Revealing the Incidence-Angle-Independent Frequency Shift in the Acoustic Rotational Doppler Effect

The Doppler effect is a universal wave phenomenon that has inspired various applications due to the induced frequency shift. In the case of the linear Doppler effect, the frequency shift depends on the incident frequency and angle. Here, we unveil the frequency shift dependence induced by the acoustic rotational Doppler effect in the wave-object scattering process. We experimentally demonstrate that this frequency shift is exclusively determined by the angular speed and rotational symmetry of the spinning scatterer while remaining independent of the incident angular momentum and angle. We derive the analytical relationship between the frequency shift and the scatterer's helicity, presenting a novel approach for helical feature recognition. The angle-independent nature of the frequency shift inherently prevents spectrum broadening and offers a solution for precise motion measurement through the rotational Doppler effect. This work provides a rigorous and comprehensive understanding of the acoustic Doppler effect, enriching its applications in helicity and motion detection.