parametric array

Priority for discovery and explanation of the parametric array owes to Peter J. Westervelt,[http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JASMAN000119000005003231000004&idtype=cvips&gifs=yes Professor Peter Westervelt and the parametric array] winner of the Lord Rayleigh Medal,[http://www.ioa.org.uk/medals-and-awards/ Institute of Acoustics - Medals & Awards Programme] {{webarchive|url=https://web.archive.org/web/20090628181721/http://www.ioa.org.uk/medals-and-awards/ |date=2009-06-28 }} although important experimental work was contemporaneously underway in the former Soviet Union.

According to Muir{{Harvard citation no brackets|Muir|1976}}, p. 554. and Albers,{{Harvnb|Albers|1972}} 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{{Harvard citation no brackets|Westervelt|1963}} was published as an extension of Westervelt's classic work on the nonlinear Scattering of Sound by Sound.{{Harvard citation no brackets|Roy|Wu|1993}}{{Harvnb|Beyer|1974}}{{Harvnb|Bellin|Beyer|1960}}

The foundation for Westervelt's theory of sound generation and scattering in nonlinear acoustic{{cite journal | doi = 10.1121/1.380612 | volume=57 | issue=6 | title=The status and future of nonlinear acoustics | year=1975 | journal=The Journal of the Acoustical Society of America | pages=1352–1356 | last1 = Westervelt | first1 = Peter J.| bibcode=1975ASAJ...57.1352W }} 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).[https://dspace.mit.edu/bitstream/1721.1/28762/1/59823423.pdf Sources of Difference Frequency Sound in a Dual-Frequency Imaging System with Implications for Monitoring Thermal Surgery]{{dead link|date=January 2018 |bot=InternetArchiveBot |fix-attempted=yes }} Solutions to this equation have been developed using Green's functions{{Harvnb|Moffett|Mellen|1977}}{{Harvnb|Moffett|Mellen|1976}} and Parabolic Equation (PE) Methods, most notably via the Kokhlov–Zablotskaya–Kuznetzov (KZK) equation.{{Cite web|url=http://people.bu.edu/robinc/kzk/|title = Texas KZK Time Domain Code}}

An alternate mathematical formalism using Fourier operator methods in wavenumber space, was also developed and generalized by Westervelt.{{Harvnb|Woodsum|Westervelt|1981}} 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,{{Harvnb|Woodsum|2006}} 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.{{Harvnb|Cabot|Putterman|1981}}

Practical applications are numerous and include:

• underwater sound
• sonar
• depth sounding
• sub-bottom profiling
• non-destructive testing
• and 'see through walls' sensing{{cite journal | doi = 10.1016/S0041-624X(99)00109-2 | pmid=11243456 | volume=37 | issue=8 | title=A non-contact technique for evaluation of elastic structures at large stand-off distances: applications to classification of fluids in steel vessels | year=2000 | journal=Ultrasonics | pages=531–536 | last1 = Kaduchak | first1 = Gregory | last2 = Sinha | first2 = Dipen N. | last3 = Lizon | first3 = David C. | last4 = Kelecher | first4 = Michael J.| url=https://zenodo.org/record/1259727 | doi-access = free }}
• remote ocean sensing{{cite journal | doi = 10.1121/1.414208 | volume=98 | issue=5 | title=Remote ocean sensing by parametric array | year=1995 | journal=The Journal of the Acoustical Society of America | page=2915 | last1 = Naugolnykh | first1 = Konstantin A. | last2 = Esipov | first2 = Igor B.| bibcode=1995ASAJ...98.2915N | doi-access=free }}
• medical ultrasound{{cite journal | doi = 10.1088/0031-9155/46/11/314 | pmid=11720358 | volume=46 | issue=11 | title=A focused ultrasound method for simultaneous diagnostic and therapeutic applications—a simulation study | year=2001 | journal=Physics in Medicine and Biology | pages=2967–2984 | last1 = Konofagou | first1 = Elisa | last2 = Thierman | first2 = Jonathan | last3 = Hynynen | first3 = Kullervo| bibcode=2001PMB....46.2967K | s2cid=2036873 | url=https://semanticscholar.org/paper/85b7f120e6568d0a912d79040fd1b0d7810b1053 }}
• and tomography{{cite journal |last1=Zhang |first1=Dong |last2=Chen |first2=Xi |last3=Xiu-fen |first3=Gong |year=2001 |title=Acoustic nonlinearity parameter tomography for biological tissues via parametric array from a circular piston source—Theoretical analysis and computer simulations |journal=The Journal of the Acoustical Society of America |volume=109 |issue=3 |pages=1219–1225 |bibcode=2001ASAJ..109.1219Z |doi=10.1121/1.1344160 |pmid=11303935}}
• underground seismic prospecting{{cite journal | doi = 10.1121/1.2022023 | volume=76 | issue=S1 | title=High-resolution seismic profiling with a low-frequency parametric array | year=1984 | journal=The Journal of the Acoustical Society of America | page=S78 | last1 = Muir | first1 = T. G. | last2 = Wyber | first2 = R. J.| bibcode=1984ASAJ...76...78M }}
• active noise control{{cite web |url=http://www.mecheng.adelaide.edu.au/anvc/abstract.php?abstract=378 |title=Active control of sound using a parametric array |accessdate=2006-12-05 |url-status=dead |archiveurl=https://web.archive.org/web/20070309235859/http://www.mecheng.adelaide.edu.au/anvc/abstract.php?abstract=378 |archivedate=2007-03-09 }}
• and directional high-fidelity commercial audio systems (Sound from ultrasound)n:Elwood Norris receives 2005 Lemelson-MIT Prize for invention.

