Sound propagation in a duct with axial sound speed variation: An exact solution

Abstract

The equation describing sound propagation in an ideal gas with exponential variation of static temperature in the direction of propagation is solved exactly in terms of known functions. Specific solutions for sound propagation in both infinite and semi-infinite length ducts with rigid walls are obtained. The alteration of the modal cut-off condition associated with an isothermal duct by the temperature variation is examined as well as the approach of other aspects of the solution to the familiar results for isothermal ducts. Comparison is also made with experimental data.