Experimental and numerical study of the rotational Doppler shift in acoustic waves using static microphones

The rotational Doppler shift in acoustic waves carrying orbital angular momentum (OAM) has been applied in experiments to demonstrate the Zel'dovich amplification, which is analogously linked with the black hole radiance. However, rotating microphones used in the published experiments are difficult to assemble and intrinsically weak in the frequency response at frequencies around 0Hz. To circumvent the limitations, this paper proposes an experimental method to study the rotational Doppler shift in acoustic OAM waves using static microphones. The Doppler shifted signals viewed by a rotating observer were extracted from the original acoustic signals at frequencies around 100Hz, where the microphones had flat frequency response. The measured results not only demonstrated the extreme Doppler shift to a negative frequency but also showed that the acoustic amplitudes were very low when the Doppler shifted frequency was 0Hz. This phenomenon was explained by showing in a time-domain numerical simulation that the wave was co-rotating with the observer. In addition, the characteristics of the simulated pressure contours of the rotating wave have been discussed. The proposed methods can further be used to study the physics related to the wave carrying OAM, such as the acoustic super-radiance.