Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

On waves in gases. Part I: Acoustics of jets, turbulence, and ducts

L. M. B. C. Campos

L. M. B. C. Campos

  • Instituto Superior Técnico, 1096 Lisboa Codex, Portugal, and Instituto de Física-Matemática, 1099 Lisboa Codex, Portugal

Rev. Mod. Phys. 58, 117 – Published 1 January, 1986

DOI: https://doi.org/10.1103/RevModPhys.58.117

Abstract

This review on some aspects of waves in gases concentrates first (Part I) on modern research in the acoustics of fluids at rest or in steady or turbulent motion, in free space, in the presence of obstacles, or in ducts. The study of sound, for which the sole restoring force is pressure, will be extended in a later paper (Part II) to include the other three restoring forces, namely, gravity, electromagnetic, and Coriolis forces, leading to current research on internal, magnetic, and inertial waves and their couplings. The Introduction at the beginning of Part I, and the discussion at the end of Part II, concern all four types of waves in gases, and their relevance in physics and engineering. In Part I, the following areas of acoustics are addressed: the generation of noise by turbulence, inhomogeneities or bubbles, in natural and engineering flows, e.g., wind or jets; the scattering of sound by interfaces and diffraction by turbulence, and their effects on spectral and directional redistribution of energy; propagation in ducts, without or with mean flow, e.g., the horns of musical instruments and loudspeakers, and inlets and exhausts of engines; the effects of dissipation and nonlinearity on waves, e.g., in laboratory and engineering shock tubes, and in geophysical and astrophysical conditions. Underlying these topics is the interaction of acoustics with manking, ranging from the processes of human hearing and speech to the reproduction of desirable sounds (music) and reduction of undesirable sounds (noise).

References (637)

  1. Abramowitz, M., and I. Stegun, 1964, Handbook of Mathematical Functions (Dover, New York)
  2. Achenbach, J. D., 1973, Waves in Solids (North-Holland, Amsterdam)
  3. Acheson, D. J., and R. Hide, 1973, "Hydromagnetics of rotating fluids," Rep. Prog. Phys. 36, 159
  4. Adam, J. A., 1982, "Asymptotic solutions and spectral theory of linear wave equations," Phys. Rep. 86, 217
  5. Aggarwal, H. R., 1984, "The calculation of transonic rotor noise," Am. Inst. Aeron. Astron. J. 22, 996
  6. Ahmed, B. M., and I. A. Eltayeb, 1980, "On the propagation, reflexion, transmission and stability of atmospheric Rossby-gravity waves on a beta-plane in the presence of latitudinally sheared zonal flows," Philos. Trans. R. Soc. London, Ser. A 298, 6
  7. Akasofu, S. I., and S. Chapman, 1972, Solar-Terrestrial Physics (Oxford University, New York)
  8. d'Alembert, J. R., 1747, Opuscules Mathématiques (Gauthier-Villars, Paris), p. 1
  9. Alfvén, H., 1942, "The existence of electromagnetic hydrodynamic waves," Ark. Mat. Astron. Fys. B 29, 1
  10. Alfvén, H., 1948, Cosmical Electrodynamics (Oxford University, London)
  11. Alfvén, H., and C. G. Falthammar, 1962, Cosmical Electrodynamics (Oxford University, London)
  12. Aranha, J. A., D. K. Yue, and C. C. Mei, 1982, "Non-linear waves near a cut-off frequency in an acoustic duct—a numerical study," J. Fluid Mech. 121, 465
  13. Arbey, H., and J. Bataille, 1983, "Noise generated by airfoil profiles placed in an uniform laminar flow," J. Fluid Mech. 134, 33
  14. Athay, R. G., 1976, The Quiet Sun (Reidel, Dordrecht)
  15. Atvars, J., L. K. Schubert, and H. S. Ribner, 1964, "Refraction of sound from a point source placed in a jet," J. Acoust. Soc. Am. 37, 168
  16. Ballantine, S., 1927, "On the propagation of sound in the general Bessel horn of infinite length," J. Franklin Inst. 203, 85
  17. Balsa, T. F., 1976a, "The far-field of high-frequency convected singularities in sheared flows, with an application to jet noise prediction," J. Fluid Mech. 74, 193
  18. Balsa, T. F., 1976b, "Refraction and shielding of sound from a source in a jet," J. Fluid Mech. 76, 443
  19. Banos, A., 1955, "Magneto-hydrodynamic waves in uncompressible and compressible fluids," Proc. R. Soc. London, Ser. A 233, 350
  20. Barclay, D. W., T. B. Moodie, and J. B. Haddow, 1977, "Waves in thin-walled, non-uniform, perfectly elastic tubes containing an incompressible inviscid fluid," J. Acoust. Soc. Am. 62, 1
  21. Barraclough, D. R., J. M. Harwood, B. R. Leaton, and S. C. B. Malin, 1975, "A model of the geomagnetic fluid at epoch," Geophys. J. R. Astron. Soc. 43, 645
  22. Barrat, M. J., P. O. A. L. Davies, and M. J. Fisher, 1963, "The characteristics of turbulence in the mixing region of a round jet," J. Fluid Mech. 16, 337
  23. Barton, E. H., 1908, "On spherical radiation and vibration in conical pipes," Philos. Mag. 15, 69
  24. Basset, A. B., 1888, Treatise on Hydrodynamics, 2 vols. (Deighton and Bell, London; reprinted 1961 by Dover, New York)
  25. Batchelor, G. K., 1953, Theory of Homogeneous Turbulence (Cambridge University, Cambridge, England)
  26. Batchelor, G. K., 1967, Fluid Mechanics (Cambridge University, Cambridge, England)
  27. Bateman, H., 1915, Electrical and Optical Wave Motion (Cambridge University, Cambridge, England; reprinted 1954 by Dover, New York)
  28. Bateman, H., 1929, "Notes on a differential equation which occurs in the two-dimensional motion of a compressible fluid and the associated variational problems," Proc. R. Soc. London, Ser. A 125, 598
  29. Bateman, H., 1932, Partial Differential Equations of Mathematical Physics (Cambridge University, Cambridge, England)
