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
