Excerpt from Back Scattering From a Finite ConeThe back scattering from a finite cone is calculated in this report by means of the geometrical theory of diffraction. Three different physical problems are considered. One is that of an acoustic wave incident upon a rigid cone. The second is that of an acoustic wave incident upon a perfectly soft (pressure-release) cone. The third, and perhaps most important, is that of an electromagnetic wave incident upon a perfectly conducting cone. In all cases two different types of cones are treated. One is a truncated right circular cone with a flat base. The other has a rounded base which is a portion of a sphere. The sphere and cone join smoothly, with no sharp edge. For simplicity the incident wave is assumed to be plane and only the back-scattered field is found, although both of these limitations could easily be removed.The theory employed here represents the back-scattered field as a superposition of fields on various rays. Some of these are the ordinary optical rays which are reflected from the cone and the others are diffracted rays. In the next section the various rays are described and a qualitative description of the back scattering process is given. In Sections 3-5 the quantitative results are derived and examined. Graphs of the back scattering cross section are also presented. In the conclusion. Section 6, suggestions are made about shaping an object to minimize its back-scattering cross section.Most of the previous theoretical results on back scattering from cones have concerned semi-infinite cones. For such cones the acoustic diffraction problem was solved exactly and explicitly by H. S. Carslaw and the electromagnetic problem by W. W. Hansen and L. I. Schiff. Their solutions were given as infinite series which were difficult to evaluate.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis 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.