A New Fundamental Asymmetric Wave Equation and its Application to Acoustic Wave Propagation

TL;DR

This paper introduces a new fundamental asymmetric wave equation derived from group representations, providing a comprehensive description of wave propagation phenomena including Doppler effects and invariance across inertial frames.

Contribution

The paper presents a novel asymmetric wave equation that is fundamental and accounts for key wave phenomena, improving upon existing symmetric equations.

Findings

The new wave equation accurately models Doppler effects.

It ensures wave speed invariance in all inertial frames.

Applied to acoustic waves, it determines Lamb's cutoff frequency.

Abstract

The irreducible representations of the extended Galilean group are used to derive the symmetric and asymmetric wave equations. It is shown that among these equations only a new asymmetric wave equation is fundamental. By being fundamental the equation gives the most complete description of propagating waves as it accounts for the Doppler effect, forward and backward waves, and makes the wave speed to be the same in all inertial frames. To demonstrate these properties, the equation is applied to acoustic waves propagation in an isothermal atmosphere, and to determine Lamb's cutoff frequency.