  30. Bateman, H., F. P. Murnaghan, and H. L. Dryden, 1956, Hydrodynamics (Dover, New York)
  31. Baumeister, K. J., W. Eversman, R. J. Astley, and J. W. White, 1984, "Acoustics in a variable-area duct: Finite element and finite difference comparisons to experiment," Am. Inst. Aeron. Astron. J. 21, 193
  32. Baxter, S. M., 1984, "The first-order non-linear sound field of a two-frequency spherical source," J. Sound Vib. 94, 337
  33. Baxter, S. M., and C. L. Morfey, 1983, "Modal power distribution in ducts at high frequency," Am. Inst. Aeron. Astron. J. 21, 74
  34. Bechert, D. W., U. Michel, and E. Pfizenmaier, 1977, "Experiments on the transmission of sound through jets," Am. Inst. Aeron. Astron. Paper 79-575
  35. Bechert, D., and E. Pfizenmaier, 1975, "On the amplification of broadband jet noise by pure tone excitation," J. Sound Vib. 43, 581
  36. Beckmann, P., and A. Spizzichino, 1963, The Scattering of Electromagnetic Waves from Rough Surfaces (McGraw-Hill, New York)
  37. Beer, T., 1974, Atmospheric Waves (Wiley, New York)
  38. Bekesy, G., 1960, Experiments in Hearing (Delft University, Delft, Netherlands)
  39. Belcher, J. W., and L. Davis, 1971, "Large-amplitude Alfvén waves in the interplanetary medium," J. Geophys. Res. 76, 3534
  40. Benade, A. H., 1976, Fundamentals of Musical Instruments (Oxford University, New York)
  41. Benade, A. H., 1980, Horns, Strings and Harmony (Doubleday, New York)
  42. Benade, A. H., and E. V. Jansson, 1974, "On plane and spherical waves in horns with nonuniform flare. I: theory of radiation, resonance, frequencies and mode conversion," Acustica 31, 79
  43. Benjamin, T. B., 1967, "Internal waves of permanent form in fluids of great depth," J. Fluid Mech. 29, 559
  44. Beranek, L. L., 1954, Acoustics (McGraw-Hill, New York)
  45. Berg, R. E., and D. G. Storck, 1982, The Physics of Sound (Prentice-Hall, Englewood, Cliffs, New Jersey)
  46. Bergmann, P. G., 1946, "The wave equation in a medium with a variable index of refraction," J. Acoust. Soc. Am. 17, 329
  47. Bernoulli, D., 1767, "Mémoire sur les vibrations des cordes d'une épaisseur inégale, " Mem. Acad. Sci. Berlin 21, 281
  48. Berry, M. V., 1973, "The statistical properties of echoes refracted from rough surfaces," Philos. Trans. R. Soc. London, Ser. A 273, 611
  49. Beyer, R. T., 1972, "Nonlinear acoustics (experimental)," in American Institute of Physics Handbook (McGraw-Hill, New York), p. 3-206
  50. Beyer, R. T., 1974, Non-Linear Acoustics (Naval Sea Systems Command Report, Washington, D.C.)
  51. Beyer, R. T., and M. S. Korman, 1980, "The scattering of sound by turbulence in water," J. Acoust. Soc. Am. 67, 1980
  52. Bies, D. A., 1962, "Tapering bar of uniform stress in longitudinal oscillation," J. Acoust. Soc. Am. 34, 1567
  53. Bjørnø, L., 1974, Finite amplitude wave effects in fluids (I.P.C. Science and Technology Press, Guildford, England)
  54. Bjørnø, L., and P. N. Larsen, 1984, "Noise of air jets from rectangular slits," Acustica 54, 247
  55. Blackstock, D. T., 1964, "Thermoviscous attenuation of plane, periodic, finite-amplitude sound waves," J. Acoust. Soc. Am. 36, 534
  56. Blackstock, D. T., 1965, "Connection between the Fay and Fubini solutions for plane sound waves of finite amplitude," J. Acoust. Soc. Am. 39, 1019
  57. Blackstock, D. T., 1972, "Nonlinear acoustics (theoretical)," in American Institute of Physics Handbook (McGraw-Hill, New York), p. 3-183
  58. Blanc-Benon, P., and D. Juvé, 1981a, "Effet d'un jet turbulent sur le niveau d'onde cohérente et sur l'intensité d'un faisceau acoustique," C. R. Acad. Sci. Ser. II 292, 493
  59. Blanc-Benon, P., and D. Juvé, 1981b, "Élargissement d'un faisceau ultrasonore par transversée d'un champ turbulent," C. R. Acad. Sci. Ser. II 292, 551
  60. Blanc-Benon, P., and D. Juvé, 1982a, "Coherence spatialle d'un faisceau ultrasonare après transversée d'une turbulence cinématique," C. R. Acad. Sci. Ser. II 294, 1221
  61. Blanc-Benon, P., and D. Juvé, 1982b, "Corrélations spatiotemporelles d'un faisceau après transversée d'une turbulence cinématique," C. R. Acad. Sci. Ser. II 294, 1255
  62. Blevins, R. D., 1984, "Review of sound induced by vortex shedding from cylinders," J. Sound Vib. 92, 455
  63. Blokhintsev, D. I., 1946, "The propagation of sound in an inhomogeneous and moving medium," J. Acoust. Soc. Am. 18, 322
  64. Bolza, O., 1904, Lectures on the Calculus of Variations (University of Chicago, Chicago)
  65. Bolza, O.Bonnet, R. M., and K. Dupree, 1980, Eds., Solar Phenomena in Stars and Stellar Systems (Reidel, Dordrecht)
  66. Born, M., and E. Wolf, 1959, Principles of Optics (Pergamon, New York; 6th ed. 1975)
  67. Bostrom, A., 1983, "Acoustics waves in a duct with periodically varying cross section," Wave Motion 5, 59
  68. Boussinesq, J., 1871, "Théorie de l'intumescence liquide, appelée onde solitaire ou de translation, se propageant dans un canal rectangulaire," C. R. Acad. Sci. 72, 755
  69. Bray, R. J., and R. E. Loughhead, 1974, The Solar Chromosphere (Chapman and Hall, London)
  70. Brekhovskikh, L. M., 1960, Waves in Layered Media (Academic, New York; 2nd ed. 1980)
  71. Brekhovskikh, L. M., and Y. P. Lysanov, 1982, Acoustic Propagation in the Ocean (Springer, Berlin)
  72. Bretherton, F. P., 1968, "Propagation in slowly varying waveguides," Proc. R. Soc. London, Ser. A 302, 555
  73. Bretherton, F. P., and C. J. R. Garrett, 1969, "Wavetrains in inhomogeneous moving media," Proc. R. Soc. London, Ser. A 302, 529
  74. Brillouin, L., 1926, "La mécanique ondulataire de Schrödinger: une méthode générale de solution par approximations successives," C. R. Acad. Sci. 183, 24
