Diffraction at high frequencies by a circular disc

It is shown how to convert the integral equation for the pressure distribution on a circular disc in an axisymmetric sound wave into a singular integral equation of the first kind. This singular integral equation has a simple kernel and can be transformed easily into an integral equation of the second kind which is especially useful at high frequencies. Although a direct iteration on this last integral equation fails, an indirect method is devised which ensures that each iterate is of lower order than the preceding at high frequencies. The form of the general term in the iteration is given together with the first terms of its asymptotic behaviour. It is relatively simple to estimate the error caused by stopping at any particular iterate. Detailed calculations are made for a plane wave striking the disc at normal incidence.