Acoustic Radiation from a Thin Torus, with Application to the Free-Flooding Ring Transducer

The toroidal wavefunctions developed by V. H. Weston [Quart. Appl. Math. 16, 237–257 (1958)] are used to solve the problem of acoustic radiation from a thin torus, and some of the technical difficulties associated with more-general toroid problems are briefly discussed. The thin-torus solution is worked out in complete detail for a normal velocity on the torus that approximates the motion of the free-flooding ring transducers that are commonly used in underwater sound applications. Comparison of the calculated results with measurements shows that the thin torus is a useful theoretical model for farfield radiation from ring transducers, but better models are needed for a more complete description of the sound field.