TABLE OF CONTENTS The model of a rigid circular disc vibrating transversely to its plane in a coplanar rigid baffle is amenable to mathematical analysis and also constitutes a reasonable representation of a loudspeaker cone in a baffle or cabinet. In addition, this model has application to the design of cylindrical sonar transducers, which are usually mounted on baffles. The model is shown in Fig. 3.4. As with most sound radiation problems, it is difficult to evaluate the field at a distance from the source surface comparable with, or much less than, a typical source dimension. The problem of evaluating the field on the vibrating surface is particularly difficult and will be treated in Chapter 4 on fluid loading of vibrating structures.
The difficulty in evaluating the integral in Eq. (3.4) for distances not greater when compared to the source dimensions is associated with the fact that the distance R between elementary source and the source point is generally a rather complicated function of the coordinates of the two points. However, if the observation point is at a distance greater compared to the source dimensions, R in the denominator of Eq. (3.4) may be approximated by a constant that is an average distance. On the other hand, the phase variation with r s, given by exp( ? jkr), is a rapidly varying function of R: hence this term must be left within the integral. ...
