An experimental verification of Rayleigh’s interpretation of the Sondhauss tube

Abstract

The interaction of a sound wave in a compressible fluid in contact with solid boundaries produces thermoacoustic effects. A century ago, Lord Rayleigh gave a general qualitative explanation of the acoustic power production by unsteady heat transfer to compressible fluid in terms of the relative phase of the pressure wave and the heat transferred to the fluid. In quantitative terms his interpretation is equivalent to saying that a wave is promoted if the absolute value of this relative phase is less than π/2; otherwise the wave is attenuated. In this paper, an experimental investigation of the attenuation or promotion of an acoustic wave as a function of an axial temperature gradient at the wall of the waveguide is presented. Using the techniques previously developed [J. Acoust. Soc. Am. 103, 1532–1537 (1998)], acoustic temperature and pressure oscillations measurements in the thermal boundary layer of an acoustic standing wave in air were made. The results reported here experimentally confirm the validity of Rayleigh’s interpretation of the power production for this case. This confirmation is more direct than any previous evidence.