Abstract
A recent Letter has reported that sound waves can carry gravitational mass. I analyze this effect in a Hooke's law solid, considering a wave packet moving in the $z$ direction with an amplitude that is independent of $x$ and $y$. The analysis shows that, at second order in an expansion around small amplitude vibrations, there is a small net motion of material, and thus mass, in the direction opposite to the wave packet propagation. This is a straightforward consequence of Newton's laws.
Highlights
In a recent paper [1], Esposito et al have argued that sound waves can carry gravitational mass
Considering the first nonlinear corrections to the motion of the material, there is a much larger mass associated with the wave packet, M ∝ E /cL2, where cL is the speed of sound in the material [1]
Considering the nonlinear terms in the equations of motion, one finds that the atom has moved slightly in the −z direction
Summary
In a recent paper [1], Esposito et al have argued that sound waves can carry gravitational mass. Considering the first nonlinear corrections to the motion of the material, there is a much larger mass associated with the wave packet, M ∝ E /cL2 , where cL is the speed of sound in the material [1]. This result generalizes an analogous result [2] for phonons in a superfluid. Considering the nonlinear terms in the equations of motion, one finds that the atom has moved slightly in the −z direction. This is a very small effect, but it is not zero. This is the interpretation given in Ref. [1]
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