Nonlinear Acoustics

  • Steven L. Garrett
Part of the Graduate Texts in Physics book series (GTP)


A fundamental assumption of linear acoustics is that the presence of a wave does not have an effect on the properties of the medium through which it propagates. Under that assumption, two sound waves can be superimposed when they occupy the same space at the same time, but one wave will have no effect on the other wave and once they part company, there will be no evidence of their previous interaction. This is illustrated in Fig. 15.1. By extension, the assumption of linearity also means that a waveform is stable since any individual wave does not interact with itself.


Sound Speed Radiation Force Pump Wave Sound Field Levitation Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    I. Rudnick, On the attenuation of high amplitude waves of stable saw-tooth form propagated in horns. J. Acoust. Soc. Am. 30(4), 339–342 (1958)ADSCrossRefGoogle Scholar
  2. 2.
    A. Myers, R.W. Pyle Jr., J. Gilbert, D.M. Campbell, J.P. Chick, S. Logie, Effects of nonlinear sound propagation on the characteristic timbres of brass instruments. J. Acoust. Soc. Am. 131(1), 678–688 (2012)ADSCrossRefGoogle Scholar
  3. 3.
    R.T. Beyer, Nonlinear Acoustics (Acoust. Soc. Am., Woodbury, 1997); ISBN 1-56396-724-3. §3.1Google Scholar
  4. 4.
    E.C. Everbach, Ch. 20: Parameters of nonlinearity of acoustic media, in Encyclopedia of Acoustics, vol. I, ed. by M.J. Crocker (Wiley, New York, 1997); ISBN 0-471-17767-9Google Scholar
  5. 5.
    S.L. Garrett, Nonlinear distortion of 4th sound in superfluid helium 3He-B. J. Acoust. Soc. Am. 69(1), 139–144 (1981)ADSCrossRefGoogle Scholar
  6. 6.
    R.T. Beyer, in American Institute of Physics Handbook, 3rd edn., ed by D. E. Grey. Nonlinear Acoustics (Experimental) (McGraw-Hill, New York, 1972), pp. 3–208 See Table 30-3Google Scholar
  7. 7.
    M. Greenspan, C.E. Tschiegg, Radiation-induced acoustic cavitation: apparatus and some results. J. Res. Natl. Bur. Stand Sect C 71, 299–312 (1959)Google Scholar
  8. 8.
    M.S. Cramer, A. Kluwick, On the propagation of waves exhibiting both positive and negative nonlinearity. J. Fluid Mech. 142(1), 9–37 (1984)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    I. Rudnick, Physical Acoustics at UCLA in the Study of Superfluid Helium, in Proc. E. Fermi Summer School, Varenna, 1974Google Scholar
  10. 10.
    S.J. Putterman, Superfluid Hydrodynamics (North-Holland, Amsterdam, 1974); ISBN 0-7204-030104Google Scholar
  11. 11.
    S. Putterman, S. Garrett, Resonant mode conversion and other second-order effects in superfluid He-II. J. Low Temp. Phys. 27(3/4), 543–559 (1977)ADSCrossRefGoogle Scholar
  12. 12.
    Z.A. Gol’dberg, Second approximation acoustic equations and the propagation of plane waves of finite amplitude. Soviet Phys. Acoust. 2, 346–350 (1956)Google Scholar
  13. 13.
    A. Larraza, S.L. Garrett, S. Putterman, Dispersion relations for gravity waves in a deep fluid: second sound in a stormy sea. Phys. Rev. A 41(6), 3144–3155 (1990)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    L.D. Landau, E.M. Lifshitz, Fluid Mechanics, 2nd edn. (Butterworth-Heinemann, Oxford, 1987); ISBN 0-7506-2767-0. See Eq. 86.1Google Scholar
  15. 15.
    I. Rudnick, On the attenuation of a repeated sawtooth shock wave. J. Acoust. Soc. Am. 25(5), 1010–1011 (1953)ADSCrossRefGoogle Scholar
  16. 16.
    I. Rudnick, On the attenuation of finite amplitude waves in a liquid. J. Acoust. Soc. Am. 30(6), 564–567 (1958)ADSCrossRefGoogle Scholar
  17. 17.
    S. Earnshaw, On the mathematical theory of sound. Philos. Trans. R. Soc. Lond. 150, 133–148 (1860)CrossRefGoogle Scholar
  18. 18.
    L.E. Hargrove, Fourier series for the finite amplitude sound waveform in a dissipationless medium. J. Acoust. Soc. Am. 32(4), 511–512 (1960)ADSCrossRefGoogle Scholar
  19. 19.
    E. Fubini-Ghiron, Anomalie nella propagazione di onde acustiche di grande ampiezza (Anomolies in acoustic wave propagation of large amplitude). Alta Frequenza 4, 530–581 (1935)Google Scholar
  20. 20.