  75. Brindley, G. S., 1973, "Speed of sound in bent tubes and the design of wind instruments," Nature (London) 246, 479
  76. Broadbent, E. G., and D. W. Moore, 1979, "Acoustic destabilization of vortices," Philos. Trans. R. Soc. London 290, 353
  77. Brueckner, K. A., and S. Jorna, 1974, "Laser-driven fusion," Rev. Mod. Phys. 46, 325
  78. Bruzek, A., and C. J. Durrant, 1977, Glossary for Solar Physics (Reidel, Dordrecht)
  79. Bryan, G. H., 1918, "Compressible fluids," Aeron. J. 22, 255
  80. Bull, M. K., and M. P. Norton, 1980, "The proximity of coincidence and acoustic cut-off frequencies in relation to acoustic radiation from pipes with disturbed internal turbulent flow," J. Sound Vib. 69, 1
  81. Burgers, J. M., 1948, "A mathematical model illustrating the theory of turbulence," Adv. Appl. Math. 10, 171
  82. Burgers, J. M., 1974, The Non-Linear Diffusion Equation (Reidel, Dordrecht)
  83. Cabannes, H., 1970, Theoretical Magnetofluid-Dynamics (Academic, New York)
  84. Campos, L. M. B. C., 1977, "On the generation and radiation of magneto-acoustic waves," J. Fluid Mech. 81, 529
  85. Campos, L. M. B. C., 1978a, "On the emission of sound by an ionized inhomogeneity," Proc. R. Soc. London, Ser. A 359, 65
  86. Campos, L. M. B. C., 1978b, "The spectral broadening of sound by turbulent shear layers. Part I: Transmission of sound through turbulent shear layers," J. Fluid Mech. 89, 723
  87. Campos, L. M. B. C., 1978c, "The spectral broadening of sound by turbulent shear layers. Part II: Spectral broadening of sound and aircraft noise," J. Fluid Mech. 89, 751
  88. Campos, L. M. B. C., 1982, "On anisotropic, dispersive and dissipative wave equations," Portug. Math. 41, 13
  89. Campos, L. M. B. C., 1983a, "Modern trends in research on waves in fluids. Part I: Generation and scattering by turbulent and inhomogeneous flows," Portug. Phys. 11, 121
  90. Campos, L. M. B. C., 1983b, "On three-dimensional acoustic-gravity waves in model non-isothermal atmospheres," Wave Motion 5, 1
  91. Campos, L. M. B. C., 1983c, "On viscous and resistive dissipation of hydrodynamic and hydromagnetic waves in atmospheres," J. Méc. Théor. Appliq. 2, 861
  92. Campos, L. M. B. C., 1983d, "On the heating of the solar chromosphere by hydromagnetic waves with a five-minute period," Mem. Soc. Astrop. Ital. 55, 267
  93. Campos, L. M. B. C., 1983e, "On waves in non-isothermal, compressible, viscous and ionized atmospheres," Solar Phys. 82, 355
  94. Campos, L. M. B. C., 1983f, "On magnetoacoustic-gravity waves propagating or standing vertically in an atmosphere," J. Phys. A 16, 417
  95. Campos, L. M. B. C., 1983g, "Modern trends in research on waves in fluids. Part II. Propagation and dissipation in compressible and ionized atmospheres," Portug. Phys. 14, 145
  96. Campos, L. M. B. C., 1984a, "On some general properties of the exact acoustic fields in horns and baffles," J. Sound Vib. 95, 177
  97. Campos, L. M. B. C., 1984b, "On the propagation of sound in nozzles of strongly varying cross section containing a low-Mach-number mean flow," Z. Flugwiss. Weltraumf. 8, 97
  98. Campos, L. M. B. C., 1984c, "Sur la propagation du son dans les écoulements non-uniformes et non-stationaires," Rev. Acoust. 67, 217
  99. Campos, L. M. B. C., 1984d, "On a theory of solar spicules and the atmospheric mass balance," Mon. Not. R. Astron. Soc. 205, 547
  100. Campos, L. M. B. C., 1984e, "Mass and energy transfer by waves in atmosphere," in 25th Liège Astrophysics Symposium, edited by A. Noels and H. Gabriel (Liège University, Belgium), p. 393
  101. Campos, L. M. B. C., 1984f, "The effects of atmospheric disturbances on aircraft aerodynamics," J. R. Aeron. Soc. Paper 1085, June/July issue, p. 257
  102. Campos, L. M. B. C., 1984g, "On a concept of derivative of complex order with application to special functions," I.M.A. J. Appl. Math. 33, 109
  103. Campos, L. M. B. C., 1985a, "On the fundamental acoustic mode in variable-area, low-Mach-number nozzles," Prog. Aerosp. Sci. 22, 1
  104. Campos, L. M. B. C., 1985b, "On linear and non-linear wave equations for the acoustics of high-speed potential flows," J. Sound Vib. (to be published)
  105. Campos, L. M. B. C., 1985c, "On vertical hydromagnetic waves in a compressible atmosphere under an oblique magnetic field," J. Geophys. Astrophys. Fluid Dyn. 32, 217
  106. Campos, L. M. B. C., 1985d, "On longitudinal acoustic propagation in convergent and divergent nozzle flows," unpublished
  107. Campos, L. M. B. C., and J. F. P. G. Leitão, 1985, "On the computation of special functions with applications to waves in fluids," unpublished
  108. Candel, S. M., 1975, "Acoustic conservation principles and an application to plane and model propagation in nozzles and diffusers," J. Sound Vib. 41, 207
  109. Candel, S. M., 1983, "Sound source radiation in two-dimensional shear flow," Am. Inst. Aeron. Astron. J. 21, 221
  110. Candel, S. M., A. Guédel, and A. Julienne, 1976, "Refraction and scattering of sound in an open wind tunnel flow," in Proceedings of the 6th International Congress on Instrumentation in Aerospace Simulation Facilities, Ottawa; tiré à part 1975-79, Office National d'Études et de Recherches Aerospatiales (ONERA, Paris), p. 288
  111. Candel, S. M., A. Julienne, and M. Julliand, 1975, "Étude de l'effet de masque produit par un écran fluide," Société Nationale d' Étude et Construction de Moteurs d'Aviation (SNECMA), Villaroche, Paris, Fiche Tech. YKA-869
  112. Cantrell, R. H., and R. W. Hart, 1964, "Interaction between sound and flow in acoustic cavities: mass, momentum and energy considerations," J. Acoust. Soc. Am. 36, 697
