science

Parametric array

Parametric array is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Parametric array rather than just read about it. In short: A parametric array, in the field of acoustics, 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 waves, effectively overcoming the diffraction limit (a kind of spatial 'uncertainty principle') associated with linear acoustics. The main side lobe-free beam of low frequency sound is created as a re…

Key takeaways

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Reference excerpt

A parametric array, in the field of acoustics, 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 waves, effectively overcoming the diffraction limit (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. 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 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 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 depth sounding sub-bottom profiling non-destructive testing and 'see through walls' sensing remote ocean sensing medical ultrasound 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.

References

Further reading H.C. Woodsum and P.J. Westervelt, "A General Theory for the Scattering of Sound by Sound", Journal of Sound and Vibration (1981), 76(2), 179-186. Peter J. Westervelt, "Parametric Acoustic Array", Journal of the Acoustical Society of America, Vol. 35, No. 4 (535-537), 1963 Mark B. Moffett and Robert H. Mellen, "Model for Parametric Sources", J. Acoust. Soc. Am. Vol. 61, No. 2, Feb. 1977 Mark B. Moffett and Robert H. Mellen, "On Parametric Source Aperture Factors", J. Acoust. Soc. Am. Vol. 60, No. 3, Sept. 1976 Ronald A. Roy and Junru Wu, "An Experimental Investigation of the Interaction of Two Non-Collinear Beams of Sound", Proceedings of the 13th International Symposium on Nonlinear Acoustics, H. Hobaek, Editor, Elsevier Science Ltd., London (1993) Harvey C. Woodsum, "Analytical and Numerical Solutions to the 'General Theory for the Scattering of Sound by Sound”, J. Acoust. Soc. Am. Vol. 95, No. 5, Part 2 (2PA14), June, 1994 (Program of the 134th Meeting of the Acoustical Society of America, Cambridge Massachusetts) Robert T. Beyer, Nonlinear Acoustics, 1st Edition (1974),. Published by the Naval Sea Systems Command. H.O. Berktay and D.J. Leahy, Journal of the Acoustical Society of America, 55, p. 539 (1974) M.J. Lighthill, "On Sound Generated Aerodynamically”, Proc. R. Soc. Lond. A211, 564-687 (1952) M.J. Lighthill, “On Sound Generated Aerodynamically”, Proc. R. Soc. Lond. A222, 1-32 (1954) J.S. Bellin and R. T. Beyer, “Scattering of Sound by Sound”, J. Acoust. Soc. Am. 32, 339-341 (1960) M.J. Lighthill, Math. Revs. 19, 915 (1958) H.C. Woodsum, Bull. Of Am. Phys. Soc., Fall 1980; “A Boundary Condition Operator for Nonlinear Acoustics” H.C. Woodsum, Proc. 17th International Conference on Nonlinear Acoustics, AIP Press (NY), 2006; " Comparison of Nonlinear Acoustic Experiments with a Formal Theory for the Scattering of Sound by Sound", paper TuAM201. T.G. Muir, Office of Naval Research Special Report - "Science, Technology and the Modern Navy, Thirtieth Anniversary (1946-1976), Paper ONR-37, "Nonlinear Acoustics: A new Dimension in Underwater Sound", published by the Department of the Navy (1976) V.M. Albers,"Underwater Sound, Benchmark Papers in Acoustics, p.415; Dowden, Hutchinson and Ross, Inc., Stroudsburg, PA (1972) M. Cabot and Seth Putterman, "Renormalized Classical Non-linear Hydrodynamics, Quantum Mode Coupling and Quantum Theory of Interacting Phonons", Physics Letters Vol. 83A, No. 3, 18 May 1981, pp. 91–94 (North Holland Publishing Company-Amsterdam) Nonlinear Parameter Imaging Computed Tomography by Parametric Acoustic Array Y. Nakagawa; M. Nakagawa; M. Yoneyama; M. Kikuchi. IEEE 1984 Ultrasonics Symposium. Volume, Issue, 1984 Page(s):673–676 Active Nonlinear Acoustic Sensing of an Object with Sum or Difference Frequency Fields. Zhang, W.; Liu, Y.; Ratilal, P.; Cho, B.; Makris, N.C.; Remote Sens. 2017, 9, 954. https://doi.org/10.3390/rs9090954

Worked examples

Example 1 — a first encounter with Parametric array

Start with the simplest possible case. Write down what Parametric array claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Parametric array before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Parametric array ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Parametric array

In research: Parametric array appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Parametric array in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Parametric array is common in secondary-school and first-year university syllabi. It links to neighbouring topics Acoustics, Nonlinear systems, Sound, so understanding it makes those chapters shorter.
In everyday life: Look for Parametric array outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Parametric array in 20 minutes

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Frequently asked questions

What is Parametric array in simple terms?

Why does Parametric array matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Parametric array?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Parametric array.