    J.L.S. Bellin, R.T. Beyer, Scattering of sound by sound. J. Acoust. Soc. Am. 32(3), 339–341 (1960)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    P.J. Westervelt, Parametric acoustic array. J. Acoust. Soc. Am. 35(4), 535–537 (1963)ADSCrossRefGoogle Scholar
  22. 22.
    H. Lamb, Dynamical Theory of Sound, 2nd edn. (E. Arnold & Co., 1931); reprinted (Dover, 1960). See §63 and §95Google Scholar
  23. 23.
    A.L. Thuras, R.T. Jenkins, H.T. O’Neill, Extraneous frequencies generated in air carrying intense sound waves. J. Acoust. Soc. Am. 6(3), 173–180 (1935)ADSCrossRefzbMATHGoogle Scholar
  24. 24.
    Metals Handbook (Desk Edition), ed. by H.E. Boyer, T.L. Gall (Am. Soc. for Metals, 1985), pp. 2–16; ISBN 0-87170-188-X. Table 1Google Scholar
  25. 25.
    G.L. Jones, D.R. Kobett, Interaction of elastic waves in an isotropic solid. J. Acoust. Soc. Am. 35(1), 5–10 (1963)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    R.R. Rollins Jr., L.H. Taylor, P.H. Todd Jr., Ultrasonic study of three-phonon interactions. II. Experimental results. Phys. Rev. 136(3A), 597–601 (1964)ADSCrossRefGoogle Scholar
  27. 27.
    L.D. Landau, E.M. Lifshitz, Fluid Mechanics, 2nd edn. (Butterworth-Heinemann, Oxford, 1987); ISBN 0-7506-2767-0. See Eq. 86.1, §139Google Scholar
  28. 28.
    S. Garrett, S. Adams, S. Putterman, I. Rudnick, Resonant mode conversion in He II. Phys. Rev. Lett. 41(6), 413–416 (1978)ADSCrossRefGoogle Scholar
  29. 29.
    P.M. Gammel, A.P. Croonquist, T.G. Wang, A high-powered siren for stable acoustic levitation of dense materials in the Earth’s gravity. J. Acoust. Soc. Am. 83(2), 496–501 (1988)ADSCrossRefGoogle Scholar
  30. 30.
    F.H. Busse, T.G. Wang, Torque generated by orthogonal acoustic waves—theory. J. Acoust. Soc. Am. 69(6), 1634–1638 (1981)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    H.W.St. Clair, Electromagnetic sound generator for producing intense high frequency sound. Rev. Sci. Instrum. 12(5), 250–256 (1941)ADSCrossRefGoogle Scholar
  32. 32.
    C.H. Allen, I. Rudnick, A powerful high-frequency siren. J. Acoust. Soc. Am. 19(5), 857–865 (1947)ADSCrossRefGoogle Scholar
  33. 33.
    B.L. Smith, G.W. Swift, Measuring second-order time-averaged pressure. J. Acoust. Soc. Am. 110(2), 717–723 (2001)ADSCrossRefGoogle Scholar
  34. 34.
    J.W. Strutt (Lord Rayleigh), On the circulation of air observed in Kundt’s tubes, and on some allied acoustical problems. Philos. Trans. R. Soc. Lond. 175, 1–21 (1883); Collected Works, vol. II (Dover, 1964), §108.Google Scholar
  35. 35.
    H. Mukai, S. Sakamoto, H. Tachibana, Experimental study on the absorption characteristics of resonance-type brick/block walls. J. Acoust. Soc. Jpn (E) 20(6), 433–438 (1999)CrossRefGoogle Scholar
  36. 36.
    M.B. Barmatz, Acoustic agglomeration methods and apparatus, U.S. Patent No. 4,475,921, 9 Oct 1984Google Scholar
  37. 37.
    J.W. Strutt (Lord Rayleigh), Theory of Sound, vol. II (Macmillan, 1896), §253b; (Dover, 1945)Google Scholar
  38. 38.
    V. Dvořák, Ueber die ackustiche Abstoggung. Ann. Phys. 239(3), 328–338 (1878)CrossRefGoogle Scholar
  39. 39.
    A.M. Mayer, Philos. Mag. 6, 225 (1878)CrossRefGoogle Scholar
  40. 40.
    J.W. Strutt (Lord Rayleigh), Theory of Sound, vol. II (Macmillan, 1896), §253a; (Dover, 1945)Google Scholar
  41. 41.
    W. König, Hydrodynamisch-akustische Untersuchungen. Wied. Ann. 43, 51 (1891)Google Scholar
  42. 42.
    J.W. Strutt (Lord Rayleigh), On an instrument capable of measuring the intensity of aerial vibrations, Philos. Mag. 14, 186–187 (1882); Collected Works, vol. II (Dover, 1964), §91Google Scholar
  43. 43.
    L.L. Beranek, Acoustic Measurements (Wiley, New York, 1949), pp. 148–158Google Scholar
  44. 44.
    L.V. King, On the theory of the inertia and diffraction corrections for the Rayleigh disk. Proc. R. Soc. Lond. A 153, 17–40 (1935)ADSCrossRefzbMATHGoogle Scholar
  45. 45.
