Ceperley proposed a concept of a traveling wave heat engine [“A pistonless Stirling engine—The traveling wave heat engine,” J. Acoust. Soc. Am. 66, 1508–1513 (1979).] that provided a starting point of thermoacoustics today. This paper verifies experimentally his idea through observation of amplification and strong damping of a plane acoustic traveling wave as it passes through axial temperature gradients. The acoustic power gain is shown to obey a universal curve specified by a dimensionless parameter ωτα; ω is the angular frequency and τα is the relaxation time for the gas to thermally equilibrate with channel walls. As an application of his idea, a three-stage acoustic power amplifier is developed, which attains the gain up to 10 with a moderate temperature ratio of 2.3.