EIGENFREQUENCIES OF AN ACOUSTIC RECTANGULAR CAVITY CONTAINING A RIGID SMALL SPHERE

Analytical expressions are derived for the eigenfrequencies of any mode in a hard-walled acoustic rectangular cavity, containing an acoustically small rigid sphere. A straightforward and simple approach is employed to obtain a first-order perturbation of the cavity eigenfunctions and the corresponding eigenfrequency shifts. Rectangular wave functions, as well as their expansion in terms of cylindrical wave functions and finally in terms of spherical ones, are used. The results are useful in 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.