A finite difference method for computing sound propagation in nonuniform ducts

A method is presented for computing the propagation of sound in an axially symmetric duct with nonuniform cross section. The nonuniform duct is mapped onto a cylindrical duct with constant cross section using a conformal map. The sound propagation in the cylindrical duct is then determined by the method of finite differences and these results transformed back to the original nonuniform duct using the inverse map. The method is checked by comparing the results for a hard wall conical duct with the exact analytical solution. A study is made for the same conical duct to determine the uniform lining yielding the greatest attenuation of sound within the duct.