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The near field, Westervelt far field, and inverse-law far field of the audio sound generated by parametric array
Jiaxin Zhong1, Ray Kirby1, Xiaojun Qiu1
1Centre for Audio, Acoustics and Vibration, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, New South Wales 2007, Australia.
Abstract:
The near and far fields of traditional loudspeakers are differentiated by whether the sound pressure amplitude is inversely proportional to the propagating distance. However, the audio sound field generated by a parametric array loudspeaker (PAL) is more complicated, and in this article it is proposed to be divided into three regions: near field, Westervelt far field, and inverse-law far field. In the near field, the audio sound experiences strong local effects and an efficient quasilinear solution is presented. In the Westervelt far field, local effects are negligible so that the Westervelt equation is used, and in the inverse-law far field, a simpler solution is adopted. It is found that the boundary between the near and Westervelt far fields for audio sound lies at approximately a2/λ - λ/4, where a is transducer radius and λ is ultrasonic wavelength. At large transducer radii and high ultrasonic frequencies, the boundary moves close to the PAL and can be estimated by a closed-form formula. The inverse-law holds for audio sound in the inverse-law far field and is more than 10 meters away from the PAL in most cases. With the proposed classification, it is convenient to apply appropriate prediction models to different regions.
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