  113. Carafoli, E., 1969, Wing Theory in Supersonic Flight (Pergamon, New York)
  114. Caratheodory, C., 1935, Calculus of Variations (Teubner, Leipzig; reprinted, Chelsea, New York, 1982)
  115. Caratheodory, C., 1950, Functions of a Complex Variable (Birkhauser, Basel; reprinted, Chelsea, New York, 1974)
  116. Cargill, A. M., 1982, "Low-frequency sound radiation and generation due to the interaction of unsteady flow with a jet pipe," J. Fluid Mech. 121, 59
  117. Carslaw, H. S., and J. C. Jaeger, 1946, Conduction of Heat in Solids (Oxford University, London; 2nd ed. 1959)
  118. Caussé, R., J. Kergomard, and X. Lurton, 1984, "Input impedance of brass musical instruments—comparison between experiment and numerical models," J. Acoust. Soc. Am. 75, 241
  119. Chandrasekhar, S., 1961, Hydrodynamic and Hydromagnetic Stability (Oxford University, London)
  120. Chandrasekhar, S., 1983, The Mathematical Theory of Black Holes (Oxford University, New York)
  121. Chandrasekhar, S., 1984, "On stars, their evolution and their stability," Rev. Mod. Phys. 56, 137
  122. Chang, P., W. K. Melville, and J. W. Miles, 1979, "On the evolution of a solitary wave in a gradually varying channel," J. Fluid Mech. 95, 401
  123. Chen, C. Y., 1977, "Predictions of aeroacoustic characteristics of coaxial jets," Am. Inst. Aeron. Astron. J. 15, 297
  124. Cheng, H., 1984, "An exact solvable non-linear partial differential equation with solitary-wave solutions," Stud. Appl. Math. 1, 183
  125. Chernov, L. A., 1967, Wave Propagation in a Random Medium (Dover, New York)
  126. Chester, W., and A. Moser, 1982, "On an equation which describes the resonant oscillations of a gas in an open-ended tube," Proc. R. Soc. London, Ser. A 380, 409
  127. Cho, Y. C., 1980, "Rigorous solution for sound radiation from circular ducts with hyperbolic horn or infinite plane baffle," J. Sound Vib. 69, 405
  128. Cho, Y. C., and K. Y. Ingard, 1983, "Mode propagation in non-uniform circular ducts with potential flow," Am. Inst. Aeron. Astron. J. 21, 970
  129. Clarke, R. H., 1973, "Theory of acoustic propagation in a variable ocean," Saclant A.S.W. Research Center, La Spezia, Italy, Memo SM-28
  130. Clebsch, A., 1857, "Über eine allgemeine transformation der hydrodynamischen Gleichungen," Crelle 64, 150
  131. Cole, J. D., 1950, "A quasilinear parabolic equation occurring in aerodynamics," Q. J. Appl. Math. 9, 225
  132. Cole, J. E., 1979, "Sound propagation in a duct with axial sound speed variation: an exact solution," J. Sound Vib. 63, 237
  133. Courant, R., and K. Friedrichs, 1948, Supersonic Flow and Shock Waves (Interscience, New York)
  134. Courant, R., and D. Hilbert, 1953, Methods of Mathematical Physics, 2 vols. (Academic, New York)
  135. Cowling, T. G., 1957, Magnetohydrodynamics (Interscience, New York; 2nd ed. 1980)
  136. Cowling, T. G., 1981, "Present status of dynamo theory," Annu. Rev. Astron. Astrophys. 19, 115
  137. Crandall, I. B., 1927, Theory of Vibrating Systems and Sound (MacMillan, London)
  138. Crighton, D. G., 1975, "Basic principles of aerodynamic noise generation," Prog. Aerosp. Sci. 16, 31
  139. Crighton, D. G., 1979, "Model equations for nonlinear acoustics," Annu. Rev. Fluid Mech. 11, 11
  140. Crighton, D. G., 1981, "Acoustics as a branch of fluid mechanics," J. Fluid Mech. 106, 261
  141. Crighton, D. G., 1984, "Transmission of energy down a periodically ribbed elastic structure under fluid loading," Proc. R. Soc. London, Ser. A 394, 405
  142. Crighton, D. G., and J. E. Ffowcs-Williams, 1969, "Sound generation by turbulent two-phase flow," J. Fluid Mech. 36, 585
  143. Crighton, D. G., and F. G. Leppington, 1973, "Singular perturbation methods in acoustics: diffraction by a plate of finite thickness," Proc. R. Soc. London, Ser. A 335, 313
  144. Crighton, D. G., and J. F. Scott, 1979, "Asymptotic solutions of model equations in non-linear acoustics," Philos. Trans. R. Soc. London, Ser. A 292, 101
  145. Crocco, L., and S. I. Cheng, 1967, Theory of Combustion Instability in Liquid Propellant Rocket Motors (Butterworths, London)
  146. Cummings, A., 1984, "Acoustic non-linearities and power losses at orfices," Am. Inst. Aeron. Astron. J. 22, 786
  147. Cummings, A., A. V. Parrett, and R. J. Astley, 1982, "A comparison of measured and computed sound pressure levels in a non-uniform acoustically lined duct," J. Sound Vib. 85, 407
  148. Curle, N., 1955, "The influence of solid boundaries upon aerodynamic sound," Proc. R. Soc. London, Ser. A 231, 505
  149. Curle, N., and H. J. Davies, 1968, Modern Fluid Mechanics (Van Nostrand, Princeton)
  150. Davies, P. O. A. L., 1981, "Flow-acoustic coupling in ducts," J. Sound Vib. 77, 191
  151. Davies, P. O. A. L., J. L. B. Coelho, and M. Bhattacharya, 1980, "Reflection coefficients for an unflanged pipe with flow," J. Sound Vib. 72, 543
  152. Deissler, R. G., 1984, "Turbulent solutions of the equations of fluid motion," Rev. Mod. Phys. 56, 223
  153. Deissler, R. G.Delloue, J., and P. Halley, 1972, Eds., Effects of Atmospheric Acoustic-Gravity Waves on Electromagnetic Wave Propagation, Advisory Group for Aerospace Research and Development, Paris, Conference Proceedings CP-115
  154. Denskat, K. U., and L. F. Burlaga, 1977, "Multi-spacecraft observations of microscale fluctuations in a solar wind," J. Geophys. Res. 82, 2693
  155. Dirac, P. A. M., 1927, Quantum Mechanics (Cambridge University, Cambridge, England; 4th ed. 1958)
  156. Disselhorst, J. H. M., and L. Van Wijngaarden, 1980, "Flow in the exit of open pipes during acoustic resonance," J. Fluid Mech. 99, 293
