High frequency difraction by a soft circular disc. I the plane wave at normal incidence

Abstract

The far scattered field off the axis of symmetry of the disc is found for a high frequency, harmonic, normally incident, plane wave. The method used is due to Jones and involves the solution of a singular integral equation of the first kind for the field on the disc. This integral equation can be converted into an integral equation of the second kind which is of particular value at high frequencies. In the present work the known function in the equation is written in the form of a contour integral. A suitable change of unknown function then produces extensive cancellation and yields a single function fundamental to the problem. The detailed calculations of the far field give terms which are believed to be new. In executing these calculations some interesting relationships between the terms involved are demonstrated.