wave velocity relative to the gas, and the duct is assumed to behave as a half-wave resonator. Therefore, the product of the measured frequency and twice the duct length does not yield the average wave velocity, but rather this latter quantity multiplied by a factor of (1 — M). For a resonant frequency of 730 cps, a duct length of 2 ft, and an average wave velocity of 3360 fps, the Mach number as determined from the previous equations is 0.367. Since the nozzle entrance Mach number on the motors used in these tests is 0.45, and the duct length includes the convergent portion of the nozzle, the average Mach number as determined from the resonant frequency appears to be reasonable. It is obvious that for low Mach numbers and large contraction ratios the effect on the resonant frequency is small, but as the Mach number increases, the reduction in natural or resonant frequency increases. If one has a beforehand knowledge of the wave velocity relative to the gas, say 3360 fps, and uses simple acoustic theory (M = 0), the resonant frequency for a 2-ft chamber would be 840 cps. As the Mach number is increased to 0.367, a 13% decrease in resonant frequency is noted. An important conclusion to be derived from the foregoing discussion is that acoustic theories will not give accurate quantitative results of the analysis of wave oscillations in rocket motors, especially those having small contraction ratios with resultant high Mach number profiles.