A modal collocation algorithm for high-frequency propagation in discontinuous waveguides

A procedure for analyzing high-frequency propagation in adjoining constant width waveguides was presented previously [Ginsberg, JASA 134, 4217 (2013)]. The parallel walls were taken to be rigid, and no results were provided. This presentation uses that development as the foundation for the analysis of waveguides having an arbitrary number of sections, each of whose walls have arbitrary local impedance. The analytical basis is description of the pressure field in terms of transverse pressure modes, each of which is associated with upstream and downstream propagation at wavenumbers that may be complex, depending on the wall properties. Pressure and particle velocity conditions at junctions of two segments are enforced exactly by collocation along the common cross section. Initiating the procedure at a passive termination leads to recursion relations for modal reflection and transmission coefficients at each junction, which are independent of the nature of the excitation. Satisfaction of the conditions at th...