A Theoretical Investigation of Finite Amplitude Standing Waves in Rigid Walled Cavities

Abstract

The Coppens- Sanders perturbation solution for the one- dimensional non- linear acoustic wave equation with dissipative term describing the viscous and thermal energy losses encountered in a rigid walled, closed tube with large length-to-diameter ratio was extended to include sixth order terms. The solution was then investigated to determine the region of validity. Computer programs were written to evaluate and graph the resulting waveforms. Available experimental results were compared with the theoretical predictions and good correlation was found to exist in the region of low Mach numbers. This agreement was found to gradually deteriorate as the Mach number was increased. A Fourier synthesis approach is also presented and the leading terms of the first ten harmonics are derived.