  157. Doppler, C., 1893, "Über das Farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels," Ostwarld Klass Exakt. Wiss. 161, 1
  158. Dowling, A. P., 1976, "Convective amplification of real simple sources," J. Fluid Mech. 74, 529
  159. Dowling, A. P., 1983, "Sound generation by turbulence near an elastic wall," J. Sound Vib. 90, 309
  160. Dowling, A. P., and J. E. Ffowcs-Williams, 1983, Sound and Sources of Sound (Harwood, London)
  161. Dowling, A. P., J. E. Ffowcs-Williams, and M. E. Goldstein, 1978, "Sound production in a moving stream," Philos. Trans. R. Soc. London, Ser. A 288, 321
  162. Drazin, P. G., 1984, Solitons (Cambridge University, Cambridge, England)
  163. Drazin, P. G., and W. H. Reid, 1981, Hydrodynamic Stability (Cambridge University, Cambridge, England)
  164. Duhamel, J. M. C., 1839, "Sur les vibrations des gas dans les tuyaux cylindriques, coniques, etc...." J. Math. Pures Appl. 14, 49
  165. Durbin, P. A., 1983a, "High-frequency Green's function for aerodynamic noise in moving media. Part I: General theory," J. Sound Vib. 91, 519
  166. Durbin, P. A., 1983b, "High-frequency Green's function for aerodynamic noise in moving media. Part II: Noise from a spreading jet," J. Sound Vib. 91, 527
  167. Eckart, C., 1960, Hydrodyanmics of Oceans and Atmospheres (Pegamon, London)
  168. Eddington, A. S., 1923, Mathematical Theory of Relativity (Cambridge University, Cambridge, England; 3rd ed. 1937; reprinted, Chelsea, New York, 1975)
  169. Eisenberg, N. A., and T. W. Kao, 1969, "Propagation of sound through a variable-area duct with a steady compressible flow," J. Acoust. Soc. Am. 49, 169
  170. Eisner, E., 1963, "Design of sonic amplitude transformers for high magnification," J. Acoust. Soc. Am. 35, 1367
  171. Eisner, E., 1964, "The design of resonant vibrators," in Physical Acoustics: Principle and Methods, 12 Vols., edited by W. P. Mason (Academic, New York), Vol. 1, p. 353
  172. Eisner, E., 1966, "Complete solutions of `Webster' horn equation," J. Acoust. Soc. Am. 41, 1126
  173. Eisner, E.Emmons, H. W., 1958, Ed., Fundamentals of Gas Dynamics, 8 vols. (Princeton University, Princeton, N.J.)
  174. Eisner, E.Erdelyi, A., 1953, Ed., Higher Transcendental Functions (McGraw-Hill, New York)
  175. Esclangon, E., 1917, "Réflexion et réfraction d'ondes acoustiques à la surface de séparation de deux fluides en repos ou en mouvement, dans l'acoustique des canons et des projectiles," C. R. Acad. Sci. 164, 99
  176. Esgolts, L., 1970, Differential Equations and the Calculus of Variations (Mir, Moscow)
  177. Essen, H. H., 1974, "Wave-facet interaction model applied to acoustic scattering by a rough sea surface," Acustica 31, 107
  178. Euler, L., 1759, "Supplément aux et continuation des recherches sur la propagation du son," Mem. Acad. Sci. Berlin 15 (1766), 210 (Opera Omnia, Teubner, Bern, Vol. 3, 1, p. 451)
  179. Euler, L., 1764, "De motu vibratorum cordarum inequaliter crassarum," Nov. Comm. Acad. Sci. Petr. 9, 246 (Opera Omnia, Vol. 2, 10, p. 293)
  180. Euler, L., 1766, "Recherches sur le mouvement des cordes inégalement grosses," Misc. Turnin. 3, 27 (Opera Omnia, Vol. 2, 10, p. 397)
  181. Euler, L., 1772, "De Motus Aeris tubis," Nov. Comm. Acad. Sci. Petr. 16, 281 (Opera Omnia, Vol. 2, 13b. p. 264)
  182. Euler, L., 1818, "Testamen novae theoricae musicae," Tip. Acad. Sci. Petr. (Opera Omnia, Vol. 3, 1, p. 197)
  183. Fabrikant, A. L., 1983, "Sound scattering by vortex flows," Akust. Zh. 29, 262
  184. Fanelli, M., A. Prosperetti, and M. Reali, 1984, "Shape oscillations of gas-vapour bubbles in liquids," Acustica 55, 213
  185. Ferraro, V. C. A., and C. Plumpton, 1958, "Hydromagnetic waves in an horizontally stratified atmosphere," Astrophys. J. 127, 149
  186. Ferraro, V. C. A., and C. Plumpton, 1963, An Introduction to Magneto-Fluid Dynamics (Oxford University, London; 2nd ed. 1966)
  187. Ffowcs-Williams, J. E., 1963, "The noise from turbulence convected at high speed," Philos. Trans. R. Soc. London, Ser. A 255, 471
  188. Ffowcs-Williams, J. E., 1964, "Sound production at the edge of a steady flow," J. Fluid Mech. 66, 791
  189. Ffowcs-Williams, J. E., 1969, "Hydrodynamic noise," Annu. Rev. Fluid Mech. 1, 197
  190. Ffowcs-Williams, J. E., 1984a, "The acoustic analogy thirty years on," I.M.A. J. Appl. Math. 32, 113
  191. Ffowcs-Williams, J. E., 1984b, "Anti-sound," Proc. R. Soc. London, Ser. A 395, 63
  192. Ffowcs-Williams, J. E., and D. L. Hawkins, 1968, "Sound generation by turbulence and surfaces in arbitrary motion," Philos. Trans. R. Soc. London, Ser. A 264, 321
  193. Ffowcs-Williams, J. E., and M. S. Howe, 1975, "The generation of sound by density inhomogeneities in low Mach number nozzle flows," J. Fluid Mech. 70, 605
  194. Ford, R. D., 1984, "Power requirement for active noise control in ducts," J. Sound Vib. 92, 411
  195. Fornberg, B., and G. B. Whitham, 1978, "A numerical and theoretical study of certain non-linear wave phenomena," Philos. Trans. R. Soc. London 289, 373
  196. Forsyth, A. R., 1885, Treatise on Differential Equations (MacMillan, London; 6th ed., 1929)
  197. Forsyth, A. R., 1926, Calculus of Variations (Cambridge University, Cambridge; reprinted, Dover, New York, 1960)
  198. Frank, N., and R. Von Mises, 1931, Differential- und Integral-gleichungen (Vieweg, Braunschweig; reprinted, Dover, New York, 1961)
  199. Franken, P. A., and U. Ingard, 1956, "Sound propagation in a moving medium," J. Acoust. Soc. Am. 27, 1044
  200. Francescutto, A., and R. Nabergoj, 1984, "A multiscale analysis of gas bubble oscillations: transient and steady-state solutions," Acustica 56, 12
