The diffraction of sound pulses I. Diffraction by a semi-infinite plane

Abstract

This paper contains the results of some calculations which show the changes undergone by a sound pulse when it is diffracted by an infinite screen or wall with a straight edge. The incident pulse is travelling in such a manner that its wave front is parallel to the plane of the wall and the motion is assumed to be two-dimensional. The calculations are carried out for a certain pulse in which the pressure rises instantaneously and then decays exponentially, and—in less detail—for several other types of incident pulse. The pressure changes in the geometrical shadow and near its boundary are investigated, as well as the pressure at points on the screen itself. A remarkable feature is the propagation of the initial pressure discontinuity along the boundary of the geometrical shadow as an instantaneous pressure discontinuity across this boundary. The problem could be treated by the application of Fourier transforms to Sommerfeld’s well-known solution of the diffraction of simple harmonic waves by a straight edge, but the analysis utilized in this paper offers many advantages, particularly when the incident pulse starts with a discontinuous pressure rise. It is also shown that, although the two solutions of the problem treated in this paper (which are due to Sommerfeld and Lamb respectively) differ in form, one can be obtained from the other by a suitable transformation.