The scattering of sound by two semi-infinite parallel staggered plates. II. Evaluation of the velocity potential for an incident plane wave and an incident duct mode

In a recent paper Abrahams & Wickham showed how to exactly solve the diffraction problem for two parallel semi-infinite plates that are arranged to form a duct. The edges of the plates are misaligned so that the geometry is asymmetric with respect to the central line of the duct. In this paper we examine in detail the effect of this asymmetry on the field radiated from the duct when a fundamental travelling mode is excited within it, and the scattered field when a plane wave is excited at infinity. To evaluate the field in either case it is first necessary to solve the integral equations derived in our paper. Here we show how this is effected using the expansion theorem also enunciated in that paper. This solution is then used to calculate a number of physically interesting quantities such as the variation of the energy capture by the duct (when irradiated by an incident plane wave) as the stagger is increased and the asymmetric radiation pattern from an incident duct mode. The numerical computations are checked using an energy balance argument and, finally, a simple heuristic approximation is given for the scattering problem that in many situations accurately reproduces the essential physical characteristics of the solution.