Sound penetration through an arbitrarily shaped aperture in a rigid screen: Analytical determination of the quadratic terms in low-frequency expansion

Abstract

Van Bladel has reduced the problem of low-frequency scattering through an aperture in a rigid screen to a sequence of static integral equations. Analytical solutions are known at the moment for a circular and an elliptic aperture only. A new analytical method is proposed here which is valid for the nonelliptical apertures. The method is based on an integral representation for the reciprocal distance between two points obtained earlier by the author. Specific approximate formulae are derived for evaluating the average value of the quadratic term in the low-frequency expansion for an aperture in the shape of a polygon, a rectangle, a rhombus, and a cross. All the formulae are checked against the solutions known in the literature, and a good accuracy is confirmed in a sufficiently wide range of the aspect ratio.