Abstract: Nonlinear sound wave propagation is solved rigorously for progressive and standing waves and applied to composite tubes including thermoacoustic stacks with temperature gradient. The tube is characterized by its cross-sectional area and wave number, the latter is usually complex, representing the phase velocity and dissipation. These are found for tubes of different configurations, including thermoacoustic stacks. On the other hand, the temperature gradient contributes important nonlinearity to the tube, and, as such, is included in the solution of the nonlinear wave equation. It is found that the sound waves propagating in the direction of increasing temperature are amplified and conversely. Composite tubes containing sections of different characters are treated as cascade wave filters to find their performances. A three-section tube is computed, extension can be done with ease. The results provide the basis on which the performance of the whole thermoacoustic system can be predicted