Julius O. Smith, III
Ctr. for Comput. Res. Music and Acoust., Stanford Univ., Stanford, CA 94305-8180
The flared 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 specification 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 satisfies Poisson's equation when viscous effects 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. Results are also compared to acoustic measurements.