An overview of parametric array loudspeaker

Have you ever found yourself hearing the music loud and clear, but your friend sitting across the table hears practically nothing? Picture a loudspeaker beaming music at you, almost as if it were a beam of light. While products that do this are relatively new, technology for doing it was prototyped as far back as 1983, and its theoretical possibility was investigated as far back as 1963! Did I say "loud and clear"? Not quite yet, perhaps – the Parametric Array Loudspeaker (PAL), which this technology is called, generates far more distortion than an audiophile could tolerate.

A bewildering diversity of research papers has sprung up in the last few years on the subject of PALs, and most of them are very specialised and very heavy on math and calculus. For this article, rather than review one of these specialised papers, I picked on a relatively less heavy but useful overview paper titled "A review of parametric acoustic array in air" by Woon-Seng Gan, Jun Yang, and Tomoo Kamakura published in the journal Applied Acoustics, Dec 2012.

Ultrasound beaming 101
The basic principle uses ultrasound beams as "carriers" of an audio signal. Suppose you have two closely spaced ultrasonic transducers directing ultrasound beams of frequencies f1 and f2 in the same direction, with f2 > f1. At low signal levels, the resultant beam, which is the linear superposition of two waveforms of frequencies f1 and f2, would exhibit the phenomenon of beats:

cos(w₁t) + cos(w₂t) = 2cos((w₁+ w₂)/2)t × cos((w₁- w₂)/2)t

That is to say, the amplitude would be modulated at the rate f2-f1. However, as you increase the signal strength, something very different happens. The air starts to respond non-linearly to the acoustic pressure waves, and this so-called propagation distortion leads to the generation of a distinct additional frequency f2-f1 which is unrelated to the phenomenon of beats (a sum frequency is also generated, but that is not of much utility). At this point it will no doubt occur to you that the frequency f2-f1 could be designed to correspond to the acoustic signal that we are trying to capture. A relevant question however is, will the propagation of this audio component spread out like any other audio wave? What is intriguing, as discovered by Westervelt in 1963, is that the difference frequency f2-f1 also travels as a very narrow beam. The formula for the angle which describes the spread of the audio component is where α_T is the sound absorption coefficient of the carrier and k is the wavenumber of the difference-frequency wave.