ACOUSTIC EIGENFREQUENCIES AND MODES IN A SOFT-WALLED SPHERICAL CAVITY WITH AN ECCENTRIC INNER SMALL SPHERE

Analytical expressions are derived for the acoustic eigenfrequencies and modes in a soft-walled spherical cavity with an eccentric inner acoustically small sphere. A straightforward and very simple approach is employed to obtain a first-order perturbation of the cavity eigenfunctions and the corresponding eigenfrequency shifts. The results are useful in a variety of problems connected with acoustic levitation and with excitation or probing of resonant cavities. Some suggestions are made about the best positioning of the probe, for more exact measurement of the eigenfrequency of any mode in the unperturbed cavity. Graphical results for some of the lower-order modes are given for various values of the parameters.