Parametric receiving arrays can also be formed for directional reception.{{Cite book |doi = 10.1109/ICASSP.1979.1170632|chapter = Experiments with a large aperture parametric acoustic receiving array|title = ICASSP '79. IEEE International Conference on Acoustics, Speech, and Signal Processing|year = 1979|last1 = Reeves|first1 = C.|last2 = Goldsberry|first2 = T.|last3 = Rohde|first3 = D.|volume = 4|pages = 616–619}} In 2005, Elwood Norris won the $500,000 MIT-Lemelson Prize for his application of the parametric array to commercial high-fidelity loudspeakers.

{{Reflist}}

• {{Wikicite|reference=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.|ref=CITEREFWoodsumWestervelt1981}}
• {{Wikicite|reference=Peter J. Westervelt, "Parametric Acoustic Array", Journal of the Acoustical Society of America, Vol. 35, No. 4 (535-537), 1963|ref=CITEREFWestervelt1963}}
• {{Wikicite|reference=Mark B. Moffett and Robert H. Mellen, "Model for Parametric Sources", J. Acoust. Soc. Am. Vol. 61, No. 2, Feb. 1977|ref=CITEREFMoffettMellen1977}}
• {{Wikicite|reference=Mark B. Moffett and Robert H. Mellen, "On Parametric Source Aperture Factors", J. Acoust. Soc. Am. Vol. 60, No. 3, Sept. 1976|ref=CITEREFMoffettMellen1976}}
• {{Wikicite|reference=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)|ref=CITEREFRoyWu1993}}
• 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)
• {{Wikicite|reference=Robert T. Beyer, Nonlinear Acoustics, 1st Edition (1974),. Published by the Naval Sea Systems Command.|ref=CITEREFBeyer1974}}
• 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)
• {{Wikicite|reference=J.S. Bellin and R. T. Beyer, “Scattering of Sound by Sound”, J. Acoust. Soc. Am. 32, 339-341 (1960)|ref=CITEREFBellinBeyer1960}}
• 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”
• {{Wikicite|reference=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.|ref=CITEREFWoodsum2006}}
• {{Wikicite|reference=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)|ref=CITEREFMuir1976}}
• {{Wikicite|reference=V.M. Albers,"Underwater Sound, Benchmark Papers in Acoustics, p.415; Dowden, Hutchinson and Ross, Inc., Stroudsburg, PA (1972)|ref=CITEREFAlbers1972}}
• {{Wikicite|reference=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)|ref=CITEREFCabotPutterman1981}}
• 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

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Category:Sound

Category:Acoustics

Category:Nonlinear systems