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Can we apply the de Broglie relations to a sound waves ? Is it possible? if yes how do you do that? what would be the mass(m) in the equation?

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You have to quantize the microscopic degrees(the atoms that the material is composed of), and see what comes out, As John Rennie Points out for a lattice, you would observe phonons, whose long wavelength limit is a sound wave. – Prathyush May 22 '13 at 10:53

Sort of. I'm not sure about sound waves in air, but sound waves in a lattice can be described by quasi-particles called phonons. However I'm not sure whether the wavelength of the vibration would then correspond to the de Broglie wavelength of the phonon. The Wikipedia article states the momentum of the phonon (subject to some matters of interpretation!) is $\hbar k$, so regarding the wavelength of the vibration as analogous to the de Broglie wavelength of the phonon seems plausible.

Phonons are normally considered massless, though see this question.

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