Vibrational relaxation accounts for absorption and dispersion of acoustic waves in gases that can be significantly greater than the classical absorption mechanisms related to shear viscosity and heat conduction. This vibrational relaxation results from retarded energy exchange between translational and intramolecular vibrational degrees of freedom. Theoretical calculation of the vibrational relaxation time of gases based on the theory of Landau and Teller [Phys. Z. Sovjetunion 10, 34 (1936); 1, 88 (1932): 2, 46 (1932)] and Schwartz et al. [J. Chem. Phys. 20, 1591 (1952)] has been applied at room temperature to ternary mixtures of polyatomic gases containing nitrogen, water vapor, and methane. Due to vibrational-translational and vibrational-vibrational coupling between all three components in ternary mixtures, multiple relaxation processes produce effective relaxation frequencies affecting the attenuation of sound. The dependence of effective relaxation frequencies and the attenuation on mole fractions of the constituents was investigated. The acoustic attenuation in a mixture that is primarily nitrogen is strongly dependent on the concentrations of methane and water vapor that are present. However, the attenuation in a mixture that is primarily methane is only weakly dependent on the concentrations of nitrogen and water vapor. The theory developed in this paper is applicable to other multicomponent mixtures.

Attenuation in a gas results from a combination of classical attenuation, attenuation from diffusion, and attenuation due to molecular relaxation. In previous papers [J. Acoust. Soc. Am. 109, 1955 (2001); 110, 2974 (2001)] a model is described that predicts the attenuation from vibrational relaxation in gas mixtures. In order to validate this model, the attenuation was measured using a pulse technique with four transducer pairs, each with a different resonant frequency. The attenuation calculated using the model was compared to the measured values for a variety of gases including: air, oxygen, methane, hydrogen, and mixtures of oxygen/nitrogen, methane/nitrogen, carbon dioxide/nitrogen, and hydrogen/nitrogen. After the measured data is corrected for diffraction, the model matches the trends in the measured attenuation spectrum for this extensive set of gas mixtures.

Sound travelling through a gas propagates at different speeds and its intensity attenuates to different degrees depending upon the composition of the gas. Theoretically, a real-time gaseous composition sensor could be based on measuring the sound speed and the acoustic attenuation. To this end, the speed of sound was modelled using standard relations, and the acoustic attenuation was modelled using the theory for vibrational relaxation of gas molecules. The concept for a gas composition sensor is demonstrated theoretically for nitrogen-methane-water and hydrogen-oxygen-water mixtures. For a three-component gas mixture, the measured sound speed and acoustic attenuation each define separate lines in the composition plane of two of the gases. The intersection of the two lines defines the gas composition. It should also be possible to use the concept for mixtures of more than three components, if the nature of the gas composition is known to some extent.

Acoustic attenuation in a mixture of gases results from the combined effects of molecular relaxation and the classical mechanisms of viscosity and heat conduction. Consequently, the attenuation depends on the composition of the gas mixture, acoustic frequency, temperature, and pressure. A model of the relaxational attenuation that permits the calculation of acoustic attenuation is used to predict the effect of composition, frequency, temperature, and pressure on the acoustic attenuation in a three-component gas mixture of nitrogen, methane, and water vapor. The attenuation spectrum is dependent upon the composition through the appearance of peaks in the spectrum related to the relaxation frequencies of the particular components and their relaxing complexes. The relaxation peak related to methane dominates except at low methane concentrations, where the nitrogen peak, which is dependent upon the water vapor and methane concentration, is evident. Temperature and pressure significantly alter the relaxation frequency and the degree of attenuation, but water vapor plays little role in the attenuation.

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