Parametric array
List of References
[1] 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.
[2] Peter J. Westervelt, "Parametric Acoustic Array", Journal of the Acoustical Society of America, Vol. 35, No. 4 (535-537), 1963.
[3] H.C. Woodsum, Ph.D. Thesis in Physics, Brown University (1979), "A General Theory for Sound-Sound Scattering with Parametric Array Applications", published by University Microfilms, Inc.
[4] Mark B. Moffett and Robert H. Mellen, "Model for Parametric Sources",
J. Acoust. Soc. Am. Vol. 61, No. 2, Feb. 1977
[5] Mark B. Moffett and Robert H. Mellen, "On Parametric Source Aperture Factors", J. Acoust. Soc. Am. Vol. 60, No. 3, Sept. 1976 (see Figure 2)
[6] 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).
[7] "Introduction to Quantum Mechanics", Chapter IX-32, Linus Pauling and E. Bright Wilson, Dover Publications, New York.
[8] Harvey C. Woodsum (I 980). "Enhancement of Parametric Efficiency by Saturation Suppression", Journal of Sound and Vibration, Vol. 69(l), 27-33;
[91 Harvey C. Woodsum and William Hogan, "Work by Virtual Sources Against In-phase and Quadrature Components of a Pressure Field: Impact on Nonlinear Attenuation", J. Acoust. Soc. Am., Vol. 88 Suppl. 1 (4PA4), Nov. 1990
[10] P.J. Westervelt, in Proc. 3rd Intl. Cong. Acoustics, L. Cremer, Editor; (Elsevier, Amsterdam, 1960) P. 316.
[11] 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)
[12] Albert Messiah, "Quantum Mechanics, Volume II", John Wiley & Sons., 6th printing, September 1966.
[13] Robert T. Beyer , Nonlinear Acoustics, 1st Edition (1974),. Published by the Naval Sea Systems Command.
[14] H.O. Berktay and D.J. Leahy, Journal of the Acoustical Society of Amercia, 55,
p. 539 (1974),
[15a] James J. Truchard, ”The Parametric Array and the Scattering of Sound by Sound”, Applied Research Laboratories (University of Texas at Austin) Technical Publication, No. ARL-TP-76-19, 9 June, 1976
[15b] Peter J. Westervelt, ”On the Absorbtion of Sound by Sound”, Applied Research Laboratories (University of Texas at Austin) Technical Publication, No. ARL-TP-76-7.
[16] Peter J. Westervelt,”Absorption of Sound by Sound”, Journal of the Acoustical Society of America, Vol .69, No. 4, pp. 760-764, April 1976.
[17] J.M. Jauch and F. Rohrlich, “The Theory of Photons and Electrons: The Relativistic Quantum Field Theory of Charged Particles with Spin One-half”, (Second Expanded Edition), Appendix A6. Published by Springer-Verlag, 1976.
[18] H.Euler and B. Kockerl, Naturwiss. 23, 246 (1935)
[19] V. Weisskpf, Kgl. Danske Videnskab, Selskab 14, No. 6 (1936)
[20] Robert B. Boyd”Nonlinear Optics”, Academic Press (1992); see equations 1.15, and Chapter 1, re equations of nonlinear optics and nonlinear optical susceptibility.
[21] R.P. Feynman,”Quantum Electrodynamics”, W.A. Benjamin Inc., New York, 1962.
[22] Leonard I. Schiff, “Quantum Mechanics”, McGraw Hill (1968).
[23] E.G. Norris Journal of the Acoustical Society of America, 101, 3072 (A), 1997
[24] David T. Blackstock, “Audio Applications of the Paramtric Array”, 134 th Meeting of the Acoustical Society of America, paper 2pEA5, San Diego California, December 1997.
[25] Zhong-Yue Jiang and James F. Greenleaf, “The Nonlinear Interaction of Two Plane Waves in a Viscous Medium”, 130th Meeting of the Acoustical Society of America, Saint Louis Missouri, Paper 1aPA2, Nov. 27, 1995.
[26] T.G. Muir and J.G. Willette, “Parametric Acoustic Transmitting Arrays”, Journal of the Acoustical Society of America, Vol. 52, Number 5 (part 2), 1972.
[27] Peter J. Westervelt,”The Status and Future of Nonlinear Acoustics”, Journal of the Acoustical Society of America, Vol. 57, No. 6, Part I, pp. 1352-1356, June 1975.
[28] P.J. Westervelt, ”Acoustics and General Relativity”, in In Honor of Philip M. Morse, H.Feshbach and K.U. Ingard, Eds. (M.I.T. Press, Cambridge, 1969)
[29] P.J. Westervelt, Acta Physica Polnica, XXXV (1969)
[30] H. J..Maris, Physical Review Letters 28, 277 (1972)
[32] P.Alais, and P.Y. Hennion, “Etude par une methode de Fourier de l’interaction non lineaire de deux rayonnements acoustiques dans un fluide absorbant. Cas particulier de l’emssion parametrique.”, Acustica, Volume 43, No. 1 (1979)
[33] Z.W. Quian “On the Scattering of Sound by Sound”, Proceedings of the 12th International Symposium on Nonlinear Acoustics, Austin Texas, USA, 27-31 August, 1990. Elsevier Science Ltd., London (1990), Paper H3.
[34] Peter J. Westervelt, “Scattering of Sound by Sound”, Proceedings of the 12th International Symposium on Nonlinear Acoustics, Austin Texas, USA, 27-31 August, 1990. Elsevier Science Ltd., London (1990), Paper H23.
[35] Pierre Cervenka and Pierre Alais, “Optimization of a Parametric Transmitting Array”, Proceedings of the 12th International Symposium on Nonlinear Acoustics, Austin Texas, USA, 27-31 August, 1990. Elsevier Science Ltd., London (1990), Paper F3.
[36] M.J. Lighthill, “ On Sound Generated Aerodynamically”, Proc. R. Soc. Lond. A211, 564-687 (1952)
[37] M. J. Lighhill, “ On Sound Generated Aerodynamically”, Proc. R. Soc. Lond., A222, 1-32 (1954)
[38] J.S. Bellin and R. T. Beyer, “Scattering of Sound by Sound”, J. Acoust. Soc. Am. 32, 339-341 (1960)
[39] M. J. Lighthill, Math.Revs. 19, 915 (1958)]
[40] T.K. Stanton and R.T. Beyer, “Interaction of Sound with Noise in Water”, J. Acoust. Soc. Am. 1667-1680 (1978)
[41] M. Cabot and S. Putterman, “Renormalized Classical Non-linear Hydrodynamics, quantum mode coupling, and quantum theory of interacting phonons”, Physics Letters A, Vol 83, Issue 3, 18 May 1981, pp. 91-94. [42] H.C. Woodsum, infinity, Bull. Of Am. Phys. Soc., Fall 1980; “A Boundary Condition Operator for Nonlinear Acoustics” [43] Johnathan Thierman (private communication