Scattering of sound waves by an infinite grating composed of rigid plates

A plane sound wave is incident at an angle h upon an infinite array of rigid plates, equally spaced and lying along the yaxis, where (x, y) are two-dimensional Cartesian coordinates. The boundary value problem is formulated into a matrix Wiener–Hopf equation whose kernel is, when the plates and interstices are of equal length, decomposable into two factors which commute and have algebraic behaviour at infinity. A closed form analytical solution is then obtained following the usual Wiener–Hopf procedure and numerical results are given for various angles of incidence, as well as different spacings. 2006 Elsevier B.V. All rights reserved.