User:Brews ohare/sandbox

In response to Jclemens: Although it may appear from Blackburne's perspective that simple head-butting took place on Talk:Wavelength, in fact the discussion did evolve and resulted in changes of the proposed text, a change in scope and in purpose to meet objections about its relevance, to become only a cross-reference between Wavelength and the important role of Fourier series for periodic functions. At this point, I recognize that even this proposal is rejected.

In the past, several extended discussions on Talk:Wavelength have proved useful. For example, long discussion resulted ultimately in additions in the article text, accompanied by 8 figures of my creation. These additions have improved coverage by Wavelength.

A different extended discussion about periodic envelopes on Talk: Wavelength led to my creation of a separate article, Envelope (waves), again a positive outcome for WP.

So there is some reason to believe that these prolonged interactions have resulted overall in positive results for WP. You have advised "all parties to work together toward improving the articles in question", and this has in fact happened, although not actually in an atmosphere one would recommend to other editors.

One might wish that interactions between myself and Dicklyon, with occasional participation by Srleffler, were less confrontational, but that is to be worked upon between ourselves, and doesn't require Arbitration. There was no need for Blackburne to interrupt under the guise of a "request for clarification" of an expired sanction, which now he is attempting to morph into an "inevitable visit to arbitration". The only "inevitability" here is Blackburne's efforts to cause me trouble, both with Adminstrators:, , leading to , blanking Talk page contributions , and with an unending succession of trivia.

http://en.wikipedia.org/w/index.php?title=User_talk:Equazcion&diff=prev&oldid=483385587

http://en.wikipedia.org/w/index.php?title=User_talk:Equazcion&diff=prev&oldid=483444604

http://en.wikipedia.org/w/index.php?title=Wikipedia_talk:Avoiding_talk-page_disruption&diff=483394563&oldid=483393753#Comment_8

http://en.wikipedia.org/wiki/User_talk:Equazcion/Archive_6#Remark_on_your_remark

dispersion

Fourier integral

general discussion

wave packets

Fourier integral

Fourier transform

Fourier transform

harmonics in instruments

in speech

Helmholtz theory of the vowels

violin

sound waves made visible

wavelength p.10

sound modifiers in stringed instruments

sonometer

manometric flames organ tones displayed in space

Helmholtz theory of timbre

construction

math

construction

construction

modeling

modeling

modeling

woodwind

transmission line

transmission line

Fourier integral & distributions

Suppose the driving force is Fourier analyzed at its point of application as having two nearby frequencies. In the dispersive medium they travel at speeds v1 and v2. The waveform at a distant location is made up of the summation:
 * $$ f = A_1 \sin\left[\frac{2\pi}{\lambda_1} (x-v_1 t)\right] + A_2 \sin \left[\frac{2\pi}{\lambda_2}(x-v_2 t)\right] $$
 * $$= A_1 \left( \sin\left[\frac{2\pi}{\lambda_1} (x-v_1 t)\right] + \sin \left[\frac{2\pi}{\lambda_2}(x-v_2 t)\right]\right)+(A_2-A_1)\sin\left[\frac{2\pi}{\lambda_2} (x-v_2 t)\right]$$
 * $$=2A_1 \sin 2\pi \left(x (1/2\lambda_1 +1/2\lambda_2)-(v_1/\lambda_1+v_2/\lambda_2)t/2\right)\cos 2\pi\left(x (1/2\lambda_1 -1/2\lambda_2)-(v_1/\lambda_1-v_2/\lambda_2)t/2\right) +(A_2-A_1)\sin (x/\lambda_2-v_2 t) $$
 * $$\approx \left [ 2A_1 \cos\left[\frac{2\pi}{\lambda}\left(\frac {\Delta \lambda}{\lambda}(x-vt)-\Delta vt\right)\right] +(A_2-A_1)\right ]\sin\left[\frac{2\pi}{\lambda} (x-v t)\right] $$

so we see a rapidly varying oscillation propagating quickly with a slowly propagating envelope of different wavelength superposed.