Abstract
The eigenfrequencies of a hard‐walled acoustic 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. As the size of the obstacle shrinks to zero, the eigenfunction does not approach an eigenfunction of the empty cavity. Thus a singular 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 values determined by a boundary‐integral‐equation method (A. E. Woodling, Ph.D. thesis, University of Delaware, 1986) and experimentally [M. Barmatz et al., J. Acoust. Soc. Am. 73, 725–732 (1983)]. [Work supported in part by NASA.]
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