velocity change, and on what state variable you're measuring. For example, in a mechanical system, velocity depends on spring constants and masses, either or both of which might be varying, and you can be plotting displacement or velocity or force or acceleration. In a 2D or 3D cochlea model, it's got complications from the nature of the wave geometry and the dispersion relation. If you want to talk about a sqrt dependence, you'll need to specify a lot more, and that makes it too narrow and less relevant, so let's leave that to the linked article. Dicklyon (talk) 15:05, 1 July 2009 (UTC)

Process
I find as of this writing that the article looks pretty good.

Many of the topics added to this page began with me, and were abusively resisted by Dicklyon, who blanket deleted attempts to expand the content of the article in several directions, despite every sentence being impeccably sourced, including direct quotes and reference to specific equations and figures; and deleted material awaiting RfC.

Fortunately, Dicklyon's obstructionism and my own tendency to undue elaboration were successfully resisted by Srleffler, who injected a bit of sanity here and there. Brews ohare (talk) 16:32, 1 July 2009 (UTC)


 * The article is definitely improving through all the back and forth editing. I agree that many good additions to the page started with you, and many of those are well sourced. I'm sure Dick would agree. We could have gotten to this point much faster if your editing style were different. If you try to stay focused on the topic at hand, and really listen to the objections other editors raise, you will find that you get much less resistance and the article can be improved more quickly, with less strife.


 * Note that sourcing is a necessary condition, not a sufficient one. Material can be impeccably sourced, and still be unsuitable for any given article for a variety of reasons.--Srleffler (talk) 17:01, 1 July 2009 (UTC)


 * Agreed. There has been net progress, but it has been really hard, and without my "abusive" pushback the net result would have been awful.  Dicklyon (talk) 17:13, 1 July 2009 (UTC)

In the case of impeccably sourced material added to a topic, who is the arbiter of whether it is germane to the article? Obviously the contributing editor thought it germane enough to track down the sources and summarize the topic (and design illustrations). The resisting editor who blanket deletes the contribution with some cryptic remark or abusive reference to the editor's style of editing strikes me as failing in method and approach. Engagement requires specific, detailed comment and alternatives from the standpoint of technical relevance, not pontification from Mount Olympus. Brews ohare (talk) 17:16, 1 July 2009 (UTC)


 * That arbiter would be us; see WP:CONSENSUS. All my deletions have been well explained, but not repeated every time. Dicklyon (talk) 17:41, 1 July 2009 (UTC)


 * That is simply untrue, Dick. You blank entire sections with a 10 word explanation like "Brews, this seems to be just one more of your idiosyncratic over-complicating approaches to a topic; stick with a more conventional approach." or "irrelevant WP:SYN; cited section does not mention wavelength" neither of which is an attempt at really talking to me or trying to engage. You are basically a hit and run editor, making snap judgments, trying for the one-two knockout, and taking insufficient time to either understand the gist or respond in an informed manner. Many of the topics you claimed were irrelevant, excess nonsense, and whatever, not only here in wavelength, but in centrifugal force, electromotive force etc.you have gradually come round to when the drip-drip-drip of repetition finally sank it in. If you were to take for granted that I'm trying hard and trying to be accommodating, you could come to these realizations sooner, and be a lot more pleasant about it. Brews ohare (talk) 23:02, 1 July 2009 (UTC)


 * Subject to constraints of policy and guidelines, consensus decides. It goes faster, though, if editors on both sides listen to one another's objections and take them seriously. You ask for specific, detailed comment, but you tend to ignore it when you get it, or to respond by adding more detail or more sources when lack of detail or lack of sources was not the problem.


 * It's not our fault if you invest a bunch of effort in researching something that isn't suitable for the article. Your judgement of the worth of material carries no more weight than anyone else's, and you can be mistaken. Sometimes material can be fixed, sometimes the best alternative is removal.--Srleffler (talk) 17:46, 1 July 2009 (UTC)


 * I am not impressed with my judgment viz a viz anyone else's, and vice versa. Brews ohare (talk) 23:02, 1 July 2009 (UTC)

I undid some shuffling of material around. The paragraphs that give examples of wavelengths need to be where they were. They provide context to the material above. Those paragraphs are not exclusively about light. Sound waves are also mentioned. Also note that WP:MOSHEAD cautions against using the same section heading more than once in an article. --Srleffler (talk) 17:32, 1 July 2009 (UTC)
 * As a general rule, in nonspecialist articles explanation needs to come ahead of mathematics. Examples of wavelengths of light and sound are more important to the general audience than the mathematical formalism for sinusoidal waves.--Srleffler (talk) 17:35, 1 July 2009 (UTC)
 * It seems to me your answer begs the question: who is the arbiter deciding that an article is a "nonspecialist article"? Who decides that a classification scheme that pigeon-holes articles into "nonspecialist" and "technical" is appropriate to a given topic? May it not happen, for example, that an article evolves over time, beginning in several categories with sections that are "nonspecialist" and sections that are "technical", thus only partly interesting to any reader, and with time breaks into separate articles as more is added? Brews ohare (talk) 17:47, 1 July 2009 (UTC)


 * I thought all wikipedia articles were for nonspecialists. Was I wrong?  Dicklyon (talk) 17:56, 1 July 2009 (UTC)

Hi Dick: Take a look at Canonical bundle; Serre duality; C*-algebra; Curvature of Riemannian manifolds; Differential form; Fermionic field; Penrose–Hawking singularity theorems; Axisymmetric spacetime; Conformal geometry, Bogoliubov transformation … need I continue? Brews ohare (talk) 18:04, 1 July 2009 (UTC)


 * No, please don't; you've made your point. What was the question again?  Dicklyon (talk) 00:36, 2 July 2009 (UTC)

wavepackets


This topic is somewhat more complicated than a 10 word summary can convey. For example, see. Localization can be achieved with a few terms. In the case of a modulated wave, the localization can be obtained with very few terms, but the envelope is then a periodic function instead of a solitary peak. Brews ohare (talk) 17:34, 1 July 2009 (UTC)


 * Right, the only thing you can get with a finite sum is a periodic train of wave packets. Hardly relevant here.  Dicklyon (talk) 17:40, 1 July 2009 (UTC)

And why is a periodic train of wavepackets irrelevant to a general article on wavelength? In fact it is interesting because such a train is an example where both types of wavelength occur, the periodic wavelength and the local wavelength. Brews ohare (talk) 17:53, 1 July 2009 (UTC)


 * Last time we looked at that, we didn't have a source for the "global wavelength" concept; do you have one now? Dicklyon (talk) 17:55, 1 July 2009 (UTC)

You are being obtuse, Dick. We already have the global periodic wavelength defined in the article as the periodicity of f(x-vt) in a traveling periodic wave. Apparently the technical term is "envelope periodicity" Popper. If we define the envelope function, say F(x), then F(x+λ) =F(x) defines the envelope periodicity.Guenther Brews ohare (talk) 18:06, 1 July 2009 (UTC)


 * Ah, yes, I see I was not diligent enough at removing your unsourced generalizations. But even if we do find a source for the wavelength of an arbitrary periodic traveling wave, that doesn't usually apply to a periodically modulated carrier, except when the carrier is a multiple of the modulation frequency.  Does anyone really ever refer to a wavelength of this sort?  Not that I've ever seen.  Dicklyon (talk) 00:41, 2 July 2009 (UTC)


 * I've taken out most of that section now, since the part you wanted to rely on for your next logical jump was unsourced, and the rest was sourced but the sources didn't mention any connection to the topic of wavelength. Dicklyon (talk) 03:58, 2 July 2009 (UTC)

New bogus section: Modulated waves
Brews, for the record, you added this text and your local/global wavelength picture:

Modulated waves


A waveform that resembles a train of wavepackets is the modulated wave of signal processing found in systems from computers to animal communication. In simplest form, such a wave consists of a short wavelength sinusoid with an amplitude that varies sinusoidally with a longer wavelength. The short wavelength, the local wavelength for this waveform, is called the carrier or fine structure and the longer wavelength amplitude wave outlining the shape of the waveform the envelope. Of course, the envelope may assume an arbitrary shape, and need not be sinusoidal. Brews ohare (talk) 02:53, 2 July 2009 (UTC)

I guess I should have copied the source text to make it easier to check your references, but I already checked, and none of the cited sources support your concept or a "global wavelength", or connect the notion of the modulator or envelope to the wavelength at all. That's why I'm about to revert it. Let me know if I missed something. Dicklyon (talk) 00:07, 2 July 2009 (UTC)


 * Dick: setting the source aside for the moment, isn't it clear to you that there are two wavelengths in this case by looking at the picture? In other words, are you simply being a stickler for a source, or you really don't get it? Brews ohare (talk) 02:36, 2 July 2009 (UTC)


 * It's not unclear what you're trying to say. I'm being a stickler for a source because I don't think the term "wavelength" is used for this concept that you have applied it to.  The whole basis of my objections to your edits is that you're doing "original research" in making up connections where none exist in normal usage of the term or concept of "wavelength", which is what this article is supposed to be about.  If you derive a logical relationship or conclusion about how the term wavelength might be applied to AM modulated signals, that's not good enough, unless you can show that the term is in fact used that way in reliable sources.  Why are you having such a hard time accepting such basic tenets of wikipedia? Dicklyon (talk) 02:47, 2 July 2009 (UTC)

How about these? Denny Hutchinson WhitehouseKevorkian Newman LenstraHutchinson. More common is reference to the frequency of the modulation envelope, but I suppose that knowing there is a connection between λ and f would not move you to see any relevance, eh? Brews ohare (talk) 03:21, 2 July 2009 (UTC)


 * Yes, those are acceptable sources if you want to introduce the "wavelength of the modulation envelope"; but don't conflate that with your "global wavelength" of a periodic function, which the figure above misleadingly does. Without the sources, no; logically, it doesn't even make much sense, since there is no wave present with that wavelength, but when it's sourced, who am I to argue?  Dicklyon (talk) 03:25, 2 July 2009 (UTC)

Animations
I'm not usually a fan of animated gifs, as they're usually very distracting and jarring, or even ugly. But now I've added a few more to the wavelength article, keeping them subtle and smooth and informative I hope, and fixed up the wave packet one that was there to be less jarring. If anyone objects, I wouldn't mind going back to still images. Dicklyon (talk) 06:47, 2 July 2009 (UTC)
 * I like the images with the exception of the one on refraction, which is as you say, jarring. Brews ohare (talk) 12:55, 2 July 2009 (UTC)
 * OK, we can take it out. I had looked for a good alternative, and all the other wave refraction images that showed wavelength changing were unclear.  Maybe we'll do without.  Dicklyon (talk) 15:13, 2 July 2009 (UTC)


 * I repaired and substituted a commons image that previously didn't show the wavelength changing correctly. Dicklyon (talk) 22:45, 2 July 2009 (UTC)

"I" statements
Brews, when you ignore my advice, I feel hurt, and frustrated. I feel that wikipedia is suffering, too. Your new section "Mathematical description of wavelength in general waveforms" I feel is off topic, and references 14 through 16 are not lessening that feeling, as they don't mention "wavelength", which I feel is the topic of this article. I feel that what you said about the envelope being of the d'Alembert form is also wrong, in spite of ref 17, which is itself incorrect, or approximate, when it generalizes to a result that sort of says that without mentioning d'Alembert. I feel that the article would be better if you fixed these problems, by removing the off-topic material, or by citing sources that would help me understand the connection. Dicklyon (talk) 02:16, 4 July 2009 (UTC)

And I feel that your ref 20 insults my dear deceased friend John Pierce by using a page of his work, mis-attributed, to support a statement that the page says nothing about. Dicklyon (talk) 02:46, 4 July 2009 (UTC)


 * Let's begin with reference 20: unfortunately I am unfamiliar with the work by Pierce that is mis-attributed, as you say. My limited knowledge of his work is that it is of a much more general nature than this article. The portion of this work I wished to draw attention to is

"At low rates, these two sequences sound the same; at high rates, they sound the same when the fundamental frequencies are the same."


