DIFFRACTION BY A HARD HALF-PLANE: USEFUL APPROXIMATIONS TO AN EXACT FORMULATION

Abstract

In this paper, the problem of diffraction of a spherical wave by a hard half-plane is considered. The starting point is the Biot–Tolstoy theory of diffraction of a spherical wave by a fluid wedge with hard boundaries. In this theory, the field at a point in the fluid is composed eventually of a geometrical part: i.e., a direct component, one or two components due to the reflections on the sides of the hard wedge, and a diffracted component due exclusively to the presence of the edge of the wedge. The mathematical expression of this latter component has originally been given in an explicit closed form for the case of a unit momentum wave incidence, but Medwin has further developed its expression for the more useful case of a Dirac delta point excitation. The expression of this form is given in the time domain, but it is quite difficult to find exactly its Fourier transform for studying the frequency behaviour of the diffracted field. It is thus the aim of this paper to present various useful approximations of the exact expression. Among the approximations treated, three are most accurate for engineering purposes, and one of them is proposed, for its simplicity, as appropriate for most occurring practical situations.