Second-order boundary corrections to the radial acoustic eigenvalues for a spherical cavity

Keith A. Gillis

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Scientific Measurement and Uncertainty Evaluation Acoustic Wave Phenomena Research Acoustic Wave Resonator Technologies

Abstract

We calculated the eigenvalues of the radially symmetric acoustic modes of a gas-filled, spherical cavity to order ( δ t / a ) 2 , where δ t is the thickness of the thermal boundary layer and a is the radius of the cavity. Our results explain an anomaly revealed by high-precision acoustic measurements made to redetermine the Boltzmann constant.

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References

1988Measurement of the universal gas-constant R using a spherical acoustic resonator 1986Gas-filled spherical resonators: Theory and experiment 2006Determination of the Boltzmann constant—status and prospects 2011Measurement of the Boltzmann Constant k B Using a Quasi-Spherical Acoustic Resonator 2010Acoustic Resonator Experiments at the Triple Point of Water: First Results for the Boltzmann Constant and Remaining Challenges 2006Transport properties of argon at zero density from viscosity-ratio measurements 2011Progress in INRiM Experiment for the Determination of the Boltzmann Constant with a Quasi-spherical Resonator 2009Acoustic field in a quasi-spherical resonator: Unified perturbation model

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