Speed of sound in humid air: Accurate thermodynamic model and experimental validation

We present a thermodynamic model of speed of sound w in humid air as a function of the parameters of influence, namely temperature T, pressure p, relative humidity hr, carbon dioxide concentration xCO2, and acoustic frequency f. The validity of the model extends between 200 K and 647 K, for pressures up to 10 MPa. By implementing the most accurate thermodynamic information currently available for dry air, water vapor, and their interaction, including heat capacities, virial coefficients, and relaxation parameters, the model revises and updates the most complete previous correlation [A. J. Zuckerwar, Handbook of the Speed of Sound in Real Gases – Volume III Speed of Sound in Air (Academic Press, London, 2002)], reducing its relative standard uncertainty by more than one order of magnitude, down to 25 ppm at ordinary, near-ambient conditions. The software implementation of the model is made available by publication of source and executable files. To test the validity of the model and its practical application, we have measured the speed of sound in humid air near ambient pressure using an acoustic wavelength meter set up in a hemi-anechoic chamber and compared a subset of these experimental determinations with those obtained by flowing air, sampled from the same environment, through a spherical resonator. The results from both experiments were found consistent with the model within their combined uncertainties. The positive outcome of the comparison suggests that acoustic thermometry in humid air may be realized at the level of 0.015 K with perspectives for application to dimensional measurements, temperature and acoustic metrology, and atmospheric physics.