Acoustic Radiation from Multiple Surfaces

A significant part of the current research effort in Acoustic Radiation Theory is concerned with transducer arrays and the effects of the interaction therein. There exist two broad subclasses of the total problem: (1) one or more vibrating elements on a single common surface (baffle) and (2) one or more vibrating elements on multiple surfaces. Problems within the first subclass have been treated extensively. Few solutions exist for problems within the second subclass and those that do are very restricted. This exposition seeks to extend the list of analytic developments to include solutions to certain multiple surface problems. Initially, we obtain a formal solution to the problem of two vibrating spheres using the method of Green's functions. The extension to N vibrating spheres, or arbitrary radii and location, follows and is obtained directly from the two-sphere problem. It is shown that the method is generally applicable to the N-body problem if the individual body shapes conform to a “separable” coordinate system and the total field can be made to satisfy the Sommerfeld radiation condition.