User:Abbas moghanizadeh/sandbox

An ultrasonic wave loses its energy while it propagates through a material. Energy loss of a wave is mainly due to two mechanisms which are absorption and scattering processes. Hence, attenuation is a frequency-dependent coefficient and can be written as

(1) α (f)=αa(f)+αs(f) grain scattering losses are large compared to absorption losses ).

(2)	α(f)≈αs(f) The ultrasonic wave attenuation in the material is given by:

(3)   A=A0+exp(-ax) Where A0 is assigned as the initial amplitude of the wave, A is designated as the amplitude at a local position x, and α represents the attenuation coefficient of the material. By taking the natural logarithm of Eq. (2), We obtain:

(4) Ln A=Ln A0-ax (5) ɑ(ʄ)= (1/x)Ln(A0/A) In the Rayleigh region (our case) where α and D (l wavelength and D grain size diameter), the absorption coefficient depends linearly on the frequency and the scattering coefficient is proportional to D, and is represented by:

(6) Where D is designated as the mean grain size, f represents the frequency, Cr is assigned as a material constant, CL is labeled as the longitudinal velocity of sound in the medium, and λ represents the acoustic wavelength. In the second (stochastic) regime, the acoustic wavelength is comparable to the grain diameter (i.e., λ ≈ D). The attenuation in this regime is related as follows: Where Cs signifies a material constant. As discussed in ), (7) Where Cs is a material constant Where D is assigned as the mean grain size, f denotes the frequency, Cr represents a material constant, CL corresponds to the longitudinal velocity of sound in the medium, and λ is labeled as the acoustic wavelength.