The effect of evaporation-condensation on sound propagation in cylindrical tubes using the low reduced frequency approximation

In order to better understand the effects of water on sound attenuation in porous materials, Mao [J. Acoust. Soc. Am. 104, 664–670 (1998)] has investigated sound propagation in a gas–water vapor mixture contained in a cylindrical tube. He used the Rayleigh eigenmode calculation to evaluate the high and low frequency limits of attenuation in an air-filled tube with wet walls. However, he was unable to obtain a general analytical expression and the interpretation of the limits is difficult because of their complexity. The formulation of the problem presented in this paper parallels the “low reduced frequency method” of Tijdeman [J. Sound Vib. 39, 1–33 (1975)]. In contrast to the earlier results, an analytical solution for the propagation constant is obtained which allows for calculation of attenuation over a broad frequency range. The simple expressions obtained in the small and large shear wave number limits provide useful insight into the behavior of the gas–water vapor mixture.