A parametric array, in the field of

acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acousticia ...

, is a nonlinear transduction mechanism that generates narrow, nearly side lobe-free beams of low frequency sound, through the mixing and interaction of high frequency

sound wave In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...

s, effectively overcoming the

diffraction limit The resolution of an optical imaging system a microscope, telescope, or camera can be limited by factors such as imperfections in the lenses or misalignment. However, there is a principal limit to the resolution of any optical system, due to t ...

(a kind of spatial 'uncertainty principle') associated with linear acoustics. The main side lobe-free beam of low frequency sound is created as a result of nonlinear mixing of two high frequency sound beams at their difference frequency. Parametric arrays can be formed in water, air, and earth materials/rock.

History

Priority for discovery and explanation of the parametric array owes to Peter J. Westervelt, winner of the

Lord Rayleigh John William Strutt, 3rd Baron Rayleigh, (; 12 November 1842 – 30 June 1919) was an English mathematician and physicist who made extensive contributions to science. He spent all of his academic career at the University of Cambridge. A ...

Medal (currently Professor Emeritus at

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), although important experimental work was contemporaneously underway in the former Soviet Union. According to Muir and Albers, the concept for the parametric array occurred to Dr. Westervelt while he was stationed at the London, England, branch office of the Office of Naval Research in 1951. According to Albers, he (Westervelt) there first observed an accidental generation of low frequency sound ''in air'' by Captain H.J. Round (British pioneer of the superheterodyne receiver) via the parametric array mechanism. The phenomenon of the parametric array, seen first experimentally by Westervelt in the 1950s, was later explained theoretically in 1960, at a meeting of the

Acoustical Society of America The Acoustical Society of America (ASA) is an international scientific society founded in 1929 dedicated to generating, disseminating and promoting the knowledge of acoustics and its practical applications. The Society is primarily a voluntary org ...

. A few years after this, a full paper was published as an extension of Westervelt's classic work on the nonlinear Scattering of Sound by Sound.

Foundations

The foundation for Westervelt's theory of sound generation and scattering in nonlinear acoustic media owes to an application of Lighthill's

equation In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in F ...

for fluid particle motion. The application of Lighthill’s theory to the nonlinear acoustic realm yields the Westervelt–Lighthill Equation (WLE). Solutions to this equation have been developed using Green's functions and Parabolic Equation (PE) Methods, most notably via the Kokhlov–Zablotskaya–Kuznetzov (KZK) equation. An alternate mathematical formalism using Fourier operator methods in

wavenumber In the physical sciences, the wavenumber (also wave number or repetency) is the '' spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to te ...

space, was also developed and generalized by Westervelt. The solution method is formulated in Fourier (wavenumber) space in a representation related to the beam patterns of the primary fields generated by linear sources in the medium. This formalism has been applied not only to parametric arrays, but also to other nonlinear acoustic effects, such as the absorption of sound by sound and to the equilibrium distribution of sound intensity spectra in cavities.

Applications

Practical applications are numerous and include: * underwater sound **

sonar Sonar (sound navigation and ranging or sonic navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigate, measure distances (ranging), communicate with or detect objects on o ...

** depth sounding ** sub-bottom profiling ** non-destructive testing ** and 'see through walls' sensing ** remote ocean sensing * medical

ultrasound Ultrasound is sound waves with frequencies higher than the upper audible limit of human hearing. Ultrasound is not different from "normal" (audible) sound in its physical properties, except that humans cannot hear it. This limit varies ...

* and tomography * underground seismic prospecting * active noise control * and directional high-fidelity commercial audio systems ( Sound from ultrasound) Parametric ''receiving'' arrays can also be formed for directional reception. In 2005, Elwood Norris won the $500,000 MIT-Lemelson Prize for his application of the parametric array to commercial high-fidelity loudspeakers.

History

Foundations

Applications

References

Further reading