Ultrasonic waves in classical gases

TL;DR

This paper derives and solves a dispersion equation for ultrasonic waves in classical gases using the Boltzmann kinetic equation, providing results consistent with known regimes and enhancing understanding of sound propagation.

Contribution

It introduces a nonperturbative dispersion equation for all sound frequencies in classical gases, solved numerically within linear response theory.

Findings

Results agree with analytical solutions in different collision regimes

Provides a unified approach for sound wave analysis in gases

Enhances understanding of velocity and absorption in classical gases

Abstract

The velocity and absorption coefficient for the plane sound waves in a classical gas are obtained by solving the Boltzmann kinetic equation, which describes the reaction of the single-particle distribution function to a periodic external field. Within the linear response theory, the nonperturbative dispersion equation valid for all sound frequencies is derived and solved numerically. The results are in agreement with the approximate analytical solutions found for both the frequent- and rare-collision regimes.