 * The relevance to the article, if I understood this correctly, is that the burst frequency affects the perceived tone; as the burst rate is directly related to the period of the envelope, I felt this source supported the view stated in the article that this was the case. I have read other sources that made this point in a more technical fashion, and can hunt them down as a substitute if you prefer. Brews ohare (talk) 03:03, 4 July 2009 (UTC)


 * Ah, yes, I see the bit you're referring to now; it didn't have the words periodicity or wavelength or envelope or anything like that when I searched. Anyway, your inference is approximately right, but what it has to do with wavelength remains mysterious.  And you attributed it to Diane Deutsch instead of to Pierce. Dicklyon (talk) 03:50, 4 July 2009 (UTC)


 * I have replaced the Pierce reference with two that point out the ear responds to the period of the envelope (e.g. click rate) and not that of the carrier when the period of the envelope is short enough. Although these sources refer to period rather than wavelength, it seems wavelength is equally descriptive in view of the fact λ = vT. Brews ohare (talk) 11:59, 4 July 2009 (UTC)


 * Nonsense; the ear is small with respect to typical sound wavelengths, and esp. those envelope wavelengths, and has no conceivable way to respond to wavelength. Rewriting it in such terms is your own original research, not relevant to how hearing works or how music is perceived or produced.  Dicklyon (talk) 15:40, 4 July 2009 (UTC)


 * Now to being off-topic. You have agreed, I believe that a burst waveform has both a local and an envelope periodicity, as is very evident from the image. The issue you raised was whether the periodic nature of the envelope had any practical importance. The objective of this section was (i) to point out waveforms of the form of an envelope times a carrier waveform, and (ii) to point out that the envelope period has significance. Please advise whether you dispute these points. Brews ohare (talk) 03:03, 4 July 2009 (UTC)


 * You've pointed out several refs above that connect the concept of an modulation envelope wavelength the concept of group delay; but you didn't cite any of those, nor did you clarify the connection. Why not write it from sources that mention wavelength, and avoid the problem?  Dicklyon (talk) 03:50, 4 July 2009 (UTC)


 * Referring to the envelope E(x-vt) as being of the d'Alembert form was meant to indicate that its argument is x-vt, just like the d'Alembert f(x-vt) for a solution to the wave equation. If you prefer, I will rephrase this wording to leave d'Albembert out of it. Brews ohare (talk) 03:03, 4 July 2009 (UTC)


 * But the envelope does not generally travel without changing shape, except in the sinusoid case that comes from the analysis of two frequencies as is done in the sources. You overgeneralized to something that's not true.  Dicklyon (talk) 03:50, 4 July 2009 (UTC)


 * I'll look into your other points later. For now, I'd point out that in many cases the envelope does not change shape, although you are right that it is not the most general case. However, it was not stated that the most general case was being considered, just another case. Maybe you would care to elaborate on this point a bit: what would you like to see? Brews ohare (talk) 04:17, 4 July 2009 (UTC)


 * It's true enough for narrowband signals, but not wideband. It's true that you did say "In many waveforms in practical use", so it's not too over-generalized.  I have to take exception with the source, still, which says "The result applies generally to arbitrary wave envelopes provided that the wavelength of the wave group is large compared to the wavelength of the dominant component."  It's hard to imagine a sense in which joint meanings of "arbitrary" and "wavelength" can result in this statement being true; I was thinking you had made the same mistake, but you didn't quite.  On the other hand, if he had said the wavenumber components of the envelope wave were all small compared to the wavenumber of the dominant component, it would obviously be true for arbitrary such envelopes (in the appropriate limit, that is).  Dicklyon (talk) 05:24, 4 July 2009 (UTC)
 * The statement limits the term "arbitrary" to cases where the range of wavelengths is small. I take the text to mean that one can look at a variety of shapes of envelope provided their Fourier analysis is band limited. This is equivalent to requesting a periodicity of the envelope that is long compared to that of the carrier. Brews ohare (talk) 10:47, 4 July 2009 (UTC)
 * Perhaps there are other issues in your comments that I have missed. If so please take the time to explain in more detail. Brews ohare (talk) 03:03, 4 July 2009 (UTC)


 * The main issue remains that I don't want to see extra inflation of the article with material that is not connected (via sources) to the topic of the article. Dicklyon (talk) 03:50, 4 July 2009 (UTC)


 * But do you agree that pointing out the envelope wavelength has bearing upon the design of radar pulse trains, and in the study of animal sounds, and in electronic music synthesizers is relevant? Do you quarrel over the use of the term "period of the envelope" as something actually different from pulse repetition rate? IMO they are directly related by the velocity of propagation of the envelope; just another example of λ = vT. Brews ohare (talk) 04:17, 4 July 2009 (UTC)


 * I'm quite familiar with some those fields, and I'd say that maybe in radar they do use that envelope wavelength concept, but certainly not in animal communication sounds nor in music. Just because they talk about periods or pulse rates doesn't mean the so-called wavelength is relevant, except in radar where it's relevant to range resolution; but even in radar, your refs don't show it, so why did you put something about that into the article?  You're entitle to your opinion about the relationship, and I don't dispute that; but it's original research if it your logically derived relationship as opposed to a relationship actually used in the technical field in question.  Dicklyon (talk) 05:24, 4 July 2009 (UTC)

Please engage a bit further here. The spacing between pulses is the same as the spacing of (say) the peaks in envelope, yes? The pulse repetition rate times the velocity of the pulse is this distance. This distance also is the wavelength of the envelope function λe, say. So in a discussion where PRR comes up, one can equally use λe, no? Is it original research to substitute λe in place of ve/PRR when λe = ve/PRR ?? Is the "concept" of λe different from the "concept" of PRR. I just don't see that. Please comment. Brews ohare (talk) 10:42, 4 July 2009 (UTC)


 * Yes, original and unwarranted if the concept of wavelength is not used in those fields, and misleading if it implies that the concept is somehow useful or relevant there. For example, the concept of wavelength (not envelope wavelength) is useful and relevant in animal communcation sounds, as it correlates directly with the size of the animal making the sound; the pulse rep rate or envelope wavelength has no such direct relationship and has not ever been mentioned as a relevant concept as far as I'm aware.  Dicklyon (talk) 15:44, 4 July 2009 (UTC)


 * I agree with Dick here. If the source talks about pulse repetition rate, period, etc. but doesn't talk about envelope wavelength, it is synthesis for you to introduce envelope wavelength into the discussion of that source. Envelope wavelength is not a universal concept. You have found some limited sources in narrow fields that use it; this may be sufficient to include the concept in the article as long as the treatment is not unduly long, but it is not acceptable for you to extend this concept to other fields where it is not used.--Srleffler (talk) 16:20, 4 July 2009 (UTC)

I took the section out. If Brews wants to apply the concept of envelope wavelength as it is done in sources, for example where they work out the formula for group velocity, I would have no objection to that. But if it's only sourced to things that don't mention the concept he's pushing, it will come out again. Dicklyon (talk) 16:28, 4 July 2009 (UTC)


 * Excuse me here. There are two questions. One is whether PRR is used. Dick thinks not, but I believe the cited sources say otherwise. I'll give you quotes if you cannot make the connection. The second question is hypothetical: if λe is reciprocal to PRR, is it not the case that either λe or PRR refer to the same concept, and therefore these ideas are not separate?


 * Bear in mind that all is said in the article is that this commonly used PRR is related to wavelength λe, and a diagram given to illustrate what λe is. Brews ohare (talk) 16:34, 4 July 2009 (UTC)


 * I don't believe I indicated thinking that pulse rep rate is not used. It is common enough.  It's not generally connected with wavelength though.  I think some of the material you added could have a place in the article, if you'd cite sources that both support what you want to say and connect it to the topic of the article, which is wavelength, not waves in general. Dicklyon (talk) 16:59, 4 July 2009 (UTC)


 * Dick: You agree that PRR is used, but think it is not connected with wavelength. However, the PRR multiplied by the wave speed is the wavelength of the envelope describing its periodic repetition: λ = vT. So one cannot state a PRR without implying an exact value for the wavelength corresponding to the periodicity of the envelope: it is logically inseparable. Brews ohare (talk) 21:44, 4 July 2009 (UTC)


 * It really doesn't matter if I think it's connected or not; what matters is only whether you demonstrate the connection by citing a source that does it. Dicklyon (talk) 22:00, 4 July 2009 (UTC)


 * It is clear that in many fields that use repetitive signals, the concept of "envelope wavelength" is not used. It is therefore incorrect to say that envelope wavlength is reciprocally related to repetition rate in those fields, and the onus is on you to establish, with sources, when it is valid to use the concept of "envelope wavelength". The onus is also on you then to write the article in a way that makes the scope of this concept clear. Attempting to present the concept as being more broadly applied than it actually is is not acceptable, and must be reverted.--Srleffler (talk) 03:49, 5 July 2009 (UTC)

d'Alembert
Inasmuch as the d'Alembert form for a wave is very well documented and, indeed, ubiquitous in discussion of waves, and inasmuch as it leads directly to the connection between periodicity of f and λ, why is this material removed? Brews ohare (talk)


 * No source that made that connection of the d'Alembert form to the concept of wavelength was cited, and the d'Alembert form is not needed in this respect, as the connection is already made for the case of sinusoids, which is the case for which wavelength is usually applicable. The generalizations that you've added have generalized beyond what was in the sources you cited.  Dicklyon (talk) 16:57, 4 July 2009 (UTC)


 * First, notice that the d'Alembert form includes the sinusoidal example as was pointed out, which provedes a very direct connection to wavelength that, in fact, has been made the central point of the article. The d'Alembert form is a more general case, as the diagram of wavelength in the general case points out. You are, of course, being disingenuous because you don't want to see the d'Alembert form in the article for some personal, unexpressed reason. There can be no doubt in your minds that the period of f in d'Alembert's f is the wavelength of the periodic traveling wave, nor that there is certainly some good in pointing out this widely used general solution and its relation to wavelength. To force a citation that says so in so many words is simply perverse.  For the connection stated in the deleted text, see the cited reference and in addition, for example, Filippov; Crocker; Wazwaz;González-Velasco; Kammler. Brews ohare (talk) 21:31, 4 July 2009 (UTC)


 * The point is that the extra generality of the d'Alembert form is not helpful in understanding the concept of wavelength; or if it is, then find us the source where someone uses it so. Dicklyon (talk) 21:58, 4 July 2009 (UTC)


 * I'm inclined to say the general form, as shown in the picture, is helpful in visualizing wavelength in broader context; likewise, the d'Alembert form provides a wider context than a simple sine wave formulation. Such generalization is an act of imagination, and as such is not easily come by, and should be summarized for the reader, who might well otherwise have the restricted view that wavelength has a meaning confined to sinusoids. Also, for one coming to this article from reading wave equation or d'Alembert solution for example {we cannot guess how this reader got here), they are looking for exactly this connection to wavelength, which therefore is helpful. Brews ohare (talk) 22:08, 4 July 2009 (UTC)


 * The reader should be left with the restricted view that wavelength is almost entirely confined to sinusoids, but that the concept is sometimes extended to cover spatial periodicity in more general waveforms (Local crest-to-crest measurements in waves that aren't quite periodic, measures of envelope periodicity, etc.) These extensions are not really wavelength per se, but rather are extensions of the concept beyond its fundamental definition. The article should not confuse these things. --Srleffler (talk) 04:16, 5 July 2009 (UTC)


 * The d'Alembert form is not a more general case. As has been pointed out to you repeatedly, it is a very rare special case. Physically, sinusoids propagate unchanged in all linear media. General waves do not generally propagate according to the d'Alembert formula. Media where the d'Alembert form applies are rare. It is a convenient fiction for beginning to understand wave propagation, but is not a suitable base for understanding the concept of wavelength. --Srleffler (talk) 04:16, 5 July 2009 (UTC)


 * The first two of your refs above (Filippov and Crocker) connect the concept of "wavelength" only after specializing to the sinusoidal wave; our article already makes that connection; they don't say that the concept would apply to more general periodic f. The other three don't appear to mention "wavelength" at all near the pages that mention d'Alembert.  If I'm wrong, point out where.  I know you'd like to generalize the concept of wavelength a lot, but the sources you're using don't support where you're going with it.  Dicklyon (talk) 22:19, 4 July 2009 (UTC)

Because I'm sure you understand that "wavelength" applies to waveforms more general than the sinusoid, as shown in the figure, and as I'm sure you understand that a periodic f(x-vt) describes the waveform in the figure, I am unclear why you think wavelength is not connected to the f(x-vt) formula. On one hand you say:
 * "Sure it's connected, but what insight does that provide?"

My answer to this was that some readers coming to this article form Wave equation or d'Alembert's formula or whatever, will want to know this information. Given the widespread use of these topics, such readers may not be uncommon. On the other hand you say,
 * "Hey, f(x-vt) has nothing to do with wavelength because your source mentions this only using the example of a sinusoid; you must find a source that says in so many words that the wavelength of a f(x-vt) is the period of the function."

