Summary: Scattering of sound waves by an infinite grating
composed of rigid plates
Barisß Erbasß a,*, I. David Abrahams b
a
Anadolu University, Department of Mathematics, Yunusemre Campus, 26470 Eskisßehir, Turkey
b
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
Abstract
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].

Source: Abrahams, I. David - Department of Mathematics, University of Manchester

Collections: Mathematics