Super-Spherical Wave Simulation in Flaring Horns

The ared horn is modeled according to Webster's equation. A change of variables transforms the equation into the form of the one dimensional Schrodinger wave equation. The Schrodinger form facilitates speci cation of arbitrary axisymmetric wavefronts for the acoustic disturbance within the horn. To provide a physically motivated choice of wavefront shape, Poisson's equation is solved inside the horn subject to the boundary condition that the normal component of the potential gradient is zero at the boundary of the horn. Since the disturbance within the horn must satisfy the wave equation, the velocity potential satis es Poisson's equation when viscous e ects and losses are ignored. Physical data from brass instrument bells are used to model musical horns using the Poisson solution, and results are compared to those obtained by traditional models which assume spherical wavefronts. Acknowledgment This work was made possible by the generous cooperation of Mr. Greg Hilliard of Frank Holton and Company who provided us with precise physical measurements of a test bell.