Mechanical wave momentum from the first principles

TL;DR

This paper derives fundamental relations for mechanical wave momentum in waveguides from first principles, clarifying the connection between wave energy and momentum, and analyzing conditions for momentum carriage in various wave types.

Contribution

It provides a first-principles derivation of wave momentum relations, including the structure of binary waves with self-equilibrated momentum and conditions for longitudinal waves to carry momentum.

Findings

Relations for axial momentum from conservation laws

Expression for the wave-associated mass

Conditions for longitudinal waves to carry momentum

Abstract

For steady-state and some other types of mechanical waves of an arbitrary form, intensity and nature, propagating in a free uniform waveguide, we present the following. Relations for the axial momentum as it directly follows from the conservation laws. The mass associated with the wave. The connection between the wave energy and momentum. The structure of a binary wave which possesses a self-equilibrated momentum, in particular, a transverse-longitudinal wave formed upon excitation of flexural waves. Conditions under which longitudinal sinusoidal waves can carry momentum and the physical meaning of the so-called "wave momentum".