TOROIDAL WAVE FUNCTIONS AND THEIR APPLICATION TO THE FREE-FLOODING RING TRANSDUCER.
Scientific rept. no. 2,
PARKE MATHEMATICAL LABS INC CARLISLE MASS
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Solutions of the wave equation have been derived in toroidal coordinates which can be used to solve the problem of acoustic radiation from a torus. The wave equation is not separable in toroidal coordinates and special methods are required to obtain solutions. Westons solutions are not orthogonal functions, which also requires special methods in applying them to radiation problems. However, the special case of a torus of infinitesimally thin cross section can be solved by the usual methods, and in this report this thin torus problem is worked out in detail. The usefulness of this problem as a theoretical model for free-flooding ring transducers is shown by comparison of calculations and measurements. The calculation of toroidal wave functions is also discussed, and numerical results are given for those functions which are needed in transducer problems. Author