Determining the Speed of Sound and Heat Capacity Ratios of Gases by Acoustic Interferometry

In this paper, we describe an experiment for the undergraduate physical chemistry laboratory in which students determine the speed of sound in the gases He, N2, CO2, and CF3CH2F. The experimental apparatus consists of a closed acrylic tube containing the gas under study. White audio noise is injected into one end of the tube, and the sound amplitude is recorded as a function of time at the other end. The data are recorded and Fourier transformed in real time with a spectrum analyzer application on an Apple iPad. The resulting frequency spectrum of the cavity standing waves is used to determine the speed of sound in the gas by least-squares fitting, with experimental values that fall within about 0.2% or less of the accepted values. The speed of sound is related to the heat capacity ratio in the ideal gas limit, providing students with quantitative evidence of the nonideality of the gases at ambient pressure and temperature. The experiment demonstrates the power and accuracy of interferometry and Fourier analysis using a modern tablet computer.