  201. Freehafer, J. E., 1940, "Acoustical impedence of the infinite hyperbolic horn," J. Acoust. Soc. Am. 27, 1044
  202. Freeman, N. C., 1979, "A two-dimensional distributed soliton solution of the Korteweg-de Vries equation," Proc. R. Soc. London, Ser. A 366, 185
  203. Fuller, C. R., 1982, "Propagation and radiation of sound from flanged circular ducts with circumferentially-varying wall admittances," J. Sound Vib. 93, 341
  204. Fuller, C. R., and R. J. Silcox, 1984, "Experiments in sound radiation from a duct with a circumferentially varying liner," Am. Inst. Aeron. Astron. J. 22, 781
  205. Gabriel, A. H., 1976, "A magnetic model of the solar transition region," Philos. Trans. R. Soc. London, Ser. A 281, 339
  206. Gardner, C. S., J. M. Greene, M. D. Kruskal, and B. M. Miura, 1967, "Method for solving the Korteweg—de Vries equation," Phys. Rev. Lett. 19, 1095
  207. Gardner, C. S., J. M. Greene, M. D. Kruskal, and R. M. Miura, 1974, "Korteweg—de Vries equations and generalizations. VI: Methods for exact solution," Commun. Pure Appl. Math. 27, 97
  208. Garrett, C. J. R., 1967, "The adiabatic invariant for wave propagation in a non-uniform moving medium," Proc. R. Soc. London, Ser. A 299, 26
  209. Gazanhes, C., P. Arzeliés, and J. Léandre, 1984, "Propagation acoustique dans un milieu diphasique eau-bulles d'air; application à la caractérization d'un milieu diphasique par voie acoustique," Acustica 55, 113
  210. Gazanhes, C., and J. Léandre, 1974, "Propriétés statistiques d'une onde sonore diffusée par une surface aléatorie. Application à la réflexion sous-marine de surface," Acustica 30, 12
  211. Giovanelli, R. G., and J. M. Beckers, 1982, "Observations of Alfvén waves simultaneously in Hα and K," in Solar and Stellar Magnetic Fields: Origins and Coronal Effects, I.A.U. Symposium Number 102, edited by J. O. Stenflo (Reidel, Dordrecht), p. 407
  212. Glimm, J., G. Marshall, and B. Plohr, 1984, "A generalized Riemann problem for quasi-one-dimensional gas flows," Adv. Appl. Math. 5, 1
  213. Goldstein, M. E., 1976, Aeroacoustics (McGraw-Hill, New York)
  214. Goldstein, S., and N. W. McLachlan, 1935, "Sound waves of finite amplitude in the exponential horn," J. Acoust. Soc. Am. 6, 275
  215. Golub, L., R. Rosner, G. S. Vaiana, and N. O. Weiss, 1981, "Solar magnetic field: the generation of emerging flux," Astrophys. J. 243, 309
  216. Gossard, E. E., and W. Hooke, 1975, Waves in the Atmosphere (Elsevier, Amsterdam)
  217. Gottlieb, P., 1959, "Sound transmission through a fluid discontinuity," J. Acoust. Soc. Am. 31, 1036
  218. Green, G., 1837, "On the motion of waves in a variable canal of small depth and width," Proc. Cambridge Philos. Soc. 6, 457
  219. Greenspan, H. P., 1968, The Theory of Rotating Fluids (Cambrige University, Cambridge, England)
  220. Greenwood, J. A., 1984, "A unified theory of surface roughness," Proc. R. Soc. London, Ser. A 393, 133
  221. Grigoryan, F. E., 1984, "Theory of the circular waveguide with an abrupt change of cross section," Akust. Zh. 30, 39
  222. Grimshaw, R., 1981, "Slowly-varying solitary waves in deep fluids," Proc. R. Soc. London, Ser. A 376, 319
  223. Groen, P., 1948, "Contribution to the theory of internal waves," K. Ned. Akad. Met. Inst. 125b, 11
  224. Grosche, F. R., H. Stiewitt, and B. Binder, 1977, "Acoustic wind-tunnel measurements with a highly directional microphone," Am. Inst. Aeron. Astron. J. 15, 1590
  225. Guelfand, I. M., and G. Chilov, 1962-1970, Les Distributions, 5 vols. (Dunod, Paris)
  226. Haines, C. R., 1981, "A Wiener-Hopf approach to Kelvin wave generation by a semi-infinite barrier and depth discontinuity," Q. J. Mech. Appl. Math. 34, 139
  227. Hamilton, W. R., 1827-1832, "Theory of systems of rays" (with three supplements), Trans. R. Irish Acad. 15, 69 ibid.16, 1 ibid.17, 1
  228. Hanna, C. R., and J. Slepian, 1924, "The function and design of horns of loud-speakers," J. Acoust. Soc. Am. 6, 275
  229. Hansen, D. B., 1984, "Shielding of prop-pan cabin noise by the fuselage boundary layer," J. Sound Vib. 92, 591
  230. Hardin, J. C., and S. L. Lamkin, 1984, "Aeroacoustic computation of cylinder wake flow," Am. Inst. Aeron. Astron. J. 22, 51
  231. Hariharan, S. I., and H. C. Lester, 1984, "A finite difference solution for the propagation of sound in near-sonic flows," J. Acoust. Soc. Am. 75, 1052
  232. Hasan, M. A. Z., O. Islam, and A. K. M. F. Hussain, 1984, "Jet noise modification by the `Whistler nozzle,' " Am. Inst. Aeron. Astron. 22, 340
  233. Hasegawa, A., 1983, "Propagation of sound in acoustic slow waveguides," Acustica 52, 237
  234. Hayes, H., 1980, "Energy flux for trains of inhomogeneous plane waves," Proc. R. Soc. London, Ser. A 370, 417
  235. Hayes, W. D., 1958, "Gas dynamic discontinuities," in Fundamentals of Gas Dynamics, 8 vols., edited by H. W. Emmons (Princeton University, Princeton, N.J.), Sec. D., Vol. 3, p. 480
  236. Hayes, W. D., 1968, "Energy invariant for geometric acoustics in a moving medium," Phys. Fluids 11, 1654
  237. Hayes, W. D., 1973, "Sonic boom," Annu. Rev. Fluid Mech. 3, 269
  238. Heaviside, O., 1882, "Contributions to the theory of propagation of current in wires," Electrical Papers (MacMillan, London, 1892), Vol. 1, p. 141
  239. Heisenberg, W., 1924, "Über stabilitat und Turbulenz von Flussigkeitsstromen," Ann. Phys. Leipzig 74, 577 [National Advisory Committee on Aeronautics TM-1291 (1951)]
  240. Heisenberg, W., 1930, Physical Principles of Quantum Theory (University of Chicago, Chicago; reprinted, Dover, New York, 1949)
