Quasispherical acoustic resonators: The shell‐gas interaction.

Abstract

Spherical acoustic cavity resonators are useful tools for high‐precision measurements of the speed of sound in gases. Conventionally, the gas‐acoustic resonances are corrected for coupling to the shell using analytic expressions valid for isotropic, unsupported, shells of uniform thickness. Practical resonators have nearly spherical inner surfaces but exterior surfaces with non‐spherical features and support structures. Finite‐element methods have been used to calculate the response of realistic resonator shells that are coupled to support structures. Improved corrections of the gas‐mode eigenfrequencies can be obtained in a form that is similar to the usual analytic expression, except that the shell response function must be calculated numerically. It is also shown that the coupling of gas modes through the shell is normally a weak effect proportional to the square of the static pressure and is totally negligible except in very unusual circumstances. The evolution of gas‐shell coupling is followed when the speed of sound in the gas is varied so that a radial gas mode eigenfrequency fg approaches a shell mode eigenfrequency fs. The gas mode becomes unobservable as fg nears fs due to an avoided‐crossing phenomenon similar to simple coupled oscillators.