40:(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.
115:
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
863:
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
899:
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
858:
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
910:
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
696:
Zhang, Dong; Chen, Xi; Xiu-fen, Gong (2001). "Acoustic nonlinearity parameter tomography for biological tissues via parametric array from a circular piston source—Theoretical analysis and computer simulations".
893:
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
915:
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
63:
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.
799:
918:
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.
100:
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
344:
116:
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.
73:
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
561:"A non-contact technique for evaluation of elastic structures at large stand-off distances: applications to classification of fluids in steel vessels"
838:
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.
77:. 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.
775:
234:
905:
V.M. Albers,"Underwater Sound, Benchmark Papers in Acoustics, p.415; Dowden, Hutchinson and Ross, Inc., Stroudsburg, PA (1972)
843:
Peter J. Westervelt, "Parametric Acoustic Array", Journal of the Acoustical Society of America, Vol. 35, No. 4 (535-537), 1963
853:
Mark B. Moffett and Robert H. Mellen, "On Parametric Source Aperture Factors", J. Acoust. Soc. Am. Vol. 60, No. 3, Sept. 1976
74:
479:
Sources of Difference Frequency Sound in a Dual-Frequency Imaging System with Implications for Monitoring Thermal Surgery
811:
Reeves, C.; Goldsberry, T.; Rohde, D. (1979). "Experiments with a large aperture parametric acoustic receiving array".
358:
944:
848:
Mark B. Moffett and Robert H. Mellen, "Model for Parametric Sources", J. Acoust. Soc. Am. Vol. 61, No. 2, Feb. 1977
740:
Muir, T. G.; Wyber, R. J. (1984). "High-resolution seismic profiling with a low-frequency parametric array".
642:
333:
258:
Trenchard, Stephen E.; Coppens, Alan B. (1980). "Experimental study of a saturated parametric array in air".
70:
by Captain H.J. Round (British pioneer of the superheterodyne receiver) via the parametric array mechanism.
66:
According to Albers, he (Westervelt) there first observed an accidental generation of low frequency sound
889:
H.C. Woodsum, Bull. Of Am. Phys. Soc., Fall 1980; “A Boundary Condition Operator for Nonlinear Acoustics”
643:"A focused ultrasound method for simultaneous diagnostic and therapeutic applications—a simulation study"
169:
104:
and Parabolic Equation (PE) Methods, most notably via the Kokhlov–Zablotskaya–Kuznetzov (KZK) equation.
868:
Robert T. Beyer, Nonlinear Acoustics, 1st Edition (1974),. Published by the Naval Sea Systems Command.
749:
706:
654:
613:
453:
306:
267:
101:
779:
882:
J.S. Bellin and R. T. Beyer, “Scattering of Sound by Sound”, J. Acoust. Soc. Am. 32, 339-341 (1960)
86:
60:), although important experimental work was contemporaneously underway in the former Soviet Union.
939:
872:
H.O. Berktay and D.J. Leahy, Journal of the Acoustical Society of America, 55, p. 539 (1974)
678:
181:
478:
875:
M.J. Lighthill, "On Sound Generated Aerodynamically”, Proc. R. Soc. Lond. A211, 564-687 (1952)
722:
670:
582:
240:
230:
180:
arrays can also be formed for directional reception. In 2005, Elwood Norris won the $ 500,000
37:
816:
757:
714:
662:
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572:
461:
314:
275:
108:
57:
49:
878:
M.J. Lighthill, “On Sound Generated Aerodynamically”, Proc. R. Soc. Lond. A222, 1-32 (1954)
362:
90:
32:-free beams of low frequency sound, through the mixing and interaction of high frequency
753:
710:
658:
617:
457:
310:
271:
934:
666:
577:
184:
for his application of the parametric array to commercial high-fidelity loudspeakers.
928:
813:
ICASSP '79. IEEE International Conference on Acoustics, Speech, and Signal Processing
94:
53:
682:
293:
Johnson, P. A.; Meegan, G. D.; McCall, K.; Bonner, B. P.; Shankland, T. J. (1992).
202:
559:
Kaduchak, Gregory; Sinha, Dipen N.; Lizon, David C.; Kelecher, Michael J. (2000).
820:
154:
112:
33:
25:
444:
Westervelt, Peter J. (1975). "The status and future of nonlinear acoustics".