  241. Herlofson, N., 1950, "Waves in a compressible fluid conductor," Nature (London) 165, 1020
  242. Hermite, C., 1864, "Sur un nouveau développement en serie de fonctions," C.R. Acad. Sci. 53, 93, 266
  243. Heyvaerts, J., and E. R. Priest, 1983, "Coronal heating by phase-mixed Alfvén waves," Astron. Astrophys. 117, 220
  244. Hines, C. O., 1974, The Upper Atmosphere in Motion (American Geophysical Union, Washington, D.C.)
  245. Hinze, J. O., 1975, Turbulence (McGraw-Hill, New York)
  246. Ho, C. M., and L. S. G. Kovasznay, 1976a, "Propagation of a coherent acoustic wave through a turbulent shear flow," J. Acoust. Soc. Am. 60, 40
  247. Ho, C. M., and L. S. G. Kovasznay, 1976b, "Acoustical shadowgraph," Phys. Fluids 19, 1118
  248. Hoersch, V. A., 1925, "Non-radial harmonic vibrations within a conical horn," Phys. Rev. 25, 218
  249. Hollweg, J. V., 1972, "Supergranulation-driven Alfvén waves in the solar chromosphere and related phenomena," Cosmic Electrodyn. 2, 423
  250. Hoop, A. T., and J. H. M. T. Hijden, 1984, "Generation of acoustic waves by an impulsive point source in a fluid/solid configuration with a plane boundary," Am. Inst. Aeron. Astron. J. 75, 1709
  251. Hopf, E., 1951, "The partial differential equation ut+uux=uxx," Commun. Pure Appl. Math. 3, 201
  252. Howarth, L., 1953, Modern Developments in Fluid Mechanics: High-speed Flow (Oxford University, Oxford; 2nd ed., 1964)
  253. Howe, M. S., 1970, "Transmission of an acoustic pulse through a plane vortex sheet," J. Fluid Mech. 43, 353
  254. Howe, M. S., 1973a, "Kinetic theory of wave propagation in random media," Philos. Trans. R. Soc. London, Ser. A 274, 523
  255. Howe, M. S., 1973b, "Multiple scattering of sound by turbulence and other inhomogeneities," J. Sound Vib. 27, 455
  256. Howe, M. S., 1975a, "Contributions to the theory of aerodynamic sound, with applications to excess jet noise and the theory of the flute," J. Fluid Mech. 71, 625
  257. Howe, M. S., 1975b, "The generation of sound by aerodynamic sources in an inhomogeneous steady flow," J. Fluid Mech. 67, 597
  258. Howe, M. S., 1975c, "Application of energy conservation to the solution of radiation problems involving uniformly convected source distributions," J. Sound Vib. 43, 77
  259. Howe, M. S., 1976a, "The influence of vortex shedding on the generation of sound by convected turbulence," J. Fluid Mech. 76, 711
  260. Howe, M. S., 1976b, "The attenuation of sound by a randomly irregular impedance layer," Proc. R. Soc. London, Ser. A 347, 513
  261. Howe, M. S., 1978, "A review of trailing edge noise," J. Sound Vib. 61, 437
  262. Howe, M. S., 1979a, "The attenuation of sound by a low Mach number nozzle flow," J. Fluid Mech. 91, 209
  263. Howe, M. S., 1979b, "On the added mass of a perforated shell, with application to the generation of aerodynamic sound by a perforated trailing edge," Proc. R. Soc. London, Ser. A 365, 209
  264. Howe, M. S., 1979c, "A note on the interaction of unsteady flow with an acoustic liner," J. Sound Vib. 63, 429
  265. Howe, M. S., 1979d, "On the theory of unsteady high-Reynolds-number flow through a circular aperture," Proc. R. Soc. London, Ser. A 366, 205
  266. Howe, M. S., 1980, "On the diffraction of sound by a screen with circular apertures in the presence of a low Mach number grazing flow," Proc. R. Soc. London, Ser. A 370, 523
  267. Howe, M. S., 1981, "The role of displacement thickness fluctuations in hydroacoustics, and the jet-drive mechanism of the flue organ pipe," Proc. R. Soc. London, Ser. A 374, 543
  268. Howe, M. S., 1983a, "On the scattering of sound by a vortex ring," J. Sound Vib. 43, 77
  269. Howe, M. S., 1983b, "The attenuation of sound in a randomly lined duct," J. Sound Vib. 87, 83
  270. Howe, M. S., 1984a, "On the generation of sound by turbulent boundary layer over a rough wall," Proc. R. Soc. London, Ser. A 395, 247
  271. Howe, M. S., 1984b, "On the absorption of sound by turbulence and other hydrodynamic flows," I.M.A. J. Appl. Math. 32, 187
  272. Howe, M. S., and J. E. Ffowcs-Williams, 1978, "On the noise generated by an imperfectly expanded supersonic jet," Philos. Trans. R. Soc. London, Ser. A 289, 271
  273. Hudde, H., 1983, "Estimation of the area function of the human ear canals by sound pressure measurements," J. Acoust. Soc. Am. 73, 24
  274. Hudson, J. D., 1978, The Generation and Propagation of Waves in Elastic Solids (Cambridge University, Cambridge, England)
  275. Huerre, P., and K. Karamcheti, 1973, "Propagation of sound through a fluid moving in a duct of varying area," in University Research on Transportation Noise (Interagency Symposium, Stanford University), Vol. 2, p. 397
  276. Hunt, J. C. R., and J. A. Shercliff, 1971, "Magnetohydrodynamics at high Hartmann number," Annu. Rev. Fluid Mech. 3, 37
  277. Hurle, I. R., R. B. Price, T. M. Sugden, and H. Thomas, 1968, "Sound emission from open turbulent premixed flames," Proc. R. Soc. London, Ser. A 303, 409
  278. Ince, E. L., 1926, Ordinary Differential Equations (Longmans, Green, New York; reprinted, Dover, New York, 1956)
