Abstract
A series of diffraction problems in acoustics and electromagnetism are considered, and solved by various integral equation techniques. A general introduction to the method of approach is given in Chapter 1. The major problem under investigation is that of a vibrating piston mounted in a finite, acoustically rigid baffle, radiating sound, from one face only. This is solved for low frequencies in Chapter 2 by reducing the problem to the solution of a Fredholm integral equation of the second kind. Numerical techniques are used to solve this equation. The following three methods for high frequencies are then employed, in Chapter 3: (i) an approach leading to an integral equation of the second, kind, which is suitable for iterative solution at high frequencies, (ii) a Wiener-Hopf technique, and (iii) an application of Keller's geometrical diffraction theory. Far field amplitude and radiation impedance results are presented. Chapters 4 and 5 contain three cases of high frequency diffraction by a circular disc of various incident fields. These are the problems of (i) a point source of sound situated above acoustically rigid disc. (ii), an oscillating electric dipole situated above a perfectly conducting disc and oriented (a) perpendicular to the plane of the disc, and (b) parallel to the plane of the disc. The solutions are obtained by the first high frequency method mentioned above for the baffle problem. Asymptotic expansions for the far field amplitudes are given in each case. Finally, Chapter 6 is concerned with the problem of diffraction of a plane acoustic wave by a general, three-dimensional, rigid body. Certain methods are employed in an attempt to obtain the first two terms of the scattering cross section involving only the solution to one simple potential problem. The particular case of a rigid ellipsoid is discussed in detail.