The Effects of Geometry on Acoustic and Electromagnetic Resonances in a Spherical Cavity

Recent precision measurements of the speed of sound in gases have been performed using acoustic radial modes in spherical cavities. Most of the experimental uncertainty arises from determination of the resonator's volume. If the ratio of the speed of sound to the speed of light in the cavity is measured, using electric and acoustic modes, the volume measurement becomes unnecessary. However, the simplest electric modes are triply degenerate with resonance frequencies dependent to first order on the cavity shape, unlike the radial mode frequencies which are determined by its mean radius. In this work, the effect of artificial deformation of a fabricated spherical cavity on the triply degenerate electric and acoustic modes was studied by adding metal shims between the two halves of the fabricated sphere. Behavior of the acoustic radial modes and the effect of electromagnetic probe insertion were also studied. Our data show that almost all frequency splitting of both the acoustic and electric triplets can be described using two deformations: lengthening or shortening of the cavity and offset of its two parts. We also found the three component orientations of the e11 triplet and demonstrated that these depend mainly on the geometry of the cavity, and also on the coupling of the probes used to make the measurements. Mode orientation can be predicted once the cavity deformation has been found from the splitting, and our results are in good agreement with these predictions. We have also demonstrated that acoustic radial mode dispersion is of about the same order as that predicted by theory, though consistently smaller. This agrees with previous findings that the dispersion is smaller than expected. We conclude that a theoretical model is required which links coupling and perturbation of the probes with the geometric deformation of the sphere, so that the effect of these probes can be determined for all three components of the degenerate modes.