Apparently, the definition of wavelength as y(x+λ, t) = y(x, t) is insufficient to establish λ as the period of "f"? What kind of silliness is that? Can you explain how periodicity can avoid wavelength? Next I'll be told that a+b=b+a doesn't mean c+d=d+c unless I can find a source that says so using these specific letters, eh? Brews ohare (talk) 00:53, 5 July 2009 (UTC)


 * Obviously, I made no such argument; but which source are you saying shows that wavelength periodicity? I'd like to see exactly what it says that you're interpreting that way; I may have missed something when I found the word "wavelenght" was missing from the cited pages.  Dicklyon (talk) 03:50, 5 July 2009 (UTC)

Envelope
Inasmuch as the envelope of a wave is very common in the discussion of wave motion, and inasmuch as the spacing between peaks in envelope (the wavelength λe = ve /PRR where PRR = pulse repetition rate) is a commonly used parameter in discussion of such waves (as is well documented by multiple sources cited), why is this material identifying λe and a figure illustrating it for radar systems deleted? Brews ohare (talk) 16:42, 4 July 2009 (UTC)


 * I think we pretty much explained above. First of all, it's not common.  Second, none of the things you said about wavelength were supported by sources that mentioned wavelength.  And none of the things you said that were sourced were connected via sources to the topic of wavelength.  I believe we've been consistent about disallowing such complicating additions since you showed up here on June 10.  If you believe we have been inconsistent, or that we've made a mistake in interpretatin of WP:V and WP:NOR, please indicate.  Dicklyon (talk) 16:55, 4 July 2009 (UTC)


 * You say: "It" is not common, whatever "it" is. If it is the concept of envelope, it is extremely common. Do you need sources for the use of envelope? Try this google search envelope. If "it" is pulse repetition rate (PRR) or pulse repetition frequency (PRF) try this google search: PRR &PRF . Brews ohare (talk) 21:39, 4 July 2009 (UTC)


 * OK, I mispoke; what's uncommon is to connect the envelope to the notion of wavelength; I've already acknowledged that it's sometimes done, in connection with group delay in particular, and that if you cite a source that makes the connection that will be OK. Dicklyon (talk) 21:56, 4 July 2009 (UTC)

My thought was that the sources on music and hearing, for example, show clearly that the ear distinguishes PRR in preference to the carrier frequency in some situations. That establishes a role for PRR in this case. Other cases (e.g. radar) also have been mentioned. Do you say that the connection between PRR and the periodicity of the envelope is too obscure to be worth pointing out here? They are directly related by the envelope wave speed, as I have pointed out. So here is a "yes" or "no" question: Is a reference to the periodicity of the envelope unacceptable, even as an aside, to point out the relationship to PRR so long as no citation can be found using the precise wording "periodicity of the envelope" or "wavelength of the envelope" in so many words as part of the jargon of the field? Having decided yes or no, perhaps you could elaborate on why such a connection should or shouldn't be made, and when the jargon of a field should possibly be departed from. Brews ohare (talk) 22:22, 4 July 2009 (UTC)


 * It's not necessary to answer such a hypothetical when the article can be written from sources that do directly mention the "wavelength of the modulation" or "envelope wavelength" or such. Why not stick to those and what they say?  I will continue to push back on all asides that don't directly connect to the topic via sources that mention the topic, as it's the only boundary I know of that will keep this article finite in the face of your efforts to improve it.  Dicklyon (talk) 22:26, 4 July 2009 (UTC)


 * Look, you keep dwelling on PRR as if it helps your case. It doesn't. I don't care whether the ear distinguishes PRR in some situations. PRR is not wavelength. If you have a source that makes a connection between PRR and "envelope wavelength" in a particular field of study, you have grounds to add a mention that the concept of wavelength is extended to cover envelopes in that particular field. It is not sufficient for the source to talk about (temporal) periodicity of the envelope. The source must explicity talk about the envelope's wavelength, since this article is about wavelength, not temporal periodicity. Since the usage is uncommon, you cannot talk about it as if it were a generally applicable concept, since it isn't. You must limit the discussion to the specific fields in which this term is actually used, as evidenced by sources that talk specifically about the wavelength of the envelope. Not PRR. Not "periodicity of the envelope". Wavelength. I suggest you focus the exposition on the idea that this is an extension of the concept of wavelength beyond its usual definition, which is used in certain narrow fields of study. That will make the resulting text more likely to be acceptable.--Srleffler (talk) 04:01, 5 July 2009 (UTC)


 * No, PRR is not wavelength, but λ = v/PRR (a form of the relation λ = v/f already in the article), so one hardly can say that PRR has no bearing upon λ and vice versa. What is involved here is simply whether you visualize the wave traveling from the source to the ear (spatial) or staying at the ear and observing the time variation of the wave at the ear location (temporal). If the ear responds to PRR, that relates equally to a spatial characteristic of the waveform (its period is related to its wavelength). I'd say the connection between spatial and temporal periodicity is a key observation of the article, and not an excuse to eliminate one of the two viewpoints. I fail to see why a source must use the word wavelength rather than PRR to be relevant to this article. Brews ohare (talk) 13:05, 5 July 2009 (UTC)


 * I disagree that λ = v/PRR in general. In most fields, "wavelength" is not a characteristic of envelopes, but only of the carrier. Where the the term "envelope wavelength" is not in use, v/PRR is a quantity with no name. More importantly, in most cases it is a quantity with little physical significance. The ear perceives the temporal variation in air pressure (PRR), not the spatial variation along the wave. You cannot inject your own views into the article. You must support what you write with sources, and the sources do not support what you are trying to do. --Srleffler (talk) 15:30, 5 July 2009 (UTC)

Srleffler, thanks for your support in keeping this article from going off in the weeds. I'm off on a trip in the morning, so my involvement will be more sporadic for a while. Keep up the good work while I'm away. I think that the recent machinations have turned up a viable set of sources on envelope wavelength in the derivation of group delay, e.g. here and here. I was thinking of writing such a section from these sources, but don't have time right now to make it short. So maybe you and Brews can do that. The animated wave with the colored dots (File:Wave group.gif) was a good illustration of what these sources are saying: two sinusoids beating make an envelope with a different velocity; the sources show how to use that, that the envelope wavelength and period allow the calculation of that velocity, leading in the limit to the formula for group velocity as a derivative. Dicklyon (talk) 05:13, 5 July 2009 (UTC)


 * I confess to bewilderment over you two's viewpoint. I cannot understand where the invisible line is that divides the obvious from the unacceptable, and exists only in your minds. For example, the form E(x-vt)sin(2π(x-v't)/λ) cannot be put into the article even though cited from numerous sources and fields. Why? Well, according to Srleffler its "too complicated" for 11-year olds. According to Dicklyon, the sources are mistaken, or at least misleading - the form applies "only" to beating sinusoids. To Srleffler I reply, there are some 11-year olds brighter than you give them credit for, and the article is in any case not limited to those of no background, but should provide an introduction to the ideas for diverse backgrounds. In any case, Srleffler is not the judge to decide what is or is not too complicated for inclusion. To Dicklyon I reply that his myopia over the usefulness of this expression is not universal, and waves of this form are found all over the place, and are not restricted to beats - citations have been provided and erased arbitrarily.


 * Your next joint argument is that E(x-vt)sin(2π(x-v't)/λ) is unrelated to wavelength and so is irrelevant. Of course, it is difficult to relate such an expression to wavelength without being able to introduce it. And one cannot introduce Fourier analysis to explain how E introduces wavelengths adjacent to the carrier, again because it is too complicated, or because it is easier to describe in terms of wave number k = 2π/λ instead of λ = 2π / k. And if E is periodic one cannot talk about the periodicity of E because wavelength is connected to periodicity only for sine waves??   Brews ohare (talk) 12:35, 5 July 2009 (UTC)


 * The fact of the matter is that the concept of wavelength is much more complex than you two initially imagined, and still is more complex than you presently imagine. You simply wish to keep the article "contained" to whatever your present state of awareness dictates. That imposes arbitrary boundaries on the subject. You refuse to allow the connection to general expressions, to Fourier series (which is the very natural approach I introduced long ago, now at User:Brews_ohare/Wavelength), refuse to acknowledge that pulse repetition rate is the same thing as envelope periodicity, require explicit usage of the word wavelength in any acceptable cited sources, and don't allow equivalents such as T (implied by λ = vT) or f (as implied by λ = v / f). You insist that spatial aspects of waves (λ) are totally disparate from temporal aspects (f or T). Most of all, you insist on being gatekeepers of this page, excluding anything that you do not appreciate. Sourcing contributions is insufficient to get by this gatekeeping, because you also impose arbitrary content restrictions of your personal invention. Brews ohare (talk) 12:49, 5 July 2009 (UTC)


 * You are still trying to introduce ideas that you have reasoned out yourself rather than drawn directly from sources. This isn't acceptable. The sources do not support the connections you are trying to make.--Srleffler (talk) 15:33, 5 July 2009 (UTC)

That is a blanket assertion on your part, unresponsive to the issues raised immediately above your reply, and unsupported either by the record on this talk page or by the repeated deletions of sourced material on the article page. You are now suggesting I am promoting my own ideas, but previously you have used lack of sources, lack of relevancy or lack of simplicity as alternative reasons for doing exactly the same reversions. None of these arguments, nor your present one, hold water, as has been abundantly documented here. Brews ohare (talk) 15:43, 5 July 2009 (UTC)


 * Yes, it is a blanket assertion that pretty much covers the long discussion above. You repeatedly come back to the same ideas, and keep push-push-pushing them into the article. Some of what you have added has been correct, but the fundamental problem is that you are relying on your own logical analysis rather than on how the concept of wavelength is actually applied by others, as evidenced by the sources. As a result, we keep going around and around with you adding material that fits your picture of things, but is not supported by sources at all, or is supported only by limited sources in a narrow field of application. --Srleffler (talk) 16:47, 5 July 2009 (UTC)

Spatial and temporal relationships
I ended up removing the new section. I started out with the intent of condensing it, since it seemed to go into more detail than necessary. As I got into it, however, I found nothing I could save. It starts out by explaining how the argument of the cosine relates to the spatial and temporal periodicity of the wave. This is fine, but is too detailed for this article. A sentence or two at most would do, since the relevant equations have already been presented. There is no need to define a new variable and walk the reader through the derivation. I had planned to compress it to a line or two, but in the end couldn't see what the point was. It tells the reader something useful about how the mathematical form relates to the periodicity of the wave, but this isn't really directly useful in understanding wavelength.

Worse, it seems to be just more POV-pushing by Brews. The purpose of this section is revealed in the text that follows, in which Brews attempts to generalize this analysis to his favoured conclusion that assigns "wavelength" to anything that is periodic. As usual, the connection between general periodic functions and wavelength is not supported by any of the citations. Since the primary purpose of the section appears to be to promote this synthesis, I removed it.--Srleffler (talk) 19:21, 5 July 2009 (UTC)


 * Your objection to a detailed walk-through seems at variance to your earlier stand that an eleven-year old should be able to read the article. Of course, one of my objectives was to make crystal clear the role of x-vt so one could understand the commonly used d'Alembert formulation, and understand how it connected to the concept of wavelength. I am sorry you could not get the point, and yet request its compression as being already presented material.


 * Please quote any wording that said any periodic function implies a wavelength. What was said is that a function f(x-vt) did not have a wavelength unless f was periodic. What is more, the second section said the envelope is a function of x-vt, and therefore has an associated wavelength. That is just a change in designating the function from f(x-vt) to E(x-vt); hardly an unsupported assertion.


