The Transmission of Sound Inside Pipes

Methods developed in a previous paper are used to obtain an exact solution for the transmission of sound inside a rectangular pipe with absorbing material on its inner walls. Plots are given whereby it is possible to determine the phase velocity and attenuation of the simpler type waves in terms of the specific acoustic impedance of the walls and the frequency of the wave. Several examples are given of the effect of the absorbing surfaces on the distribution of the sound pressure amplitude over a plane perpendicular to the axis of the pipe. The effect of the reactive part of the material's acoustic impedance on the attenuation of the sound is also discussed. Formulas are developed for the transmission of sound in tubes of circular cross section. The plots for rectangular pipes can also be used in calculations of the acoustical properties of rectangular rooms.