Acoustic scattering in waveguides that are discontinuous in geometry and material property

Abstract

The scattering of acoustic waves at the discontinuity between two ducts of different heights is considered. At least one of the ducts is bounded by a membrane and, thus, the underlying eigenproblem is non-Sturm–Liouville. A mode-matching procedure, based on an appropriate orthogonality relation, reduces the problem to that of truncating and solving an infinite system of linear equations. The distribution of power between the fluid regions and the membrane(s) is analysed. Further, it is shown that a fundamental property of the truncated system is that the expression for power balance is always satisfied.