    J.R. Pellam, W.B. Hanson, Thermal Rayleigh disk measurements in liquid helium II. Phys. Rev. 85(2), 216–225 (1952)ADSCrossRefGoogle Scholar
  46. 46.
    T.R. Koehler, J.R. Pellam, Observation of torque exerted by pure superflow. Phys. Rev. 125(3), 791–794 (1962)ADSCrossRefGoogle Scholar
  47. 47.
    S.L. Garrett, Butterfly-valve inductive orientation detector. Rev. Sci. Instrum. 51(4), 427–430 (1980)ADSCrossRefGoogle Scholar
  48. 48.
    L.D. Landau, E.M. Lifshitz, Fluid Mechanics, 2nd edn. (Butterworth-Heinemann, Oxford, 1987); ISBN 0-7506-2767-0. See Eq. 86.1, §8Google Scholar
  49. 49.
    L.D. Landau, E.M. Lifshitz, Mechanics (Pergamon, New York, 1960) See §1–§5zbMATHGoogle Scholar
  50. 50.
    I. Rudnick, Measurements of the acoustic radiation pressure on a sphere in a standing wave field. J. Acoust. Soc. Am. 62(1), 20–22 (1977)ADSCrossRefGoogle Scholar
  51. 51.
    L.D. Landau, E.M. Lifshitz, Fluid Mechanics, 2nd edn. (Butterworth-Heinemann, Oxford, 1987); ISBN 0-7506-2767-0. See Eq. 86.1, §49Google Scholar
  52. 52.
    S.L. Garrett, R.W.M. Smith, M.E. Poese, Eliminating nonlinear acoustical effects from thermoacoustic refrigeration systems, in Proc. 17th International Symposium on Nonlinear Acoustics (ISNA 17) (Am. Inst. Physics, 2006), pp. 407–415; ISBN 0-7354-0330-9Google Scholar
  53. 53.
    Y.A. Ilinskii, B. Lipkens, T.S. Lucas, T.W. Van Doren, E.A. Zabolotskaya, Nonlinear standing waves in an acoustical resonator. J. Acoust. Soc. Am. 104(5), 2664–2674 (1998)ADSCrossRefGoogle Scholar
  54. 54.
    S. Putterman, J. Rudnick, M. Barmatz, Acoustic levitation and the Boltzmann-Ehrenfest principle. J. Acoust. Soc. Am. 85(1), 68–71 (1989)ADSCrossRefGoogle Scholar
  55. 55.
    S.J. Putterman, Adiabatic invariance, the cornerstone of modern physics. J. Acoust. Soc. Am. 83(1), S39 (1988)ADSCrossRefGoogle Scholar
  56. 56.
    M. Barmatz, in Materials Processing in the Reduced Gravity Environment of Space, ed by G. E. Rindone. Overview of containerless processing technologies (Amsterdam, Elsevier, 1982), pp. 25–37Google Scholar
  57. 57.
    J. Rudnick, M. Barmatz, Oscillational instabilities in single-mode acoustic levitators. J. Acoust. Soc. Am. 87(1), 81–92 (1990)ADSCrossRefGoogle Scholar
  58. 58.
    M.B. Barmatz, S.L. Garrett, Stabilization and oscillation of an acoustically levitated object, U.S. Patent No. 4,773,266, 27 Sept 1988Google Scholar
  59. 59.
    S. Chu, Laser manipulation of atoms and particles. Science 253(5022), 861–866 (1991)ADSCrossRefGoogle Scholar
  60. 60.
    S.L. Garrett, S. Backhaus, The power of sound. Am. Sci. 88(6), 11–17 (2004)Google Scholar
  61. 61.
    G.W. Swift, Mixture separation, in Handbook of Acoustics, ed. by T.D. Rossing (Springer, New York, 2007); ISBN 978-0-387-30446-7. See §7.6Google Scholar
  62. 62.
    W.L. Nyborg, Acoustic streaming, in Nonlinear Acoustics, ed. by M.F. Hamilton, D.T. Blackstock (Acoust. Soc. Am, 2008); ISBN 978-0-123-21860-5. See Ch. 7Google Scholar
  63. 63.
    S.J. Putterman, Sonoluminescence: sound into light. Sci. Am. 272(2), 46–51 (1995)CrossRefGoogle Scholar
  64. 64.
    R.T. Beyer, Nonlinear Acoustics (Acoust. Soc. Am., Woodbury, 1997); ISBN 1-56396-724-3. §4.7Google Scholar
  65. 65.
    D.J. Maglieri, K.J. Plotkin, Sonic Boom, NASA Tech. Report RP-1258 (1991)Google Scholar
  66. 66.
    A.B. Pippard, The Physics of Vibration (Cambridge University Press, Cambridge, 1989); ISBN 0-521-37200-3. See Ch. 8Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Steven L. Garrett
    • 1
  1. 1.Pine Grove MillsUSA

Personalised recommendations