Theory Of Acoustic Radiation Research Articles

Acoustic radiation from multiple spheres

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 sub-classes of the total problem: (i) one or more vibrating elements on a single common surface (baffle); and (ii) one or more vibrating elements on multiple surfaces. Problems within the first sub-class have been treated extensively. Few solutions exist for problems within the second sub-class 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 radiation and multiple scattering problem of two vibrating spheres using the method of Green's functions. The extension to N vibrating spheres, of arbitrary radii and location, follows, and is obtained directly from the two sphere problem. To demonstrate the practicality of the method, the problem of “two pulsating spheres” is carried through to completion. Numerical results are obtained which demonstrate the effects of interaction (scattering) on the near- and far-field pressure and the dependence of the radiation impedance of one sphere on the presence of the other. Comparisons are shown between these theoretically derived results and those obtained from experimental studies now being conducted at the Catholic University of America.

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.

Acoustic Field Generated by a Vibrating Boundary. II. Planar Array Vibration and Synthesis

The theory of acoustic radiation, extended from the theory of acoustic scattering, is shown to be applicable to the acoustic-field study of planar transducer or hydrophone arrays. The general nature of the approach is shown to give a new look at the problem of synthesis and the method of studying vibrations acoustically. In the synthesis problem, shading of amplitudes over both space and time is proposed.