Summary: Scattering of sound waves by an infinite grating
composed of rigid plates
Barisß Erbasß a,*, I. David Abrahams b
Anadolu University, Department of Mathematics, Yunusemre Campus, 26470 Eskisßehir, Turkey
University of Manchester, Department of Mathematics, Oxford Road, Manchester M13 9PL, UK
Received 1 November 2006; accepted 2 November 2006
Available online 11 December 2006
A plane sound wave is incident at an angle h upon an infinite array of rigid plates, equally spaced and lying along the y-
axis, where (x, y) are two-dimensional Cartesian coordinates. The boundary value problem is formulated into a matrix
WienerHopf 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 WienerHopf procedure and numerical results are given for various angles of incidence, as well as different spacings.
Ó 2006 Elsevier B.V. All rights reserved.
Keywords: WienerHopf technique; Matrix WienerHopf equations; Diffraction grating; Acoustics
1. Introductory remarks and background
There are numerous interesting physical problems in the fields of acoustics, electromagnetism, elasticity,
etc., which, when modelled mathematically, are exactly solvable by the WienerHopf technique [1,6,12,25].