 * Moreover, the deleted material contains other information (all sourced) unrelated to this objection about the detailed discussion of θ = x-vt, yet was reverted anyway as part of a pattern of blanket reversion on your part. Your deletions of useful sourced material based upon simple pretext simply is vandalism. Brews ohare (talk) 21:53, 5 July 2009 (UTC)


 * The connection between the argument of the cosine function and the spatial and temporal periodicity of the wave can be explained more clearly without adding five lines of math and a new variable to the article. If I thought explaining this relation benefitted the article, I would have done so. Once I got into editing the section, though, I couldn't see the point. This relation between the math and the temporal periodicity doesn't tell the reader anything new about wavelength that isn't already covered in the article. The text already shows how wavelength appears in the equation for a travelling sinusoidal wave, and how wavelength, wavenumber, velocity, and frequency are related. The new text just seemed to belabour the point. If this were an article about wave propagation, the extended discussion of the connection between the argument and the peridocity would probably be worthwhile. This article is not about wave propagation in general, however. It is specifically about wavelength. Srleffler (talk) 03:10, 6 July 2009 (UTC)


 * The material deleted establishes the relation between the d'Alembert form f(x-vt) and wavelength. As such it is not repetitive, as this form appears nowhere in the article despite its prominent position in most introductions to wave behavior, and despite the fact that the prominence of the d'Alembert form suggests some readers may wish to see this connection. Brews ohare (talk) 12:30, 6 July 2009 (UTC)


 * Yes, it's clear that your purpose was to again bring in the d'Alembert formulation, hence my comment about POV pushing. You keep trying to push this formulation into the article any way possible. The trouble is that you're working backwards. Instead of trying to show that the d'Alembert formulation helps the reader understand wavelength, you're looking for ways to connect wavelength to the d'Alembert formulation so that you can squeeze it into the article over our objections. It doesn't work; that formulation is useful, but doesn't throw any useful light on the concept of wavelength beyond what is already covered in other ways in the article. Srleffler (talk) 03:10, 6 July 2009 (UTC)


 * You suggest I'm pushing d'Alembert where he does not belong. But the d'Alembert form actually is the most common and the most general case illustrating the wavelength and period of a wave. It also has a prominent place in the literature. You personally do not think it is interesting, but who, exactly, are you?? The material is sourced, it is accurate and it is useful. Brews ohare (talk) 12:30, 6 July 2009 (UTC)


 * We do already use the d'Alembert form of the wave in the section on sinusoids; it wouldn't hurt to refer to it as that there. But to generalize it as you do to arbitrary waves and arbitrary periodic waves is mostly not so helpful in connection with the topic of wavelength.  Dicklyon (talk) 15:03, 6 July 2009 (UTC)


 * The text I removed implies that any periodic function with the d'Alembert form has a "wavelength", which has been extensively disputed above. I object to the introduction of this section that serves no useful purpose within the article other than to try (and fail) to support this disputed idea. Srleffler (talk) 03:10, 6 July 2009 (UTC)


 * The fact you think there is dispute in this matter simply indicates you do not understand the material you deleted. A periodic function f with argument x-vt necessarily exhibits wave propagation with a wavelength given by the period of the function f. Your belief that this is a subject for dispute is simply a lack of mathematical understanding. If you truly have this confusion, you need to fix it. If you are to edit this article, it would behoove you to understand what you are dealing with, or recuse yourself. Brews ohare (talk) 12:30, 6 July 2009 (UTC)


 * I carefully considered everything I deleted; it was not a blanket revert. Where I deleted sourced material, I did so because it was unhelpful to the article, or because it was not supported by the source cited. --Srleffler (talk) 03:10, 6 July 2009 (UTC)


 * I find that in fact you are, with your present background, actually incompetent to "carefully consider" the material. It is clear that you have read nothing about the d'Alembert form, have not consulted the cited literature, nor the material you reverted, and are just flying by the seat of your pants. Brews ohare (talk) 12:30, 6 July 2009 (UTC)


 * Oh, come on; if you want to start arguments about competence you're not going to get ahead that way. Recall WP:NPA.  Dicklyon (talk) 15:03, 6 July 2009 (UTC)

Documented case; accept it or not. Brews ohare (talk) 15:05, 6 July 2009 (UTC)

Radar pulses
As far as I can see, the cited source does not describe the pulse separation as determining a wavelength. Page 10 and following seems to stick with "p.r.r.". When they talk about wavelength, it is that of the carrier. Am I missing something?--Srleffler (talk) 19:28, 5 July 2009 (UTC)


 * I have removed all the material that hung on this figure and source, as it is all synthesis, not supported by the citation. If you want to introduce the idea of a wavelength related to pulse repetition rate, you need to support it with a citation that explicitly makes this connection. If I have missed such a connection in this source, I apologize, but I just don't see it there. --Srleffler (talk) 19:41, 5 July 2009 (UTC)

What you are missing is that the envelope is a periodic function  of x-vt, and so has a wavelength. It is a direct restatement of the meaning of wavelength from earlier sections, and does not require a source. Brews ohare (talk) 21:56, 5 July 2009 (UTC)


 * This is precisely the assumption that Dick and I have been disputing. Not every periodic function of x-vt has a wavelength. Sinusoidal waves have wavelengths. Whether the spatial periodicity or quasi-periodicity of other types of wave is considered to be a wavelength depends on the conventions of the field that studies or works with those waves. Such extensions of the concept of wavelength beyond its primary meaning have to be supported by citations to sources that actually show that the concept is so extended. No amount of logic, reasoning, or math will do, because this is purely a matter of convention. --Srleffler (talk) 03:22, 6 July 2009 (UTC)
 * Srleffler: Please indicate to me how it is possible for a periodic function f(x-vt) not to have a wavelength. Here is the proof:
 * f(x+λ-vt) = f(x-vt) if λ is the period of f.
 * Understanding of the material you deleted as unnecessary would assist you to pursue this argument further by realizing the connection of propagation to the form x-vt. Brews ohare (talk) 05:45, 6 July 2009 (UTC)


 * This seems to be the crux of the disagreement between us. Ironically, you responded to my comment that no amount of logic, reasoning, or math would work by presenting a logical, reasoned, mathematical argument. It doesn't work. The problem is that the variable λ is not necessarily "wavelength". You have proved only that a periodic wave of d'Alembert form is periodic in space. Whether this spatial periodicity is considered to be "wavelength" depends on the context. This is not a trivial issue. The essential problem is that you're starting from the wrong model. The d'Alembert form is not a general model of wave propagation in real media. Waves of general form do not precisely maintain their shape as they propagate, with the exception of free space and bizarre special cases. Worse, even assuming a perfectly linear and dispersionless medium, many of the cases you consider are not exactly periodic. A modulated sine wave does not exactly repeat with each cycle of the envelope, because of the difference between phase and group velocity, and because the envelope period may not be an integer multiple of the carrier period. When wavelengh is used in these situations, it is an extension of the concept beyond its basic meaning, applying the concept to signals that are only approximately or locally periodic. Researchers in some fields choose to label such quasi-peridicity "wavelength". Researchers in other fields choose not to label it that way to avoid confusion or just in recognition of the fact that the periodicity is not exact.


 * The article should talk about these things, but it can't present these extensions to the concept of wavelength as if they were universal truths. They must be presented as they are: extensions to the concept that are used in certain fields and/or by certain authors. Sources must be provided to establish where and by whom the extended concept of wavelength is used.--Srleffler (talk) 03:36, 7 July 2009 (UTC)


 * Brews, also please note that this radar ref uses the term "wavelength" repeatedly; but never in the sense that you are citing it in support of. You don't get to redefine the terminology in the radar field.  But I thought you had one that did talk about an envelope wavelength related to pulse rate.  Do I remember wrong?  If you do, why not cite it?  Dicklyon (talk) 04:18, 6 July 2009 (UTC)


 * The point is not whether or not the radar field speaks about the wavelength of the overall waveform. The point is that the wavelength (aside from the notion of "local" wavelength) refers to the distance between corresponding positions in a waveform in space. Consequently, the wavelength of the envelope is not introduced as though it were a technical term that is part of the radar jargon, but is introduced merely to make connection with the already introduced notion of wavelength as the distance between similar positions in the waveform. Brews ohare (talk) 12:44, 6 July 2009 (UTC)


 * So show us a radar source were "wavelength (aside from the notion of local wavelength) refers to the distance between corresponding positions in a waveform in space." That's what we're asking.  Not logic; just sources.  Dicklyon (talk) 14:56, 6 July 2009 (UTC)


 * Please read the above comment, to which your reply does not respond. It begins: The point is not whether or not the radar field speaks about the wavelength of the overall waveform. Brews ohare (talk) 14:58, 6 July 2009 (UTC)


 * You are mistaken about what the point is. You are advancing a definition of wavelength that is incorrect, and not supported by the literature as a general definition.--Srleffler (talk) 03:36, 7 July 2009 (UTC)

You raise another point, invalid, see Flowers. Brews ohare (talk) 04:32, 7 July 2009 (UTC)


 * Beyond that, however, in the radar field and in numerous others the pulse repetition rate is an important parameter. For example, in music the PRR determines how a sound is heard when the PRR falls in a certain range. These fields have largely chosen to analyze the phenomena in the time domain. However, it is clear that any time domain phenomena has a spatial analog connected simply by the wave speed. In particular the time domain PRR is exactly equivalent to the spatial pulse separation. It would seem reasonable therefore to make this connection for the reader, who may become more capable than are you to convert back and forth between these equivalent views of the matter. Brews ohare (talk) 12:44, 6 July 2009 (UTC)


 * Yes, ppr is important; do any sources associate a wavelength with it, or connect it in any way to the concept of wavelength? Not that you've shown us.  Dicklyon (talk) 14:56, 6 July 2009 (UTC)


 * The connection is obvious to you and to me, as pointed out just above. Therefore, you are primarily being obstructionist, although you may claim disingenuously to be simply unconvinced and require a direct quotation. As pointed out, a time domain view is equivalent to a space domain view, but a source that says so in so many words is hard to find. Still, you can lawyer the matter to death, regardless of the facts you are very familiar with. Brews ohare (talk) 15:03, 6 July 2009 (UTC)


 * That's right. It's a principle of wikipedia that we should be unconvinced and require that content be WP:Verifiable in WP:Reliable sources.  I don't believe that wavelength is a concept ever used with respect to radar pulse rates, but if it is, you'll be allowed to add it to the article.  Dicklyon (talk) 15:07, 6 July 2009 (UTC)

Your generosity is matched only by your clarity of purpose. Brews ohare (talk) 15:10, 6 July 2009 (UTC)

Deletion of material
Deletion of this material and my other recent edits is simply vandalism. Repetitively and intentionally making unconstructive edits to Wikipedia will result in a block or permanent ban. Vandalism. Brews ohare (talk) 20:32, 5 July 2009 (UTC)


 * It's not productive to throw accusations of vandalism into a content dispute. If you have concerns about my actions or words there are plenty of guidelines and dispute resolution mechanisms that you can reference to address those concerns. Calling it "vandalism" isn't going to get you anywhere, though. I have deleted material that I feel does not improve the article, and will continue to do so as needed. I am doing my best to carefully consider all your contributions, however, and to find whatever can be kept or reworked into the article. --Srleffler (talk) 03:28, 6 July 2009 (UTC)

Hey, guys, I had a great travel day and am comfortably ensconced now in the beauty of the Canadian Rockies for a while. Too bad it's business as usual on wikipedia, but I have to agree with Srleffler that there was little or nothing to be saved in the recent additions, and that removing it was reasonable, if not exactly required by policy. My suggestion above stands: work on incorporating bits that are sourced and connected in sources to the topic wavelength, like the group delay sources that talk about envelope wavelength. The rest, Brews's interpretation that any periodic wave should be attributed a wavelength corresponding to its period, and his other bit that a non-periodic wave should be interpreted as having a spread of wavelengths, are both unconventional points of view, hard to find any support for in sources. Even those might rate a mention at some point if a brief statement attributed to an actual source that supports the statement and connects it to wavelength could be cited. It continues to baffle me that Brews continue to spend time putting into the article stuff that we have already explained why we will take out, instead of putting in stuff that meets these basic requirements. And then he defends his actions by explaining his logic, as if that were the issue; it's not. And then he tries to call us vandals, when he's the one continuing to ignore sourcing policy and WP:SYN. Dicklyon (talk) 04:07, 6 July 2009 (UTC)


 * Your statement about my views: "'Brews's interpretation that any periodic wave should be attributed a wavelength corresponding to its period, and his other bit that a non-periodic wave should be interpreted as having a spread of wavelengths, are both unconventional points of view, hard to find any support for in sources. '"
 * almost states my views correctly. The first statement should be "any periodic function of (x-vt) should be attributed a wavelength equal to its period." Your apparent view that these ideas are unconventional and unsupported indicates (i) incompetence, both in understanding my views and in understanding the literature, and (ii) lack of understanding of the role of Fourier analysis in studying general waveforms.


