Abstract: A traveling wave heat engine can be used both as a heat engine and a heat pump. When it operates as an engine, thermal energy is converted into acoustical traveling waves from an acoustical wave source, which if desired, can be further converted into more conventional forms of electrical and mechanical power. When it operates as a heat pump, acoustical traveling waves supply the motivating force to pump heat. An object such as a flame holding screen, heat exchanger, or regenerator creates a stationary temperature gradient in the compressible working fluid of the engine. As acoustical traveling waves pass through this temperature gradient, they cause the fluid there to move through the gradient and back and so be heated or cooled in conjunction with the compression and expansion phases of the wave.