The frequency response of a thermoacoustic prime mover has been measured as a function of the mean gas pressure and temperature gradient across the prime mover stack. The quality factor Q and resonance frequency can be determined from the response. As the temperature gradient is increased, the Q increases, indicating a decrease in attenuation across the stack. At sufficiently large temperature differences (∼300 K), the resonator goes into self-oscillation, indicating negative attenuation. Measurements are reported for helium and argon at pressures ranging from 170–500 kPa and temperature gradients ranging from zero to that required for onset of self-oscillation. The results are explained in terms of a counterpropagating, plane-wave analysis, based on techniques commonly used in porous media investigations. In general, the predictions of the analysis are in good agreement with experiment. The predictions of Q and the change in resonance frequency with mean gas pressure are within approximately 5% and 0.4% of measured values for the no temperature gradient cases. In the cases where temperature gradients are present, the agreement is quite good for the two highest mean pressures reported (370 and 500 kPa). There are some noticeable discrepancies at the lowest pressure (170 kPa). The reasons for these discrepancies are unknown.