 * It therefore appears that your resistance to introduction of these ideas is based more upon ignorance than upon any lofty criteria of soundness or pertinence to the article. Actually, I do not believe your ignorance extends this far, but I put this face on things because I would otherwise have no explanation for your actions. Brews ohare (talk) 12:52, 6 July 2009 (UTC)


 * If we are ignorant, you can fix that by citing sources. Dicklyon (talk) 14:53, 6 July 2009 (UTC)


 * History on this talk page and the sources already cited in deleted material do not support your claim. Ignorance (or a blind eye) is bliss. Brews ohare (talk) 14:55, 6 July 2009 (UTC)


 * History is what it is. If you want to advance your position, discussing specific sources that mention "wavelength", here on the talk page, would be more useful than claims that the history proves you right. Dicklyon (talk) 15:04, 6 July 2009 (UTC)

There is no way to advance my position other than persuading you that you are wrong, and sources will not do that - you just ignore them, say they are wrong or claim they apply only to narrow venues. Brews ohare (talk) 15:07, 6 July 2009 (UTC)
 * It's generally difficult to advance a position that is incorrect. One finds it hard to locate sources that back up the position. --Srleffler (talk) 03:39, 7 July 2009 (UTC)

Your observation is valid. However, another circumstance where finding sources is difficult is the case when there is insistence upon a very narrow form of words and vocabulary, a focus far more narrow than informs the actual meaning. In this case, an insistence that λ be used in the source for it to be accepted, rather than T, even though λ = vT. Brews ohare (talk) 04:37, 7 July 2009 (UTC)


 * It really doesn't matter what variable name is used, but to conclude that vT is "wavelength" from a source that doesn't mention the word "wavelength" is a bit of a stretch, don't you think? Dicklyon (talk) 06:16, 7 July 2009 (UTC)

The relation λ = vT applies to any periodic traveling wave, as has been amply documented and mathematically derived as well. It underlies the notion that spatial and temporal analysis of such waves are just two different facets of the same behavior. Hence, where a field works in the time domain, everything said has an equivalent in the space domain, whether or not that is their choice of vocabulary. And pointing this parallelism out, saying that pulse separation in space is related to pulse repetition in time, is useful to the reader, and is accurate. It is, however, hard to source all of this in one reference, though the individual parts can be sourced. I believe any eleventh grader, and anyone who understands the space vs. time aspects of waves, gets it. Brews ohare (talk) 14:52, 7 July 2009 (UTC)


 * But you keep trying to apply this concept to things that are not exactly periodic. Wave packets are not exactly periodic. Ocean waves approaching shore are not exactly periodic. Modulated and pulsed RF signals are generally not exactly periodic because the carrier and envelope are not phase-locked. Waves in most media are not exactly periodic due to dispersion and absorption. In many of these cases, the waves are not even approximately periodic. Planar sine waves in a linear medium are perfectly periodic. They unambiguously have wavelength. Whether wavelength can be extended to cover other cases is a matter of convention; it is not something you can prove.--Srleffler (talk) 16:43, 7 July 2009 (UTC)

Srleffler: That is a misunderstanding. I do not intend to give that impression, and presumably you could help word things so that misunderstanding does not arise. For example, a note that "phase locking" is required for perfectly periodic radar bursts. Brews ohare (talk) 17:12, 7 July 2009 (UTC)


 * Maybe we can find wording that covers this, but you cannot continue presenting wavelength in the way you have been. My point is not that your arguments need to be qualified further, but that they are fundamentally flawed. Almost nothing is exactly periodic; it is pointless to specialize the discussion to this case. Rather, the article needs to discuss how the concept of wavelength is extended, by researchers working with different types of wave. In some cases, those working in a given field label a quasi-periodicity "wavelength". In other cases, they do not. We need to document the actual usage in the field with sources, not try to force-fit everything into an abstract model that is not actually backed up by real-world usage.--Srleffler (talk) 02:48, 8 July 2009 (UTC)

Perhaps one could note that the envelope is perfectly periodic but the fine structure may not be. Brews ohare (talk) 17:13, 7 July 2009 (UTC)


 * What is important is whether people actually working in the field refer to the periodicity of the envelope as a "wavelength". Nothing else matters. --Srleffler (talk) 02:48, 8 July 2009 (UTC)

I have made a modified discussion of the radar burst to meet your suggestions. Brews ohare (talk) 17:22, 7 July 2009 (UTC)


 * I'll take a look.--Srleffler (talk) 02:48, 8 July 2009 (UTC)


 * I marked the section as disputed for now. The section really needs to clarify where and by who "envelope wavelength" is used, rather than implying that it is in general use. A source is needed to document that this term is actually used at all. I think you presented such a source somewhere above, but I can't find it right now. I tried to condense the time and space section, which had a lot of redundancy. I'm still not really happy with this whole section, but am too tired to do more with it right now.--Srleffler (talk) 04:19, 8 July 2009 (UTC)


 * The refs on envelope wavelength for group velocity derivation are mentioned in this diff. The first (Denny) points out that the modulation envelope is an abstract waveform, and associates the "envelope wavelength" with that abstract waveform by the usual definition of wavelength.  The other (Graebel) says the envelope "looks much like a slowly traveling wave of wavelength..." again associating "wavelength" in the usual way with an abstract wave that the envelope looks like.  There are others, like Holton that describe the modulated wave as the product of an envelope wave that has a wavelength and a carrier of a different wavelength; they break it up this way for the purpose of seeing how fast the envelope moves, to get group velocity.  But none says that the wavelength of the envelope is the wavelength of the modulated signal, or anything to that effect.  Nothing supports Brews's statement about the radar pulses that "The overall pulse wavelength (labeled the "envelope wavelength" in the figure) is the distance traveled between repetitions of the waveform (the distance the wave travels in a time determined by the pulse repetition rate)."  Even changing the terminology there, to get rid of "overall wavelength" and such, would leave it as an unsupported extension of what's in the sources, which is the analysis of the envelope due to beating closely spaced sinusoids, making a slow sinusoidal envelope, as a way to derive group velocity.  If there are other sources on "envelope wavelength" that supports what he's trying to do, I haven't found them.    Dicklyon (talk) 05:31, 8 July 2009 (UTC)

Srleffler: There is no claim that that envelope wavelength has any special status other than being the wavelength of the envelope. That description does not imply any special technical status or usage. It is simply wavelength in exactly the same way wavelength is defined at the outset of the article, viz. the distance between similarly situated points on a wave, in this case the wave is the envelope, which is a wave just like any wave. Brews ohare (talk) 05:47, 8 July 2009 (UTC)

RFC on wavelength definition


We need comments on a long-running dispute, from persons other than those already involved. A key issue is represented in the figure at the right: is the wavelength of this signal the spatial period (labeled "envelope λ")? Or is it the crest-to-crest spacing (labeled "local λ")? Or is it both? Dicklyon (talk) 03:34, 8 July 2009 (UTC)


 * The question is posed incorrectly. The local λ is well sourced and indisputably as marked. See Cooper. It is the wavelength characterizing what is sometimes called the "fine structure" of the wave, and varies somewhat with position inside the wave (which is why it is called "local").


 * On the other hand, the wave envelope is the outline of the waveform. In many waveforms, this envelope repeats periodically in time and in space (e.g. radar bursts, bird and insect calls). The spacing between similarly situated points in the envelope, for example between its crests or between its troughs, is the wavelength characterizing the envelope itself. See Denny. So the real issue here is whether the envelope wavelength is a reasonable parameter to use in describing the envelope, which in my mind is simply a question of whether or not the envelope is periodic, inasmuch as any wave that is periodic in space has a wavelength. Maybe a question to answer is "How is it determined whether a signal envelope is periodic?"


 * Dicklyon tends to interpret a discussion about the wavelength of the envelope as a claim that the term "envelope wavelength" is a form of technical jargon. It isn't. It's just English used to designate an object: the wavelength of the envelope. Brews ohare (talk) 05:30, 8 July 2009 (UTC)

This RFC was not intended to be about the wavelength of the envelope. I accept Denny's usage there. It's about Brews's assertion that "any wave that is periodic in space has a wavelength" (by which he means equal to the spatial period). That's why I illustrated the question with his drawing of a periodic wave with a disputed wavelength. Dicklyon (talk) 15:48, 8 July 2009 (UTC)

Let me restate to clarify: in the upper figure, I agree that if one looks at the envelope as a wave, it has a wavelength equal to the marked "envelope λ" – that's not at issue in this RFC, and the radar pulse figure is pure distraction along the lines of envelopes. The question is simply about the wavelength of the red AM-modulated waveform: is it the crest-to-crest distance, or is it the spatial period? Don't let the words on the picture distract you from the question. Dicklyon (talk) 16:20, 8 July 2009 (UTC)


 * There is no "either-or" here. The "local wavelength" characterizes the fine-structure, and the "envelope wavelength" characterizes the global structure. In fact, in this particular example, I constructed the red AM-modulated waveform using exactly these two parameters, which therefore both enter the description of this waveform. Brews ohare (talk) 16:25, 8 July 2009 (UTC)


 * You have repeatedly asserted that the spatial period of any periodic waveform is its wavelength, even stating that as a definition. I'm seeking comments on that.  Can you hold off the arguments until we get some comments?  Dicklyon (talk) 16:50, 8 July 2009 (UTC)


 * More precisely, I've asserted that the shortest spatial period of any periodic function of x − vt is its wavelength. That corresponds to the envelope wavelength in some cases, for example, in the figures. However, I'll backtrack to say the local wavelength also has its utility in describing the fine structure. Also, I'd generalize to say that the envelope may actually be an abstraction from the actual waveform, leading to a periodic envelope even for a waveform that actually has no periodicity itself whatsoever because the fine structure varies non-periodically within the envelope. Thus, the envelope wavelength is a concept more useful than the period of the function f(x-vt). Brews ohare (talk) 17:54, 8 July 2009 (UTC)


 * No problem on the envelope stuff. This RFC is on your assertion "that the shortest spatial period of any periodic function of x − vt is its wavelength".  That is not a conventional definition, and leads to a difficult discontinuity and ambiguity in the case of very-nearly-periodic signals.  Nobody uses this in reality.  Wavelength is the crest-to-crest spacing in all fields that I'm aware of (and some even restrict to sinusoids, since crest-to-crest can be ambiguous, for example when wideband noise is added).  So, I'd like to get comments on these two definitions, which I think I clearly and fairly presented, in this RFC.  The envelope question is separate.  Dicklyon (talk) 18:15, 8 July 2009 (UTC)

I don't care what The Truth is. Wikipedia is about verifiable sources, not about truth. Find some reliable sources and put whatever those sources say into the article. (This may mean including information that you think is incorrect, that's one of the perils of NPOV). 82.33.48.96 (talk) 19:08, 8 July 2009 (UTC)


 * As the relevant points for the article are the wavelength of the envelope and the wavelength of the fine structure (the local wavelength) I am unsure what is accomplished by a discussion of the wavelength as the least period of f(x-vt)? This wavelength is very often the same as that of the envelope (as in the first waveform), but where it is not, the envelope wavelength is what matters (as in some practical versions of waveform where the interior structure is uncorrelated with the envelope)). Brews ohare (talk) 19:58, 8 July 2009 (UTC)


 * Indeed, it's not about "truth". It's about telling Brews to stick to sources and how they use the term.  Can you help?  Dicklyon (talk) 01:37, 9 July 2009 (UTC)

Dick, I do not quite understand your point. What exactly is it that you are objecting to? Martin Hogbin (talk) 20:50, 8 July 2009 (UTC)


 * What I object to is Brews ohare making up his logical extensions of normal terminology and practice, rather than sticking to sources. You can review the talk above for about 4 weeks of such.  Dicklyon (talk) 01:36, 9 July 2009 (UTC)

Broad comments painting the kettle black, rather argumentative, not constructive. Brews ohare (talk) 03:45, 9 July 2009 (UTC)


 * More specifically, what I object to that this RFC is about is Brews using the unconventional definition of wavelength that would make the period (the longer distance marked in the picture) be the wavelength of the AM-modulated wave shown, rather than sticking with the conventional definition that makes the shorter distance, the crest-to-crest distance, the wavelength. I don't object to the label in the figure calling this the envelope wavelength, just to him wanting to define the wavelength of the wave as its spatial period rather than its crest-to-crest spacing as is conventional.  Perhaps I confused matters by choosing as an example a figure with the word "envelope" in it.  It is OK to say that this wave has a wavelength (marked local for some reason in the picture) and that its envelope has a wavelenght (as marked); that's not the problem.  The problem is that he keeps invoking his definition that wavelength is spatial period, thereby implying unconvential and incorrect and odd results.  Dicklyon (talk) 06:04, 9 July 2009 (UTC)


 * 'Spatial period' seem to me to be a somewhat specialist term and one that does not help in explaining what wavelength is. I am a physicist and I have not come across the term before, neither is there a WP article on the term.  From a quick Google search it would seem that it refers to the longest repeating pattern, but this is only what I have deduced from the few web pages that I have looked at.  I am reasonably knowledgeable about wavelength but I certainly do not find the term 'spatial period' to be of any value on understanding the concept.  I am not sure if it helps to resolve this dispute but I suggest that we do not use this term at all in the article.


 * I also agree that it is odd to define wavelength based on the length of an exact repeat (what I presume to be the meaning of spatial period). Applied strictly to a radio station this might mean that its wavelength should based on the time between repeats of the same music track, rather than the unmodulated carrier wavelength, which is the measure that everybody understands. Martin Hogbin (talk) 12:57, 9 July 2009 (UTC)


 * Dick your comments on the deadlock at the Monty Hall problem would be welcome. Martin Hogbin (talk) 12:59, 9 July 2009 (UTC)


 * I stopped watching that one, as it was clearly going to be an infinite time sink forever. Too many dug-in positions, too little willingness to be reasonable; there's just so many of these I can handle.  Dicklyon (talk) 15:42, 9 July 2009 (UTC)

Martin: Thank you for your comments here. I'd agree that wavelength cannot be defined so as to capture all the interesting information in a wave. Evidently in the case of a carrier, the interesting part of the wave is not the carrier but the modulation of the wave, be it amplitude, frequency or phase. Thus, more must be provided than the carrier wavelength. Providing carrier and envelope wavelength is a stop-gap. You definitely need the shape of the envelope (see ADSR envelope). You probably need the spectrum. Brews ohare (talk) 13:32, 9 July 2009 (UTC)

It would be an interesting addition to the wavelength article to discuss just where wavelength is a useful concept. That may lead to a variety of definitions depending upon context. Already we have the local wavelength ideas used in water waves approaching the shore, and in the WKB method. We have the envelope vs. the fine structure. There may be more. Brews ohare (talk) 13:45, 9 July 2009 (UTC)


 * It would be an interesting addition indeed; see what you can find – but don't make it up. Dicklyon (talk) 15:42, 9 July 2009 (UTC)

Unconventional definitions
Hi Dick: May I try to phrase your objections in different words to see if I've got it?

