Scattering of acoustic waves by an n-layer periodic grating

Abstract

A waveguide approach has been taken to the problem of acoustic scattering by an N-layer periodic grating. By letting the individual scatterers of the grating have a rectangular cross-section, the wave equation can be solved by separation of variables for all the interior slots and slot intersections made up by the scatterers as well as for the half planes on either side of the scatterer arrangement. By combining all these fields by continuity of acoustic pressure and particle velocity across the interfaces, two sets of infinitely many linear, algebraic, simultaneous equations are obtained having the amplitudes of the transmitted and reflected waves as unknowns. These two sets of equations have been solved numerically for the low frequency part of the spectrum where the assumption is made that acoustic energy was transported through the scatterer structure by plane waves only. A study has also been made of wave propagation in the infinite structure obtained by letting the grating have infinitely many layers and it is shown that information obtained from this study could be used for explaining results from the study of the finite system.