Acoustic propagation in a rigid torus

The acoustic propagation in a rigid torus is analyzed using a Green's function method. Three types of surface elements are developed; a flat quadrilateral element used in modeling polygonal cavities, a curved conical element appropriate for surfaces with one curvature, and a toroidal element developed for such doubly curved surfaces as the torus. Curved elements are necessary since the acoustic pressure is sensitive to slope discontinuities between consecutive surface elements especially near cavity resonances. The acoustic characteristics of the torus are compared to those of a bend of square cross section for a frequency range that includes the transverse acoustic resonance. Two equivalences between the different sections are tested; the first conserves curvature and cross-sectional dimension while the second matches transverse resonance and duct volume. The second equivalence accurately matches the acoustic characteristics of the torus up to the cutoff frequency corresponding to a mode with two circumferential waves.