Fundamentally a definition you would agree to is something like this:

"Phenomena in nature arise in which some property (perhaps water surface displacement or electromagnetic field) goes through a sequence of values in space. If this sequence alternates between runs of increasing values and runs of decreasing values, the wavelength is the spatial separation at a given moment in time between any two immediately adjacent alternations in direction in these runs of values of the same type (that is, up-run to down-run, or vice versa). Evidently, this wavelength need not be a unique value, but may be a set of values varying with location within the wave, and in fact not necessarily the same set of values from one moment to another in time."

Period T is the time analog of λ.

On this general basis, λ = vT is a special case, not a universal property of waves. In the case of f(x-vt) with f periodic, we can define a λ = vT. Sinusoidal variations are a particular case of a periodic f(x-vt) in which f = A sin(x-vt + φ).

In the case of a wave with envelope, the envelope can fit into any category and may or may not have a λ or T. In such cases the "fine structure" inside the envelope also may or may not exhibit + and  − alternations in space or in time, and may or may not exhibit a local λ or T shorter than that of the envelope. Where both the envelope and the fine structure exhibit wavelength, specification of both the envelope λ and the local λ provide a more detailed description of the phenomena than either λ by itself.

How'm I doin' ? Brews ohare (talk) 13:21, 9 July 2009 (UTC)


 * Badly. My preferences and concepts are not really relevant.  I just want you to respect WP:V and only insert text, terminology, and interpretations that come from sources, not from your own logical extensions of what's in sources.  As to whether a wave can be more completely described by information other than its wavelength, of course that's true.  Dicklyon (talk) 15:33, 9 July 2009 (UTC)


 * Re your newly added figure above, do you have any source that suggests that any of those marked intervals would be referred to as wavelengths of some sort? Hold the logic; just a source, please. Dicklyon (talk) 15:47, 9 July 2009 (UTC)

Local wavelength: Cooper Pinet Periodic wavelength Flowers Brews ohare (talk) 16:02, 9 July 2009 (UTC)

Don't get your shirt in a knot - just trying to evolve the conversation. Brews ohare (talk) 16:10, 9 July 2009 (UTC)


 * Cooper says "The local wavelength of a dispersive wave is twice the distance between two successive zeros." Inapplicable to your figure. Dicklyon (talk) 16:24, 9 July 2009 (UTC)
 * That is so. However, it's not clear why he choose zeros instead of crests. Clearly he includes cases of nonuniform separation of zeros. Brews ohare (talk) 16:38, 9 July 2009 (UTC)


 * The difference may actually matter. I'm not sure about Cooper's case, but for example modulation of a waveform shifts the locations of the crests slightly, altering the period between them. It does not shift the locations of the zeroes.--Srleffler (talk) 17:14, 9 July 2009 (UTC)


 * Pinet doesn't have a definition per se, but clearly measures wavelength in a way consistent with Cooper's local wavelength, but between unambiguous crests, and inapplicable to the periodic squiggle in your figure. Dicklyon (talk) 16:24, 9 July 2009 (UTC)


 * The figure in Pinet is entirely consistent with my figure. His crests even include a breaking waveform, never mind the smooth crests in my figure. Brews ohare (talk) 16:38, 9 July 2009 (UTC)


 * You are hallucinating. Pinet shows that as a nearly-sinusoidal wave propagates into shorter water, its wavelength decreases; it is local in a reasonable sense (tied to location), very unlike the traveling bumps within the periodic squiggle that you drew.  Dicklyon (talk) 16:46, 9 July 2009 (UTC)


 * I see the label "breaker" in Pinet's Figure 7.7 (b) p. 242. Don't you? Rather than argue over this, try to think about the notion of a set of local wavelengths and what it might bring to a description of a waveform: Could it be equivalent to a spectrum? Could it contain information in an echo location? When is it just noise? Brews ohare (talk) 17:04, 9 July 2009 (UTC)


 * Flowers says "the period may instead be called the wavelength" but doesn't say over what space of possible signals that calling may be applied; certainly with respect to your smaller squiggle distances it's inapplicable, and there is no support in sources to say that wavelength is defined generally as spatial period; in fact that usage conflicts with common usage in radio, radar, sound, light, and such fields of use when the wave is more complicated than a sinusoid, as has been pointed out by the one useful response we got in the RFC. Dicklyon (talk) 16:24, 9 July 2009 (UTC)


 * The figure and the suggestions I have made clearly exclude Flowers from the "smaller squiggle" distances. Flowers clearly refers to a spatially periodic function of arbitrary form, which is exactly what the figure labels as λe. It is beyond all controversy that Flowers would agree that λe fits his description. His requirement is f(x+ξ)=f(x), which is exactly the case in the figure with ξ = λe. Brews ohare (talk) 16:38, 9 July 2009 (UTC)


 * That's true, and I didn't argue against it. But what I said about Flowers is also true.  Your λe is the period that Flowers discusses, and I agree that he said "the period may instead be called the wavelength".  But it is still extrapolation to say that any such period is defined to be a wavelength.  That would conflict with conventional definitions.  Dicklyon (talk) 16:46, 9 July 2009 (UTC)


 * I don't agree; it would be extrapolation to say that every wavelength is such a period. That is the converse. Brews ohare (talk) 17:04, 9 July 2009 (UTC)


 * So stop with the extrapolation of sources, and just stick to what is verifiable. Dicklyon (talk) 16:24, 9 July 2009 (UTC)
 * So there is no extrapolation of sources here at all; just a misunderstanding by yourself of what I have said and of what the sources say as well. Brews ohare (talk) 16:38, 9 July 2009 (UTC)


 * We have so far failed to find a single other editor to agree with you on any one of these unconventional definitions, and they lead to contradictions, and are based on idiosyncratic interpretations of sources. It's not OK for you to keep pushing your POV without support.  Dicklyon (talk) 16:46, 9 July 2009 (UTC)

The only editors I have noticed here are you (predominantly) and Srleffler (occasionally). Not exactly a crowd. Srleffler has made the useful observation that fine structure and envelopes are not necessarily correlated, and I have adjusted the discussion accordingly.


 * And one more in the RFC (Martin Hogbin). Dicklyon (talk) 17:02, 9 July 2009 (UTC)


 * I am here more than occasionally. I don't usually reply if Dick's responses cover all my concerns. For the record, I agree with most of what he has written in this debate.--Srleffler (talk) 17:20, 9 July 2009 (UTC)

As for yourself, I fail to see any useful commentary. You are focused upon abuse, not progress. You talk about "unconventional definitions" while I find your approach (i) vaguely defined (I tried to get a clearer picture by starting this section) and (ii) definitely unconventional. You speak of "contradictions", but never point any out. You speak of "idiosyncratic interpretations" but never point out the idiosyncrasies. You speak of POV, but never enunciate what this POV is, what you object to about it. In short, much ado about nothing. Brews ohare (talk) 16:53, 9 July 2009 (UTC)


 * I have incorporated the correct bits of your additions into the article, and have encourage you to write up what is in sources about envelope wavelength as applied to derivation of group velocity (which is the only context in which I've seen that concept). The contradictions are pointed out in many places, for example in the wave length of a sinusoidally modulated AM wave, in which the wavelength and the period are very different concepts.  Dicklyon (talk) 17:02, 9 July 2009 (UTC)


 * The wavelength of an AM wave as you understand it is the carrier wavelength. I am unsure whether you attach the same meaning to the period, or perhaps the period refers to the modulation envelope when that is a simple sine wave? In any case, I'd say talking about "the" wavelength in this context may be conventional (I don't know) but it certainly is overly restrictive inasmuch as it tells us very little about the waveform. Generalization to include a wider view of wavelength would provide a more complete description.


 * I still do not see what "contradictions" you are pointing out. Brews ohare (talk) 17:12, 9 July 2009 (UTC)

Current dispute on radar and sound envelopes and wavelengths
Brews has repeatedly re-inserted material such as the sentences

For some waveforms of this general description, the pulse envelope repeats with a wavelength determined by the pulse separation and pulse width. In such cases, the overall pulse wavelength (labeled the "envelope wavelength" in the figure) is the distance traveled between repetitions of the envelope (the distance the wave travels in a time determined by the pulse repetition rate). This distance may not correspond to the distance between any two corresponding positions in the detailed waveform because the fine structure of the waveform may not be related to the envelope in exactly the same way in each pulse. The spacing of the pulses (related to the wavelength of the envelope) is significant in some cases, for example in the perception of a musical tone.

But this is over the strenuous objects of other editors (Srleffler and Dicklyon) who point out that there is no precedent in sources for these strange applications of the concept of wavelength to radar and sound envelopes. Certainly nothing in the sources that Brews has cited supports this.

Note that this is not the same issue as the RFC above, nor is it the application of wavelength to sinusoidal envelopes, which I have agreed is supported in sources in the context of group velocity derivation. We've asked Brews repeated to stick to adding text that is supported by sources, and he has not bothered to add anything about envelope wavelength that is supported, but insists on adding this other stuff instead, for reasons I am unable to fathom, but it's consistent with his pattern at other articles. Dicklyon (talk) 15:29, 9 July 2009 (UTC)


 * I do not understand the concept that wavelength does not apply to an envelope. Dicklyon has said himself that he agrees with concept, so I don't know what his objection is here. Does he object that radar and sound waves never have an envelope? Absurd. That the envelopes of radar and sound waves never have an associated wavelength? Absurd. Brews ohare (talk) 16:07, 9 July 2009 (UTC)


 * You need to read my comments and refer to sources for how the concept of wavelength can be applied, or is applied, to envelopes. In particular, if no source refers to the spatial period of the radar pulse envelope as a wavelength, then it doesn't belong here.  Similarly for the sound pattern envelopes.  Dicklyon (talk) 17:02, 9 July 2009 (UTC)

What is this idea that there is some kind of permission required to use the notion of wavelength with an envelope? The issue is rather one of utility. Of course, one would like to see uniform usage of concepts throughout all science, but that doesn't often happen. So the concept of wavelength is common in some fields, and of period in others. I don't see that precludes the observation that the two notions have much in common and much transfers from one view to the other. Brews ohare (talk) 17:18, 9 July 2009 (UTC)


 * An envelope is not a wave, although it can be described using similar mathematics. Applying the concept of wavelength to an envelope rather than a wave is an extension of the concept, which must be sourced. Since it appears that different authors (perhaps in different fields, or studying different problems) make different choices about extending the concept in this way, Wikipedia needs to document that difference in approach and make clear when the concept is so extended, and when it is not. As per usual Wikipedia policy, our role is not to promote uniform usage of concepts throughout science, but rather to document what the actual usage is.--Srleffler (talk) 17:29, 9 July 2009 (UTC)


 * Exactly; what S says. Your statement "the overall pulse wavelength is the distance traveled between repetitions of the envelope" is your own extrapolation, not one in use in any field or source that we know of.  Your statement "The spacing of the pulses (related to the wavelength of the envelope) is significant in some cases, for example in the perception of a musical tone" is also not based on any source; the cited source does not mention wavelength, and sound perception is more tied to the temporal pattern, unrelated to how the velocity and wavelength in the sound medium might vary (e.g. same temporal signal sounds about the same underwater, wavelength difference notwithstanding).  There's no point in trying to fit what that source says into your idiosyncratic notion of wavelength.  Dicklyon (talk) 17:38, 9 July 2009 (UTC)

Srleffler: You adopt "wave" as a physical concept, and distinguish it from the mathematical concept of "wave". The article wavelength isn't necessarily a physics article or a math article, but probably is both. Thus, from the math viewpoint, no extension of the concept of wavelength is involved (as you agree). As for the physics view of wavelength, there is some guidance in the articles envelope detector & analytic signal deleted from the See Also section by Dicklyon. Brews ohare (talk) 17:47, 9 July 2009 (UTC)


 * Dicklyon: You say "Your statement "the overall pulse wavelength is the distance traveled between repetitions of the envelope" is your own extrapolation" strikes me as in violation of common sense. The pulses repeat on a a regular basis, so of course the wavelength of the pulse is the time spacing times the speed of the wave. What is so odd about that? Taking Srleffler's caveat into account, the wave may not exactly repeat each time, so it becomes a statistical statement, most easily simplified by referring to the wavelength of the envelope (which is not subject to statistical variation, or already incorporates the statistics). Do you really think this is "extrapolation" ? Brews ohare (talk) 17:47, 9 July 2009 (UTC)


