The diffraction of two-dimensional sound pulses incident on an infinite uniform slit in a perfectly reflecting screen

Abstract

In a previous paper (Fox 1948), the general solutions were obtained for the diffraction problems of a perfectly reflecting infinite strip or half-plane subjected to any incident pulse field in two dimensions. A general method is now outlined by which the results of this previous paper could be used without formal difficulty to derive solutions for any two-dimensional diffraction problem involving strips and/or half-planes as obstacles. This method is applied to the problem of a perfectly reflecting plane screen containing an infinite slit of uniform width subjected to any known incident pulse field. The special case of a plane sharp-fronted pulse of constant unit pressure incident normally on such a screen is examined numerically. The most interesting pressure phenomena to the rear of the screen are those occurring in the direct line of the slit where the pressure front exhibits an initial peak which becomes progressively thinner as the front travels farther to the rear. Apart from this effect, the general process of ultimate pressure equalization through the slit appears to be of an asymptotic character, there being no evidence that the pressure at any point to the rear ever exceeds the incident unit pressure. The results also indicate that a region of sensibly incompressible flow is soon developed in the neighbourhood of the slit, this region increasing in size with increasing time. Finally, it is found that the slit behaves, to fair accuracy, as a central two-dimensional source relatively soon after the arrival of the pressure front, for all points to the rear more distant than about 5 a from the centre of the slit, where 2 a is the width of the slit. This result and the preceding incompressible flow phenomenon enable approximate solutions to be obtained for particular use at later times when the calculation of the exact solution involving separate diffraction waves becomes unmanageable.