In general, the acoustic branches of a crystalline solid has a nonlinear dispersion relation. For small values of the wavenumber $k$ or wavelengths large compared to the equilibrium lattice separation, the said dispersion formula approximates to a linear relation $\omega=c_sk$. To the best of my knowledge, excitations of the solid in only this linear regime, are associated with sound waves. If this is really so, I would like to understand why don't the higher frequency or shorter wavelength components of the acoustic branch carry sound waves or if they do, whether the corresponding frequencies fall outside the audible range.
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1$\begingroup$ Could you define "sound wave"? $\endgroup$– lnmaurerCommented Oct 3, 2020 at 16:45
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$\begingroup$ Sorry for the late response. I am not very active on this site. It's not how I define sound waves. The issue is that textbooks define sound waves in solids as those excitations of the acoustic branch for which the dispersion relation is linear i.e. group velocity is equal to the phase velocity. If this is taken as the definition, the question is: how do we know that the sound wave is dispersion-free? $\endgroup$– SoumitaCommented Oct 19, 2020 at 15:05
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$\begingroup$ On the other hand, if by sound waves we mean 'audible frequencies' whose range is from 20Hz to 20kHz, how do we know whether for those frequencies the dispersion relation in real solids will be linear. $\endgroup$– SoumitaCommented Oct 19, 2020 at 15:06
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