Acoustic eigenfrequencies of cavities with an internal obstacle: A modified perturbation theory

Abstract

The eigenfrequencies of a hard-walled acoustic cavity resonator are found by solving the Helmholtz equation with Neumann boundary conditions. A cavity C with an internal hard obstacle B of vanishing size was considered. Because the perturbation is never small in the neighborhood of the obstacle even in the limit of a small obstacle, a modified perturbation theory is required. A formalism was developed and tested by calculating the eigenfrequencies of a cylinder with an internal sphere on the axis. The results are compared with theoretical and experimental values determined by other investigators. The difference between the perturbation calculations and the numerical results varies from less than 10−5 to about 0.02 of the unperturbed eigenfrequency, depending on the size of the perturbing sphere and the mode.