Observation of the extreme Doppler shift of acoustic rotating waves in the time domain

Abstract

When a rotating wave carrying orbital angular momentum undergoes an extreme Doppler shift, the observed frequency will become negative. The negative frequency is the prerequisite condition for rotational superradiance, which is principally in connection with the black hole radiance. This condition has been observed in a published experiment using two rotating microphones, which mainly obtained the spectral results. However, the experiment showed a few graphical details of the wave shape. We propose a numerical method not only to demonstrate the Doppler shift of the observed frequency but also to show the formation of the acoustic rotating waves in the time domain. The numerical model adopts a circular array of momentum sources to generate the rotating waves and an array of static monitoring points to simulate the rotating microphones. The time domain observation shows that a negative frequency can be explained with either the handedness reversal of orbital angular momentum or the time reversal of the signal. This point of view has never been reported. The proposed method is not only instructive for designing an experiment with static microphones which are more easily assembled than rotating microphones but also useful in exploring the physical insight of the supperadiance phenomenon.