A re-expansion method for determining the acoustical impedance and the scattering matrix for the waveguide discontinuity problem.

The paper gives a new method for analyzing planar discontinuities in rectangular waveguides. The method consists of a re-expansion of the normal modes in the two ducts at the junction plane into a system of functions accounting for the velocity singularities at the corner points. As the new expansion has an exponential convergence, only a few terms have to be considered for obtaining the solution of most practical problems. To see how the method works some closed form solutions, obtained by the conformal mapping method, are used to discuss the convergence of the re-expanded series when the number of retained terms increases. The equivalent impedance accounting for nonplanar waves into a plane-wave analysis is determined. Finally, the paper yields the scattering matrix which describes the coupling of arbitrary modes at each side of the discontinuity valid in the case of many propagating modes in both parts of the duct.