85:
The foundation for Westervelt's theory of sound generation and scattering in
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29:
21:
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355:
48:
Priority for discovery and explanation of the parametric array owes to
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131:
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Konofagou, Elisa; Thierman, Jonathan; Hynynen, Kullervo (2001).
229:. Translated by Robert T. Beyer. American Institute of Physics.
800:
n:Elwood Norris receives 2005 Lemelson-MIT Prize for invention.
223:
Novikov, B. K.; Rudenko, O. V.; Timoshenko, V. I. (1987).
168:
and directional high-fidelity commercial audio systems (
356:
Institute of Acoustics - Medals & Awards Programme
600:Naugolnykh, Konstantin A.; Esipov, Igor B. (1995).
345:
Professor Peter Westervelt and the parametric array
776:"Active control of sound using a parametric array"
295:"Finite amplitude wave studies in earth materials"
525:
124:Practical applications are numerous and include:
742:The Journal of the Acoustical Society of America
699:The Journal of the Acoustical Society of America
606:The Journal of the Acoustical Society of America
446:The Journal of the Acoustical Society of America
299:The Journal of the Acoustical Society of America
260:The Journal of the Acoustical Society of America
547:
500:
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8:
432:
886:M.J. Lighthill, Math. Revs. 19, 915 (1958)
602:"Remote ocean sensing by parametric array"
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107:An alternate mathematical formalism using
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28:mechanism that generates narrow, nearly
536:
193:
56:Medal (currently Professor Emeritus at
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421:
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7:
384:
382:
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14:
920:https://doi.org/10.3390/rs9090954
815:. Vol. 4. pp. 616–619.
334:Parametric Beam Formation in Rock
203:"Preface to the Original Edition"
89:media owes to an application of
647:Physics in Medicine and Biology
162:underground seismic prospecting
145:and 'see through walls' sensing
226:Nonlinear Underwater Acoustics
1:
578:10.1016/S0041-624X(99)00109-2
526:Woodsum & Westervelt 1981
75:Acoustical Society of America
36:, effectively overcoming the
513:"Texas KZK Time Domain Code"
821:10.1109/ICASSP.1979.1170632
667:10.1088/0031-9155/46/11/314
97:for fluid particle motion.
961:
548:Cabot & Putterman 1981
501:Moffett & Mellen 1976
490:Moffett & Mellen 1977
433:Bellin & Beyer 1960
142:non-destructive testing
170:Sound from ultrasound
165:active noise control
148:remote ocean sensing
139:sub-bottom profiling
754:1984ASAJ...76...78M
711:2001ASAJ..109.1219Z
659:2001PMB....46.2967K
618:1995ASAJ...98.2915N
458:1975ASAJ...57.1352W
311:1992ASAJ...91.2350J
272:1980ASAJ...68.1214T
207:Nonlinear Acoustics
50:Peter J. Westervelt
911:Company-Amsterdam)
361:2009-06-28 at the
182:MIT-Lemelson Prize
87:nonlinear acoustic
20:, in the field of
945:Nonlinear systems
762:10.1121/1.2022023
719:10.1121/1.1344160
653:(11): 2967–2984.
411:Roy & Wu 1993
201:Beyer, Robert T.
128:underwater sound
102:Green's functions
38:diffraction limit
24:, is a nonlinear
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109:Fourier operator
58:Brown University
52:, winner of the
18:parametric array
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748:(S1): S78.
612:(5): 2915.
565:Ultrasonics
389:Albers 1972
305:(4): 2350.
176:Parametric
111:methods in
81:Foundations
34:sound waves
929:Categories
786:2006-12-05
422:Beyer 1974
188:References
155:ultrasound
113:wavenumber
940:Acoustics
374:Muir 1976
178:receiving
91:Lighthill
30:side lobe
22:acoustics
894:TuAM201.
727:11303935
675:11720358
587:11243456
359:Archived
245:16240349
153:medical
95:equation
750:Bibcode
707:Bibcode
683:2036873
655:Bibcode
614:Bibcode
454:Bibcode
307:Bibcode
268:Bibcode
44:History
900:(1976)
859:(1993)
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233:
68:in air
935:Sound
679:S2CID
132:sonar
723:PMID
671:PMID
583:PMID
241:OCLC
231:ISBN
817:doi
758:doi
715:doi
703:109
663:doi
622:doi
573:doi
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315:doi
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