Nonlinear vibrations in a pipe closed at both ends with a plane heater in its midsection and containing a perfect gas are studied. When the frequency of a sinusoidal heat release is equal to twice the fundamental resonance frequency of the pipe, the level of fluctuation increases with time; shock waves are formed and ultimately the fluctuation attains a limiting value. It is shown that if the rate of heat release is small compared to the total enthalpy in the volume traversed by an acoustic front in a unit time, the fluctuation in the pipe, after many oscillations, builds up to (σ0/p0a0)½, where σ0 is the amplitude of the rate of heat release per unit area of the heater, and p0, a0 are respectively the initial pressure and sound speed. The nature of vibration in the pipe is found to be similar to that excited in a cylinder by a piston driven sinusoidally near a resonance frequency. The pressure and velocity at a fixed point in the pipe are shown to vary sinusoidally with time between the successive arriva...