Sound waves move matter

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.