Sound waves move matter

TL;DR

This paper analyzes how sound waves in a solid can carry gravitational mass, showing that they induce a small net motion of matter opposite to the wave's direction, based on Newton's laws.

Contribution

It provides a detailed analysis of mass transport by sound waves in a solid, clarifying the physical mechanism behind the effect reported in recent literature.

Findings

Sound waves cause a small net motion of matter opposite to wave propagation.

The effect is a direct consequence of Newton's laws.

Mass transport by sound waves is theoretically confirmed in a Hooke's law solid.

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.