Modeling of finite-amplitude sound beams: second order fields generated by a parametric loudspeaker

Abstract

The nonlinear interaction of sound waves in air has been applied to sound reproduction for audio applications. A directional audible sound can be generated by amplitude-modulating the ultrasound carrier with an audio signal, then transmitting it from a parametric loudspeaker. This brings the need of a computationally efficient model to describe the propagation of finite-amplitude sound beams for the system design and optimization. A quasilinear analytical solution capable of fast numerical evaluation is presented for the second-order fields of the sum-, differencefrequency and second harmonic components. It is based on a virtual-complex-source approach, wherein the source field is treated as an aggregation of a set of complex virtual sources located in complex distance, then the corresponding fundamental sound field is reduced to the computation of sums of simple functions by exploiting the integrability of Gaussian functions. By this result, the five-dimensional integral expressions for the second-order sound fields are simplified to one-dimensional integrals. Furthermore, a substantial analytical reduction to sums of single integrals also is derived for an arbitrary source distribution when the basis functions are expressible as a sum of products of trigonometric functions. The validity of the proposed method is confirmed by a comparison of numerical results with experimental data previously published for the rectangular ultrasonic transducer.

Effects on the Performance of Parametric Loudspeaker Caused by Nonideal Ultrasound Transducer

“…A parametric loudspeaker uses the effects of self-modulation in air to generate audible sound, which has drawn much attention recently owing to its attractive and promising feature of sharp directivity. [1][2][3][4][5][6][7][8] The first prototype was fabricated by Yoneyama et al in the 1980s, for which the double-sideband amplitude modulation (DSB-AM) technique was employed to couple the low-frequency audio signal with a high-frequency carrier signal. 4) As a result of using the DSB-AM modulation technique, early devices exhibited extreme distortion in the demodulated signal.…”

A Fast Calculation Method for the Scattered Sound Fields from Two Sound Beams Using the Gaussian-Beam Expansion Technique

“…10) Sha et al have obtained the expansion coefficients for rectangular and elliptical planar piston transducers in a two-dimensional spatial Fourier transform (k-space) domain. [11][12][13] An overview of the Gaussian-beam expansion technique has been given in ref. 14. This paper is organized as follows.…”

Development of an Acoustic Filter for Parametric Loudspeaker in Air

“…1,2) Since the first experiment on the parametric array in air performed by Bennett and Blackstock, 3) the development of a parametric loudspeaker has attracted much attention. [4][5][6][7][8][9][10][11] The accurate measurement of a parametric loudspeaker is important for understanding the principle of the parametric array and practical design in audio engineering. A spurious difference frequency signal is generated as a result of the nonlinearity at the receiving transducer.…”