Everything about The Parametric Array totally explained
The
parametric array is a nonlinear
transduction mechanism that generates narrow, nearly sidelobe free beams of low frequency sound, through the mixing and interaction of high frequency
sound waves, effectively overcoming the
diffraction limit (a kind of spatial 'uncertainty principle') associated with linear acoustics
(External Link
). Parametric arrays can be formed in water
(External Link), air
(External Link), and earth materials/rock
(External Link),
(External Link). Practical applications are numerous and include underwater sound (
sonar, depth sounding, sub-bottom profiling,non-destructive testing and 'see through walls' sensing
(External Link) remote ocean sensing
(External Link)), medical
ultrasound (External Link) and tomography
(External Link), underground sesimic prospecting
(External Link), active noise control
(External Link), and directional high-fidelity commercial audio systems (
Sound from ultrasound,
(External Link) Parametric
receiving arrays can also be formed for directional reception
(External Link). In 2005, Elwood Norris won the $500,000 MIT-Lemelson Prize for his application of the parametric array to commercial high-fidelity loudspeakers.
Priority for discovery and explanation of the Parametric Array
(External Link) owes to
Peter J. Westervelt, winner of the
Lord Rayleigh Medal
(External Link) (currently Professor Emeritus at
Brown University), although important experimental work was contemporaneously underway in the former Soviet Union
(External Link). According to Muir [16,p.554] and Albers [17], 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 [17], 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 1950's, was later explained theoretically in 1960, at a meeting of the
Acoustical Society of America. A few years after this, a full paper [2] was published as an extension of Westervelt's classic work on the nonlinear Scattering of Sound by Sound, as described in [8,6,12].
The foundation for Westervelt's theory of sound generation and scattering in
nonlinear acoustic (External Link) media owes to an application of
Lighthill's equation (see
Aeroacoustics) for fluid particle motion. The application of Lighthill’s theory to the nonlinear acoustic realm yields the Westervelt–Lighthill Equation (WLE)
(External Link). Solutions to this equation have been developed using
Green's functions [4,5] and Parabolic Equation (PE) Methods, most notably via the Kokhlov–Zablotskaya–Kuznetzov (KZK) equation
(External Link).
An alternate mathematical formalism using
Fourier operator methods in
wavenumber space, was also developed by Westervelt, and generalized in [1] for solving the WLE in a most general manner. 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 [15], 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 [18].
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