Modal Analysis of the GTD Diffraction Coefficients for the Half-Plane’s Edge

Abstract

The GTD diffraction coefficients for the half-plane’s edge are obtained by a new semi-analytic approach: From the modal expansion of the Green’s function of an acoustically soft or hard wedge the total field due an incident plane wave is derived by locating a line source at infinity and by transforming the incident line-source field to an incident plane-wave field. By means of the second Green’s theorem and by using the bilinear form of the free-space Green’s function, the scattered far field is obtained from the exact field values on the wedge’s flanks. The isolated edge-diffracted part can be identified as the difference between the far field scattered by a half plane and one half of the far field scattered by the entire plane. The obtained alternating and —in the classical sense— non-converging series are numerically evaluated by means of a linear (consistent) summation technique, and the comparison to Keller’s result shows excellent agreement. The main advantage of this new method is that it can be applied to a certain class of more difficult problems (circular and elliptic cone, plane angular sector, etc.).