Precision acoustic measurements with a spherical resonator: Ar and C2H4

Abstract

The spherical acoustic resonator is a remarkably accurate and convenient tool for the measurement of thermophysical properties of gases at low and moderate densities. The speed of sound (c) in a gas of interest can be measured with an accuracy of 0.02% merely by measuring the frequencies of the radial resonances when the resonator is filled with the gas of interest and then repeating the frequency measurements with a reference gas such as argon. The resonance frequencies of the radial modes are easily measured because these modes have very high Q’s, typically 2000–10 000. In this work the precision and accuracy of speed of sound measurements have been substantially improved by including a detailed acoustic model of the resonator in the analysis. Many of the important parameters of the model can be determined from acoustic measurements: Painstaking mechanical measurements are not required. We have used a spherical resonator to measure the speed and attenuation of sound in C₂H₄ in the temperature range 0–100 °C and the pressure range 0.15–1.0 MPa. Our measured values of c in C₂H₄ have a precision of 0.003% and agree with those of Gammon within the scatter of Gammon’s data (±0.02%). This agreement is remarkable when one considers that our spherical resonator is operated in the frequency range 4–13 kHz while Gammon has used a more conventional, cylindrical, variable path, acoustic interferometer operating at 500–2500 kHz. To attain this agreement, we did not have to make any highly accurate measurements other than frequency. Our measured values of the bulk relaxation frequency of C₂H₄ are within the scatter of the more recent values of the literature. In the course of our ’’calibration’’ measurements with argon we have redetermined the leading acoustic virial coefficient of argon. Our values for the virial are in satisfactory agreement with those in the literature. We include several practical suggestions for increasing the accuracy and/or versatility of spherical resonators.