A note on the effect of wall compliance on lowest-order mode propagation in fluid-filled/submerged impedance tubes

Abstract

Wave propagation in fluid-filled/submerged tubes is of interest in large HVAC ducts, and also in understanding and interpreting the experimental results obtained from fluid-filled impedance tubes. Based on the closed form analytical solution of the coupled wave equations, an eigenequation, which is the determinant of an 8×8 matrix, is derived and solved to obtain the axial wave number of the lowest-order longitudinal modes for cylindrical ducts of various diameter and wall thickness. The dispersion behavior of the wave motion is analyzed. It is observed that the larger the diameter of the duct and/or the smaller its wall thickness, the more flexible the impedance tube leading to more coupling between the waves in the elastic media. Also, it is shown that the wave motion in water-filled ducts submerged in water exhibits anomalous dispersion behavior. The axial attenuation characteristics of plane waves along water-filled tubes submerged in water or air are also investigated. Finally, investigations on the sound intensity level difference characteristics of the wall of the air-filled tubes are reported.