EXACT SOLUTION FOR ONE-DIMENSIONAL ACOUSTIC FIELDS IN DUCTS WITH POLYNOMIAL MEAN TEMPERATURE PROFILES

The purpose of this paper is to present closed form expressions for so und propagation in ducts with polynomial mean temperature profiles. It is shown that using appropriate transformations, the one-dimensional wave equation for ducts with an axial mean temperature gradient can be reduced to a standard differential equation whose form depends upon t he specific mean temperature profile in the duct The solutions are obt ained in terms of Bessel and Neumann functions. The analysis neglects the effects of mean flow and therefore the solutions obtained are vali d only for mean mach numbers that are less than 0.1. The developed sol ution is used to investigate the sound propagation in a quarter wave t ube with an axial mean temperature gradient The expressions for the fo ur pole parameters are also presented.