Scattering of sound waves by a periodic array of slotted waveguides

Abstract

The problem of scattering of plane acoustic waves obliquely incident upon a barrier consisting of superposed rectangular slotted waveguides is treated by taking a waveguide approach. The wave equation is solved for each interior region, bounded by parallel walls, and for the half-spaces on both sides of the scattering arrangement. The use of boundary conditions then leads to two infinite systems of algebraic equations, the solution of which generates the complex transmission and reflection coefficients. The scattering effects of comblike structures show sharp variations over the frequency spectrum. They also vary strongly at certain particular frequencies with the angle of incidence of the incoming wave. Two geometries of slotted waveguides are studied and their behavior, regarding the amplitude and phase of the transmitted sound, is compared with that of a simple grating of rectangular bars having similar dimensions. Theoretical results compare favorably with experimental values which are presented in another article forming the second part of this study.