An excursion into classical nonlinear acoustics

Abstract

This paper is concerned with the derivation of the partial differential equations that govern the propagation of sonic disturbances in an ideal gas under isentropic conditions. The result is a quasilinear hyperbolic system of first order equations and an inequality constraint. The speed of propagation is pressure dependent. It is shown how to deal with the equations and the constraint and how to calculate characteristics and solutions. It is also shown that shock discontinuities can develop which distinguishes the equations from the traditional linear wave equation.