Acoustic scattering by a sound‐hard rectangle

The scattering of an incoming plane wave by a sound‐hard infinitely thin rectangle is considered. An integral equation method which has previously been used for two‐dimensional problems [A. Bostrom, J. Appl. Mech. 84, 503–508 (1987)] and three‐dimensional axisymmetric problems [S. Krenk and H. Schmidt, Philos. Trans. R. Soc. London Ser. A 308, 167–198 (1982)] is employed. Starting from a double spatial Fourier field representation, a matching of the conditions in the plane of the rectangle leads to an integral equation for the potential jump across the rectangle. This jump is expanded in a double series of Chebyshev polynomials which fulfill the right edge conditions (but no special measures are taken for the corners where the right conditions are unknown anyway). The integral equation is thus discretized and the problem thereby solved. By a double stationary‐phase analysis the farfield is determined and some numerical examples of this are given.