Diffraction at High Frequencies by a Circular Disc (Classic Reprint)

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Excerpt from Diffraction at High Frequencies by a Circular Disc In section 1 is derived a singular integral equation of the first kind for the sound-soft disc. This singular integral equation is converted to an integral equation of the second kind in section 2 and the particular form that it takes for an incident plane wave is determined in section 3. Section A is concerned with an iterative procedure for solving the integral equation of the second kind, this procedure is especially appropriate at high frequencies. The resulting distribution on the disc is found in section 5 and the high frequency scattering coefficient in section 6. In section 7 the corresponding integral equations for the sound-hard disc are derived and section 8 is devoted to the appropriate iterative procedure. The distribution on the disc and scattering coefficient are determined in sections 9 and 10 respectively. It is shown in section ll that the solutions of the integral equations of the second kind described above are unique and that the iterative procedure does provide an asymptotic development at high frequencies. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.