Frequency shift of parametric sound by face-to-face pair of sources in relative motion

This paper reports an acoustic phenomenon regarding a parametric sound source (also referred to as a parametric array): a secondary sound wave is generated from the nonlinear interaction of multiple primary sound waves with varied frequency components, particularly when two relatively moving sound sources face each other. It was found that the frequency of the secondary wave fluctuated according to the source movement and provided a theoretical explanation for this phenomenon. It is experimentally demonstrated that this frequency shift was approximately proportional to the velocity of the moving source toward the fixed source and to the driving frequency of the moving source. This phenomenon has much in common with the Doppler's effect, but its unique property is that the frequency shift depends on neither the observation position nor the source velocity toward the observer. These sound generation principles enable measurement of the velocity of slowly moving sound sources while maintaining a low-modulation frequency band and a short measurement time. This phenomenon can potentially be applied to an alternative approach for acoustic noncontact velocimetry of moving objects.