Sound Propagation via Narrow Beam Audio Projection

Abstract

The parametric acoustic array is a nonlinear phenomenon of physics theoretically described over fifty years ago. It consists in the generation of secondary sound waves by the propagation of two collimated primary ultrasonic waves at a close frequency. The sound wave generated corresponds to the difference of the frequencies propagated and its existence is independent from the ultrasonic waves, but it maintains the high directivity of the primary waves. According to Berktay's far-field solution, one of the main equations describing this phenomenon, the sound wave produced is proportional to the second derivative of the envelope of the original ultrasonic wave. Hence, the implementation of the parametric acoustic array is based on the modulation of signals to be transmitted as ultrasound, but demodulated in the propagation medium. Due to the nonlinear nature of the phenomenon and the use of modulation techniques in the implementation of the parametric acoustic array, harmonic distortion is generated. Moreover, the models describing the parametric acoustic array are based on many approximations so the results from the equations are inaccurate in many cases. Despite Westervelt introduced the theory over five decades ago, the research on parametric acoustic arrays presents many challenges in the present day. The majority of the efforts for increasing the quality of the demodulated signal have been focused on improving the modulation stage of the parametric acoustic array based on Berktay's solution. Furthermore, recent advances in the field of parametric acoustic arrays have demonstrated the frequency response of transducers has a big impact on the generation of secondary sound waves. This thesis aims to provide a model capable of improving the representation of the parametric acoustic array. For this reason, simulations using the KZK Texas code, a time-domain algorithm which calculates the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, were carried out to replicate the parametric acoustic array in air. These results establish how the diffraction term of the KZK equation impacts on the generation of the secondary sound waves. As a result, a Burgers like equation was used instead of the KZK equation, decreasing the computation time significantly. In addition, parametric loudspeakers were simulated using k-Wave, a toolbox capable of computing linear and nonlinear propagation of acoustic waves. The results show the effects of Rayleigh distance and absorption length on the demodulated waves. Increasing the Rayleigh distance beyond the absorption length was proposed to obtain a demodulated wave 10 dB higher in the far-field, if compared to the cases where this condition is not met. Finally, an electroacoustic model describing the frequency response of the transducer generating the parametric acoustic array was developed in order to include it into the far-field solution. This model is based on a Van Dyke equivalent circuit capable of representing the frequency response of the array of piezoelectric transducers. The transfer function of the circuit was applied as a filter for the original signal and as per the definition of the far-field solution, the elements of the circuit become part of the demodulated wave. The model and the method used are based on mathematical development, simulations and experimental validation.