Acoustic propagation in two-dimensional waveguide for membrane bounded ducts

• The scattered wave potentials are expressed in terms of eigen expansion form.
• The system is non-Sturm Liouville, and, hence discussed with orthogonality relation.
• The relative merits of mode-matching and low frequency approaches have been debated.
• The results are validated using conserved power identity via algebraically and numerically.
• Using Lanczos filter, the oscillations in the normal velocity field have been removed.

This work aims to investigate the mode-matching (MM) and low frequency approximation (LFA) solutions of a two dimensional waveguide problem with flanged junction. The relative merits of each approach are compared for the scattering of fluid-coupled wave. The boundary value problem involving higher order derivatives at boundaries becomes a non-Sturm–Liouville problem where the use of standard orthogonality relation (OR) enables the MM solution. The derivation of LFA is made which proves to be surprisingly accurate for structure-borne mode incident. In order to validate the truncated model expansion the distribution of power in duct regions is discussed and Gibbs oscillations are incorporated by reconstruction of the normal velocity field using Lanczos filter.