 * Are you the first person to characterize periodic radar pulses as having an envelope wavelength? Or is that a concept that someone in the radar field would recognize, along with their usual concept of wavelength?  If you can't answer appropriately based on sources, then we should regard it as your extrapolation.  Review WP:NOR.  Dicklyon (talk) 17:57, 9 July 2009 (UTC)

I am hardly the first, as I'm sure you agree. If you prefer, I'll take all reference to radar out of the discussion and make if a purely formal mathematical discussion. Then all I need is the concepts of envelope and wavelength already cited. Like that ? Brews ohare (talk) 18:02, 9 July 2009 (UTC)


 * I will agree after you show me. Dicklyon (talk) 19:13, 9 July 2009 (UTC)

Also, you object to the use of the sources on sound and its perception because it refers to temporal behavior, and the relation between wavelength and frequency is different in water than in air (for example). However, the example is intended only to point out that the spacing between the bursts is more important than the carrier wavelength under some circumstances. It is an illustration, not a general principle. There is no grand claim here. Brews ohare (talk) 18:02, 9 July 2009 (UTC)


 * Not really because it's different in water and air, that's just an example of probably one reason that concept is not used. The ear has no access to spatial patterns like wavelength, just temporal patterns like frequency and pitch.  There's no point bringing up this topic of sound perception in an article on wavelenght, especially since no source makes that connection. Dicklyon (talk) 19:13, 9 July 2009 (UTC)

As a dispute seems to be continuing, is it possible for someone to identify the disputed text in the article itself. It is not clear to me exactly what the argument is about. Martin Hogbin (talk) 10:52, 11 July 2009 (UTC)

Wavelength and sampling
As per the example of wavelength ambiguity in crystals, I wonder if there is value in viewing the wavelength as an indication of how frequently a wave must be sampled to reproduce it. For the sine wave, the half the customary wavelength will do. In other cases more frequent sampling is necessary. Any suggestions where this connection might be found? Does this sound a likely approach? Brews ohare (talk) 17:32, 9 July 2009 (UTC)


 * Why not go the other way? Find a source on the topic, understand what it says, and report it.  That will likely be less controversial than make up an idea and then look for sources that sort of can be extrapolated to support it. Dicklyon (talk) 17:40, 9 July 2009 (UTC)

I'd be delighted to contribute to this article, but can't work in the environment. Brews ohare (talk) 12:57, 10 July 2009 (UTC)


 * The wikipedia environment isn't that bad once you get used to it; just write stuff that's relevant to the topic and backed up by reliable sources, and there'll be no trouble. Dicklyon (talk) 03:49, 12 July 2009 (UTC)

Moving forward
Brews, I again removed your stuff about envelope wavelength, as it didn't cite any source; the only sources I've seen that concept in apply it to sinusoidal envelopes, as part of the process of deriving group velocity from a pair of sine frequencies. I can write that up for you if you like, but I can't let you add unsourced stuff about square pulse trains having an envelope wavelength. Also, the lead is not adjusted to allow that the spatial period of waveforms is sometimes referred to as wavelength; it's not put in as a definition, since we have only very few sources that use it that way, and they don't seem to be attempting to define it as generally so, which would be a disaster in terms of how much conflict and confusion it would introduce into the question of the RFC above, namely what is the wavelenght of an AM modulated signal. So, I think this allowance in the lead is enough to allow what you say about it later, backed by McPherson, yes? Dicklyon (talk) 03:55, 10 July 2009 (UTC)

Also, I think we can remove the factual accuracy tag if you'll refrain from adding unsourced text and figures about envelope wavelength of modulated square pulse trains. Dicklyon (talk) 03:58, 10 July 2009 (UTC)

Srleffler has rightly called for a citation on the new lead, where it says "wavelength is usually defined as the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, in a sinusoidal or approximately sinusoidal waveform." This is of course a difficulty in trying to write such a lead, since you don't often find sources summarizing what the usual definitions are, and since most sources that illustrate wavelength do so using a sinusoid but never really state a definition and don't say whether it should be generalized, or how. Looking for such things, I find problems and questions for students, like "can wavelength be applied to non-sinusoidal waves?" and such. Maybe it's better not to try to state a usual definition, and proceed as most sources do, by just saying "the wavelength of a sinusoidal signal is...". I'm up for some suggestions. The definition that we had before for a long time, saying that wavelength was the repeat distance of a periodic signal or something to that effect, was both too general and too narrow, as well as being unsourced. Dicklyon (talk) 06:16, 10 July 2009 (UTC)


 * Of course, the lead I suggested "In physics, wavelength is the distance between any two points of the same phase in a sinusoidal waveform, whether the wave is propagating or stationary (a standing wave). It commonly is designated by the Greek letter lambda (λ). The term wavelength also is used more generally for other disturbances, even some that do not vary periodically in space, according to a variety of definitions that are discussed in their respective contexts later in the article. Examples of wave-like phenomena are light, water waves, and sound waves." is easy to source as it is found in every book. It also fits the article better, as it contains wave packets, local wavelengths, WKB, and water waves which may include Dicklyon calls "near sinsuoidal" (whatever the heck that is on any citable basis), but is not limited to same. However, there is no point discussing this with Dicklyon, who has his own views and will delete all efforts to contribute this article. Brews ohare (talk) 12:54, 10 July 2009 (UTC)


 * That source is very typical, defining wavelength in the context of a sinusoidal wave. What's harder is to find a sensible description of how generally the concept is applied; it pretty much has to be inferred from context.  Something like your lead might work, but I didn't like the "even some that do not vary periodically" as it implied that the main definition is about periodicity, rather than about being sinusoidal or approximately so.  One might say "even waves that are not locally sinusoidal" to imply that the main definition is about approximate sinusoids; or just try not to make any such implications.  Dicklyon (talk) 16:26, 10 July 2009 (UTC)

Yes, the source is typical, and the proposed introduction follows the source. Of course the general description is difficult. It varies with context. That is why the special cases should be discussed with their appropriate definitions in their appropriate sub-section, as proposed. Although you don't like the idea, the phrase "even some that do not vary periodically" is exactly the correct exclusion, as all periodic waves have a wavelength defined in exactly the same way as sine waves for exactly the same reason. That is what Flowers is trying to tell you. See also Prigo pp. 80-81 "In general, one cycle [of an extended waveform made up of repeating spatial units] can be defined between any two repeated points in the periodic waveform. The spatial length of this cycle is called the wavelength of the periodic wave." Lloyd p. 156 "Any periodic vibration of wave-length λ can be expressed mathematically by harmonic vibrations represented by sine curves of wave-lengths λ, λ/2, λ/3 ... and so forth." ; Donkin p. 51 "If any arbitrary periodic curve be drawn having a given wave-length λ, the same curve may always be produced by compounding harmonic curves having λ, λ/2, λ/3 ... for their wavelengths"; Eastwood "If B is a periodic function of the continuous variable x with a period length L then ... the wavenumber k takes only those values permitting integral numbers of wavelengths to fit in period length L.". Brews ohare (talk) 18:03, 10 July 2009 (UTC)
 * Just for clarity: note that the statements of Lloyd and Donkin can only be true for a wave that repeats exactly at intervals of λ. Quasi-periodicity as in the case of modulated waves and beat waves will not satisfy that.
 * It looks like we need to rewrite the intro, probably sticking to sourced definitions. Lloyd and Donkin's definitions are not the whole story, however, as they are clearly incompatible with common usage of the term in many areas of physics, where the "wavelength" of a signal is expressly not the spatial period for exact repetition. Modulated signals are the easiest example: "the wavelength" of a modulated signal is unambiguously the wavelength of the carrier.--Srleffler (talk) 04:19, 11 July 2009 (UTC)


 * The proposed intro does not attempt to define wavelength for every situation, but leaves to each sub-section on a different type of waveform to state the appropriate version. A blanket definition is simply too vague to be helpful. As such there is not a wavelength definition in the lead that fits cases that are not exactly periodic. Extensions are postponed. Brews ohare (talk) 05:21, 11 July 2009 (UTC)

As a argument seems to be continuing, is it possible for someone to identify the disputed text in the article itself. It is not clear to me exactly what the argument is about. Martin Hogbin (talk) 10:54, 11 July 2009 (UTC)


 * For the last four weeks, I've taken out what Brews has put in many times. Looks for my edits where the size of the articles goes down a lot, and his where it goes up a lot.  The exact nature of the dispute shifts over time.  The discussion of the lead is a recent detail.  Dicklyon (talk) 20:59, 11 July 2009 (UTC)

Summary of discussion of proposed introduction
Here is a summary of the present discussion. A new intro was proposed: "In physics, wavelength is the distance between any two points of the same phase in a sinusoidal waveform, whether the wave is propagating or stationary (a standing wave).See textbook It commonly is designated by the Greek letter lambda (λ). The term wavelength also is used more generally for other disturbances, even some that do not vary periodically in space, according to a variety of definitions that are discussed in their respective contexts later in the article. Examples of wave-like phenomena are light, water waves, and sound waves."

However, Dicklyon and Srleffler continue to hope that a general definition can be found that will (i) cover all cases, and (ii) have a source. This despite Dicklyon's remark that "it pretty much has to be inferred from context" and Srleffler's observation: "It looks like we need to rewrite the intro, probably sticking to sourced definitions."

These two editors take exception to the statement in the proposed intro:
 * "The term wavelength also is used more generally for other disturbances, even some that do not vary periodically in space, according to a variety of definitions that are discussed in their respective contexts later in the article."

mainly because they do not like the "other cases" categorized as "some that do not vary periodically in space", even though that is the required exception inasmuch as exactly periodic functions are those for which the sourced sinusoidal definition applies.

To support the view that exactly periodic functions do in fact have the same wavelength definition as a sine wave, four sources are quoted at length that state this to be the case. Brews ohare (talk) 15:20, 11 July 2009 (UTC)

My guess is that even if a source can be found with some odd-ball definition, it may not be terribly straightforward to use the odd-ball definition and explain the nuances of its application to each particular circumstance. To do that, one still will have to explain the departures of each new type of wave from a sine wave, which is all that is necessary with the proposed intro. Brews ohare (talk) 18:46, 11 July 2009 (UTC)


 * That intro wasn't a proposal, just something you stuck into the article without discussion. I don't think you have any idea about our hopes, so don't go there.  As I explained, my objection was based primarily on the "even" that you omitted from your summary of my objection; this implied that periodic was the normal case and approximately or locally sinusoidal an exception.  I agree with Srleffler that we need to get this right and based on sources.  Dicklyon (talk) 03:47, 12 July 2009 (UTC)


 * Srleffler, I don't quite understand your latest lead, esp. since the Hecht ref. is not online (I might have copy at work some place, but haven't been by there for a while). Can you tell us what he says about "exactly periodic"?  And I think the lead should at least include a definition that applies to things like wave packets, changing local wavelengths, etc., of locally sinusoidal waves. Dicklyon (talk) 03:47, 12 July 2009 (UTC)


 * I'm fine with omitting "exact". It is redundant anyway—"periodic" is sufficient. Hecht's comment is brief. He introduces wavelength as a property of sinusoidal waves, but then a page later comments that wavelength, frequency, etc. can be applied just as well to any periodic wave. The "exact" was my addition. I agree that the lead should include extensions of the basic concept.--Srleffler (talk) 04:45, 12 July 2009 (UTC)


 * Thanks. Given the scarcity of definitions, probably the best we can do is give sources usages.  Dicklyon (talk) 04:50, 12 July 2009 (UTC)

Envelope wavelength section still not properly sourced
The text that Brews added to the lead, which I moved to an appropriate subsection, says found, for example, in particle motion in a betatron,[18] in Bloch waves,[19] in Rayleigh–Bénard convection,[20] or as produced by interference between sinusoidal component waves.[21]" This may be true, but none of the four cited sources mentions the word "wavelength" in connection with the envelope anywhere near the cited pages, as far as I can find.

I can rewrite the section from the sources that I pointed about before if nobody else does, as soon as I get time. Brews, if I've missed where these sources say anything about "wavelength" of the envelope, let me know. Dicklyon (talk) 04:33, 12 July 2009 (UTC)


 * I take it that spatial periodicity and wavelength are unrelated concepts. Take it as you will. I might note that translation symmetry wrt some distance is what leads to the sin wave as an eigenfunction with a wavelength related to that distance. Brews ohare (talk) 05:00, 12 July 2009 (UTC)


 * Unrelated? Hardly.  Why would you say that?  But where are the sources that call that spatial periodicity of envelopes wavelength?  Dicklyon (talk) 05:13, 12 July 2009 (UTC)

I'm thinking about this. Brews ohare (talk) 05:18, 12 July 2009 (UTC)


 * Good; tell what it says after you think about it. I replaced the contents with a bit that has two sources that mention the wavelengths of envelopes.  Feel free to put back any of the other applications to envelopes as you find sources that mention wavelength.  Dicklyon (talk) 05:29, 12 July 2009 (UTC)

Two points, I am not sure if they will help.

