This paper presents three different solutions to a one‐dimensional model of the propagation of finite‐amplitude traveling waves in rigid‐walled ducts. The first two solutions, in the nature of perturbation solutions, provide useful information for relatively weak waves; the distances for which the solutions are valid range from α1x≪1 to α1x<∞, depending on the strength of the waveform and the particular solution considered. The third solution is based on a set of first‐order coupled nonlinear differential equations with one independent and two dependent variables. This solution is useful for all values of α1xfor strengths up to those necessary for shock formation. Results include graphs of relative harmonic distortion, predictions of waveform profiles, and representative graphs illustrating the dispersive behavior of the phase speeds of the individual harmonics.