Sound wave momentum and thermal expansion

Abstract

Travelling sound waves in anharmonic media possess momentum, at any rate if they are longitudinal. When such waves are thermally excited in a solid specimen, they are liable on that account to exert pressure on the specimen's surfaces and cause it to expand. In order to explain the thermal expansivities that are observed in practice, however, it is necessary to treat phonon excitation modes as standing rather than travelling waves. One might expect the pressure exerted by a longitudinal standing wave on a surface normal to its wavevector q to be equal to the pressure that would be exerted by an independent travelling wave having the same q but half the energy density, were the standing wave to be reflected without change in the magnitude of its momentum. In anharmonic solids, however, standing waves turn out to exert twice the pressure one would expect on that basis.