Acoustic propagation in flaring, axisymmetric horns: II. Numerical results, WKB theory, and viscothermal effects

This report presents the WKB approximation for the curvilinear horn (CH) eq uation, numerical comparisons of horn theories, and a model of viscothermal effects for acoustic wave propagation in axisymmetrical horns. The WKB sol ution is presented for the hyperbolic horn. The numerical comparisons for a hyperbolic horn profile show that the CH equations are more accurate than the plane-wave horn equation or previous spherical-wave horn equations. The CH equation using spherical coordinates has only small errors compared to the CH equation using oblate spheroidal coordinates. A variational derivati on of viscothermal losses is constructed based upon the concept of wall adm ittance using orthogonal coordinates. The important case of the spherical-w ave horn equation is considered as a special case using the first-order WKB theory. Differences from existing theory are observed near the apex of the cone.