Internal mapping of the normal modes of a liquid filled spherical resonator.

Abstract

We report on the measurements of the pressure fields set up inside a water-filled steel shell over a spectral range (10–50 kHz) that includes 75 modes of the composite system. The 9.5-in.-diameter shell has a wall thickness to radius ratio of h/R = 0.158, which is beyond the thin shell limit. Hydrophone scans of the acoustic pressure fields in the fluid were performed, from which 46 modes of the composite resonator were identified. The modal frequencies are in good agreement with those predicted by Mehl for a fluid-filled shell of arbitrary wall thickness. The radial pressure profiles of the modes are shown to fit the expected spherical Bessel profiles for solutions of the Helmholtz equation under spherical symmetry. The results are interpreted in terms of the idealized rigid shell and empty shell limits.