EXACT SOLUTION FOR ONE-DIMENSIONAL ACOUSTIC FIELDS IN DUCTS WITH A QUADRATIC MEAN TEMPERATURE PROFILE

The purpose of this Letter is to present an exact analytical solution for sound propagation in ducts with a quadratic mean temperature profi le. Using appropriate transformations, the one-dimensional wave equati on for ducts with an axial mean temperature gradient was reduced to th e hypergeometric differential equation, whose solution can be expresse d in terms of hypergeometric functions. The analysis neglects the effe cts of mean flow and is therefore valid only for small mean Mach numbe rs. (C) 1997 Acoustical Society of America.