Computational Methods for Studying Acoustic Propagation in Nonuniform Waveguides

A variational technique is used to model sound transmission through a nonuniform duct segment consisting of an axial variation in wall admittance or cross-sectional area. The method involves the Ritz minimization of functionals that have the governing equations as stationary conditions. The variational method is verified by application to segments of variables-separable geometry, for which eigenfunction expansion techniques offer an alternative solution procedure, and by comparison with the results of stepped-duct approximations to the nonuniformity. Quantitative data are presented which indicate the boundary condition matching to be a suitable measure of the accuracy of the transmitted field.