You should not be writing the lead section first. This is meant to me a summary of the article as a whole, so I suggest that it would be better to argue about the body of the article, where more explanatory detail may be given, first.

Secondly, as far as I can see, you seem to mainly disagree on whether the term, 'wavelength' can be applied to an envelope or a non-repeating waveform. It is fairly obvious that the term could be used is these contexts and I am sure that somewhere in the world this has been the case. The question is, in reliable technical sources, how often is the word used this way?

In order to say, '"The term wavelength is also sometimes applied to periodic envelopes' we would need at least one source where the word is clearly used in this way. To say anything stronger than this we would need a source where some kind of description or definition of 'wavelength' used in this way is given.  Currently, I have not seen any sources supporting even 'sometimes applied'. Martin Hogbin (talk) 09:21, 12 July 2009 (UTC)


 * We worked on the article intensively for a month before touching the lead. We found and added applications of the wavelength concept to all sorts of non-period and non-sinusoidal waves.  We added and removed lots of generalizations that found no support in sources, like Brews's assertions about wavelength of radar pulse repetition envelopes and wavelengths of envelopes of sound pulses, and "global wavelength" of AM modulated signals.  Now we're trying to write a lead that will cover what we found, but will not introduce as definition the concepts that Brews wants to be able to use to add more stuff that's not supported in sources.  At least, that's how I see it.  If you see part of the "is also applied to" that needs more illustrative sourcing beyond the two sources that I added, we can work on that.  Dicklyon (talk) 14:47, 12 July 2009 (UTC)


 * As to whether wavelength is sometimes applied to an envelope, or to a non-periodic wave, I think we all agree that it is. Any disagreement?  The disagreement comes more on applying the envelope wavelength idea to signals where the envelope is nothing like sinusoidal, and for which there is no hint of such application of sources.  Dicklyon (talk) 14:49, 12 July 2009 (UTC)

Instead of worrying about how to organize the article with the laudable objective of eliminating Brews's contributions, it would be more fruitful to focus upon a mode of organization that works for the topic. The only viable approach so far starts with the sine wave and then treats separate sub-sections related to construction of other waveforms from the basic sine wave. An example of such construction is interference of sine waves, as occurs in beat waveforms and in the Aharanov-Bohm effect. Brews ohare (talk) 16:00, 12 July 2009 (UTC)


 * Brews, we have actually incorporated a lot of your additions over the last four or five weeks, after simplifying them and finding sources to support them. It has never been among my goals to eliminate your contributions – just to tame them.  I think we've done pretty well, but I just wish it had not been so much work and pain to get where we are.  It continues to baffle me why you won't work on adding stuff from sources that talk about wavelength, even when I point out the sources that support the point you are trying to make, and instead keep adding stuff that's either unsourced or sourced to works that don't mention wavelength.  What's up with that behavior?  I'm not sure what your point is about the two refs you mention just now; I don't find anything about wavelength anywhere near the linked pages.  What am I missing?  Dicklyon (talk) 17:03, 12 July 2009 (UTC)

"Local" wavelength
Definition does not apply to the wave forms illustrated at right, nor to frequency nor phase modulated forms. Is λℓ 2 a wavelength? Brews ohare (talk) 13:05, 12 July 2009 (UTC)

A related standing waveform that might be complicated to relate to the definition is Figure 4-15. Brews ohare (talk) 13:19, 12 July 2009 (UTC)

Another odd use of wavelength is "wavelength chirping" in lasers. See wavelength vs. pulse count in Sheats & Smith. Brews ohare (talk) 13:13, 12 July 2009 (UTC)

With respect to Bloch waves or the Floquet theorem, there seems to be some ambiguity over whether the plane wave factor is the modulator as envelope of the periodic factor or vice versa. SG Johnson has one idea, the Bloch wave article another. BTW, if you want an example of an unintelligible WP article, Floquet theorem has to be on the list. In any event, the plane wave factor is the longer wavelength part and the periodic factor is the rapidly varying (and periodic but not single wavelength) part. Brews ohare (talk) 13:22, 12 July 2009 (UTC)

The sentence "'The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.'" does not explain how this is applied or what it means in reference to the definition. Brews ohare (talk) 13:30, 12 July 2009 (UTC)

Maybe Fourier had the right approach to the general solution to this question of definition: stick to sine waves. Discuss the more general cases in terms of properties of the series that represent them. Alternatively, use sine waves in the intro, and then devote sections to waves representable by special forms like E(x−vgt)sin[(2π/λ)(x–vpt)].?.? Brews ohare (talk) 13:43, 12 July 2009 (UTC)


 * I've looked long and hard for good definitions and discussions of the scope of applicability of the wavelength concept, and have not found much. Therefore, I don't at this time think we can say much more than "is also applied to", and discuss specific applications that we can find in sources.  I haven't seen any sources that suggest that your various squiggles would be characterized as having a wavelength.  Dicklyon (talk) 14:41, 12 July 2009 (UTC)

My examples go far beyond "squiggles", and include sources. Based upon your observation that at this time [I] think we [can't] say much more than "is also applied to", and discuss specific applications, the article should be reorganized to avoid a "pseudo-definition" with vague statements about its applicability, stick to the sine wave in the intro, and introduce other cases as they arise with specific sources and definitions. The basic problem, as I see it, is that one cannot make a general definition based upon the detailed appearance of a waveform, but must refer instead to the way it is constructed. Different modes of construction invite separate subsections, and all subsections build around the sine wave. Brews ohare (talk) 15:33, 12 July 2009 (UTC)


 * Do you have sources that represent something like the images File:Local and periodic wavelengths.JPG (first one agove) and File:Envelope alignment.JPG (last one)? Or sources that use something like lambda_e for the periods of such squiggles or such pulse envelopes and refer to it as a wavelength?  If so, show us, and I'm sure we can incorporate them.  If you just say that you've showed us before, I'll have to just disagree and say I haven't seen it; so if you have sources, please do repeats the links here and now as part of this discussion so we can see what you're referring to;  if they show such things and describe it as "wavelength" I will immediately admit that and apologize for missing it before.  Conversely, if you don't have such sources, please just shut up about it.  Dicklyon (talk) 17:11, 12 July 2009 (UTC)

Dick: Let's step aside on the "every source that is relevant mentions wavelength as such" viewpoint. Suppose, for example, we look at the two-slit interference pattern. It is made up of the interference between two waves of a certain wavelength passing through two slits a definite distance apart. The two parameters: the wavelength of the incident wave and the slit spacing determine the interference pattern, and this pattern can be described in terms of modulating the wavelength components, which may or may not lead to some definition appropriate only to the final resulting modulated waveform. Similarly, the Bloch wave is constructed from a plane wave and an exactly periodic function composed of a set of Fourier components related to the wavelength of the lattice. So, generally, I'm thinking that the article starts off with a sine wave and then examines various wave patterns made up of contributions with various wavelengths and explains some of the variety that results when different patterns combine in various fashions, for example, via modulation. Where appropriate, the notion of local wavelength and envelope wavelength may come up. It's a result, not an input. Brews ohare (talk) 20:36, 12 July 2009 (UTC)


 * If the notion comes up in sources that talk about it as a wavelength, let's report that. If not, let's don't.  Then we can stop arguing, and maybe keep the article finite, too.  Dicklyon (talk) 23:09, 12 July 2009 (UTC)

Wavelength and interference
Here is a rough outline of a section by this name. Are you in favor?



Basically, summarize the following:

Further reading: notes formula hologram

Point out path difference must be integer number of wavelengths. Include a couple of figures (not necessarily these, maybe Figure; comment?).

Add paragraph on beats. In acoustics, a beat is an interference between two sounds of slightly different frequencies Brews ohare (talk) 14:35, 13 July 2009 (UTC)


 * Using interference/diffraction experiment to measure the wavelength of light is worth a mention. Probably there's a better source than an anonymous-looking course notes.  As for beats in music/sound, that's always described in the time domain, and has no important coupling to wavelength, as far as I'm aware, but if you find a source that does it in terms of wavelength I won't object.  Dicklyon (talk) 14:46, 13 July 2009 (UTC)

For beat, how about:Ou; Boyes; zheng; malacra; Weedon; [http://books.google.com/books?id=O_17yydIsJcC&pg=PA271&dq=wavelength+beat&lr=&as_drrb_is=q&as_minm_is=0&as_miny_is=&as_maxm_is=0&as_maxy_is=&as_brr=0? Aggarwal]? Brews ohare (talk) 15:08, 13 July 2009 (UTC)


 * Yep, there may be something to that, esp. in two-wavelength interferometry; basically just another name for envelope wavelength. But none of those are about beat wavelengths in sound, so it's good that you took out the see-also to beat (acoustics) for now.  The section looks good, but probably doesn't need to say "wavelength" in its heading, as that's implied; how about just "Interference" or "Diffraction and interference"?  Dicklyon (talk) 23:23, 13 July 2009 (UTC)


 * Why do you keep adding massive quantities of new stuff instead of collaborating by addressing my comments first, either here or in the article? Dicklyon (talk) 17:05, 14 July 2009 (UTC)


 * In the new subsection, the only thing that really needs to be said is that diffraction-limited angular and spatial resolution are proportional to wavelenght. The rest is better covered in the linked articles.  Dicklyon (talk) 17:22, 14 July 2009 (UTC)

Sorry, I didn't realize I was ignoring your comments. I'll change the headings, if that is what you refer to. I am not convinced that nearly nothing has to be said in view of the indigestible nature of the other articles. A bit of summary is helpful. Brews ohare (talk) 18:05, 14 July 2009 (UTC)


 * Apology accepted. The other articles may be worth some simplification and clarification, but that's not a reason to recreate their content here.  Dicklyon (talk) 18:10, 14 July 2009 (UTC)


 * I've started to reorg the section a bit. The way the single-slit diffraction and diffraction-limited angular resolution were intertwined was confusing.  I've never seen a telescope treated as if it has a square aperture and is like single-slit diffraction, nor have I seen resolution parameterized that way in terms of exit pupil.  I think we should change to a  more conventional presentation; also use the Rayleigh criterion instead of the diameter to first null.  Maybe this book. Dicklyon (talk) 08:10, 15 July 2009 (UTC)

Sounds OK to me. The sinc function should be provided, however, as it gives the envelope of the double slit experiment as well as the single slit.handbook;Ingard. I'm unclear why the source with the nice figure that I provided doesn't use the Rayleigh criterion. Maybe you can figure that out? Brews ohare (talk) 16:34, 15 July 2009 (UTC)

Are you going to say something about gratings, or about lithography for electronics? Brews ohare (talk) 16:35, 15 July 2009 (UTC)


 * I worked on resolution. You can do the diffraction.  There are probably better sources and parameterizations for the sinc on some of the linked pages. Dicklyon (talk) 05:41, 16 July 2009 (UTC)

Figure showing interference
Dick: you removed this figure with this explanation: " remove distracting large figure with misleading scalings of sub-parts"

Can you explain what is misleading about "scaling" here? The labeling shows the shift between the two superposed waves in terms of fractions of a wavelength; what's the problem; wouldn't some change in caption be preferable to deletion of the figure? Brews ohare (talk) 12:19, 20 July 2009 (UTC)


 * It took me a while to realize that the reason the point of the image was so unclear was that each of the four panels was at a different vertical scale, probably due to auto-scaling. It's also a lot of space to make such a simple point.  The point that needs to be made here is actually made better by just illustrating the in-phase and out-of-phase extremes, I think, like on the Interference page.  Perhaps we should use this figure instead.  Dicklyon (talk) 14:19, 20 July 2009 (UTC)


 * I actually find the original figure (the one that Brews ohare first commented about) extremely useful. It's because most textbooks just give the two extremes, but I feel that having a visualization of the various intermediate phase-shifts lends itself to a better intuition about how waves interfere with one another. Awickert (talk) 17:10, 5 August 2009 (UTC)


 * I think showing intermediate cases could be a good idea, although I haven't looked at the context here yet; it might be too big and/or too off-topic. The vertical scale is important, though. All four panels would need to have the same scale.--Srleffler (talk) 00:52, 6 August 2009 (UTC)


 * Brews, it looks like you created the graphic. Could you re-scale them or add numbers to the y-axis? Otherwise, if you sent me vectorized files, I'd be happy to do it as well. Awickert (talk) 20:29, 6 August 2009 (UTC)

I have updated this figure to use the same vertical scale in all panels. Brews ohare (talk) 14:38, 25 August 2009 (UTC)


 * Thanks; with this fix, I think that the figure is useful and should be put in the article. Other opinions? Awickert (talk) 00:04, 30 August 2009 (UTC)