Acoustic data recorded at 1000 samples per second by two sensor arrays located at ranges of 1-113 km from three tornadoes that occurred on 24 May 2011 in Oklahoma are analyzed. Accurate bearings to the tornadoes have been obtained using beamforming methods applied to the data at infrasonic frequencies. Beamforming was not viable at audio frequencies, but the data demonstrate the ability to detect significant changes in the shape of the estimated power spectral density in the band encompassing 10 Hz to approximately 100 Hz at distances of practical value from the sensors. This suggests that arrays of more closely spaced sensors might provide better bearing accuracy at practically useful distances from a tornado. Additionally, a mathematical model, based on established relationships of aeroacoustic turbulence, is demonstrated to provide good agreement to the estimated power spectra produced by the tornadoes at different times and distances from the sensors. The results of this analysis indicate that, qualitatively, an inverse relationship appears to exist between the frequency of an observed peak of the power spectral density and the reported tornado intensity.