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 acoustician ...

, 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 In optics, any optical instrument or systema microscope, telescope, or camerahas a principal limit to its resolution due to the physics of diffraction. An optical instrument is said to be diffraction-limited if it has reached this limit of res ...

(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 Medal, 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 mathematical 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 ...

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 The Fourier operator is the integral kernel, kernel of the Fredholm integral equation#Equation of the first kind, Fredholm integral of the first kind that defines the continuous Fourier transform, and is a two-dimensional function when it correspon ...

methods in

wavenumber In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of ...

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 Sound intensity, also known as acoustic intensity, is defined as the power carried by sound waves per unit area in a direction perpendicular to that area, also called the sound power density and the sound energy flux density. The SI unit of inte ...

spectra in cavities.

Applications

Practical applications are numerous and include: * underwater sound ** sonar ** depth sounding ** sub-bottom profiling ** non-destructive testing ** and 'see through walls' sensing ** remote ocean sensing * medical

ultrasound Ultrasound is sound with frequency, frequencies greater than 20 Hertz, kilohertz. This frequency is the approximate upper audible hearing range, limit of human hearing in healthy young adults. The physical principles of acoustic waves apply ...

* 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