Diffraction of a Spherical Wave by a Hard Half-Plane: Polynomial Formulation of the Edge-Diffracted Field in the Frequency Domain

Abstract

The problem of diffraction of a spherical sound wave by a thin hard half-plane is considered. The expression of the total field at any position in the space around the half-plane is composed of two geometrical components and a third one which originating from the edge of the half-plane. This paper takes the expression of the edge-diffracted field due to a sound doublet, as formulated in the Biot-Tolstoy theory of diffraction, BTD, but rearranged for the Dirac-like pulse by Medwin. The present paper presents a development in the frequency domain of the Fourier transform of the exact expression of the edge-diffracted field as given in the time domain. This solution is composed of a serial development, expressed in simple trigonometric integral functions, and which away from the geometrical optics boundaries shows a quite rapid convergence to the numerical Fourier transform of the exact time-domain expression. The presented solution may be used as a good approximation in simulations and in real case predictions of sound scattering by thin straight-edged noise barriers.