Acoustic field in a quasi-spherical resonator: Unified perturbation model

Gas-filled quasi-spherical resonators are excellent tools for the measurement of thermophysical properties of gas and have also been retained for the determination of the Boltzmann constant with a low uncertainty, which can be derived from measurements of both the speed of sound in a noble gas and the volume of the resonator. To achieve this, a detailed modeling of the acoustic field in quasi-spherical resonators is of importance. Several phenomena and perturbations must be taken into account, including, among inertia and compressibility, heat conduction, viscosity, the shape of the resonator, small irregularities on the wall, and so on. The aim of this paper is to provide improvements to the current models of the acoustic field in such resonator. Namely, the model given here takes into account all the different perturbing elements together in a unique formalism, including the coupling between the different perturbing elements and the resulting modal coupling in a consistent manner. The first results obtained from this analytical model on a simple configuration show that the effect of modal coupling is small but should not be neglected regarding the accuracy required here, even if several improvements could still be provided to this new unified model.