  279. Ingard, K. U., 1959, "Influence of fluid motion past a plane boundary on sound reflection, absorption and transmission," J. Acoust. Soc. Am. 31, 1035
  280. Ingard, K. U., 1983, "Acoustics in physics and engineering," Acustica 50, 127
  281. Ishimaru, A., 1978, Wave Propagation and Scattering in Random Media (Academic, New York)
  282. Ishizaka, K., M. Matsudaira, and T. Kaneko, 1976, "Input acoustic impedance measurement of the sub-glottal system," J. Acoust. Soc. Am. 60, 190
  283. Jackson, A. C., J. P. Butler, and R. W. Pyle, 1978, "Acoustic input impedance of excised dog lungs," J. Acoust. Soc. Am. 64, 1020
  284. Jacques, J. R., 1975, "The acoustic response of a nozzle flow to an externally applied low-frequency pressure field," J. Sound Vib. 41, 13
  285. Jansson, E. V., and A. H. Benade, 1974, "On plane and spherical waves in horns with non-uniform flare. II: Predictions and measurements of resonance frequencies and radiation losses," Acustica 31, 185
  286. Jeans, J., 1908, The Theory of Electricity and Magnetism (Cambridge University, Cambridge, England; 5th ed. 1932)
  287. Jeans, J., 1937, Science and Music (Cambridge University, Cambridge, England; reprinted, Dover, New York, 1968)
  288. Jeffrey, A., and T. Taniuti, 1964, Non-Linear Wave Propagation (Academic, New York)
  289. Jeffrey, A., and T. Taniuti, 1966, Magnetohydrodynamic Stability and Thermonuclear Containment (Academic, New York)
  290. Jeffreys, H., 1924, "On certain approximation solutions of linear differential equations of the second order," Proc. London Math. Soc. 23, 428
  291. Jeffreys, H., and B. S. Jeffreys, 1946, Methods of Mathematical Physics (Cambridge University, Cambridge, England; 3rd ed. 1956)
  292. Johnson, C. O., and R. I. Loehrke, 1984, "An experimental investigation of wake edge tones," Am. Inst. Aeron. Astron. J. 22, 1249
  293. Jones, D. S., 1966, Generalized Functions (McGraw-Hill, New York)
  294. Jones, D. S., 1968, Electromagnetic Theory (Pergamon, New York)
  295. Jones, D. S., 1973, "Diffraction by a thick semi-infinite plate," Proc. R. Soc. London, Ser. A 217, 153
  296. Jones, D. S., 1977, "The scattering of sound by a simple shear layer," Philos. Trans. R. Soc. London 284, 287
  297. Jones, D. S., and J. D. Morgan, 1972, "The instability of a vortex sheet on a subsonic stream under acoustic radiation," Proc. Cambridge Philos. Soc. 72, 465
  298. Jones, D. S., and J. D. Morgan, 1974, "A linear model of a finite amplitude Helmholtz instability," Proc. R. Soc. London, Ser. A 338, 17
  299. Jones, H., 1979, "The generation of sound by flames," Proc. R. Soc. London, Ser. A 367, 291
  300. Jordan, E. J., 1963, Loudspeakers (Focal Press, London)
  301. Kaiser, J. E., and A. H. Nayfeh, 1977, "A wave-envelope technique for wave propagation in non-uniform ducts," Am. Inst. Aeron. Astron. J. 15, 533
  302. Kamke, E., 1944, Differentialgleichungen (Teubner, Leipzig; reprinted, Chelsea, New York, 1971)
  303. Katz, J., and D. Lynden-Bell, 1982, "A Lagrangian for Eulerian fluid mechanics," Proc. R. Soc. London, Ser. A 381, 267
  304. Keefe, D. H., 1984, "Acoustical wave propagation in cylindrical ducts: transmission line parameter approximations for isothermal and non-isothermal boundary conditions," J. Acoust. Soc. Am. 75, 58
  305. Keller, J. B., 1955, "Reflection and transmission of sound by a moving medium," J. Acoust. Soc. Am. 27, 1044
  306. Keller, J. J., 1984, "Non-linear self-excited acoustic oscillations in cavities," J. Sound Vib. 94, 397
  307. Kelly, J. J., A. H. Nayfeh, and L. T. Watson, 1982, "Acoustic propagation in partially-choked converging-diverging ducts," J. Sound Vib. 81, 519
  308. Kelvin, Lord, 1880, "Vibrations of a columnar vortex," Philos. Mag. 10, 155
  309. Kempton, A. J., 1976, "The ambiguity of acoustic sources—a possibility for active control," J. Sound Vib. 48, 475
  310. Kergomard, J., 1981, "Ondes quasi-stationnaires dans les pavillons avec pertes visco-thermiques aux parois," Acustica 48, 31
  311. Kergomard, J., 1982, "Propagation des ondes dans les lignes finies: discussion des notions d'onde évanescente et de fréquence de coupure," Rev. Phys. Appl. 17, 307
  312. Khinchin, S. I., 1948, Mathematical Foundations of Statistical Mechanics (Dover, New York)
  313. Kinsler, L. E., and A. R. Frey, 1950, Fundamentals of Acoustics (Wiley, New York; 3rd ed. 1982)
  314. Klein, F., 1933, Vorlesungen über die hypergeometrische funktion (Teubner, Leipzig)
  315. Koch, W., and W. Möhring, 1983, "Eigensolutions for liners in uniform mean flow ducts," Am. Inst. Aeron. Astron. J. 21 200
  316. Kolmogorov, A. N., 1933, Foundations of the Theory of Probability (Springer, Berlin; reprinted, Chelsea, New York, 1950)
  317. Korteweg, D. J., and G. de Vries, 1895, "On the change of form of long waves advancing in a rectangular canal, and a new type of long stationary waves," Philos. Mag. 39, 422
  318. Kramers, H. A., 1926, "Wellenmechanik und halbzahlige Quantisierung," Z. Phys. 39, 828
  319. Krasnov, N. F., 1971, Aerodynamika (Vishaia Shkola, Moscow) (NASA technical translation F-265, Washington, 1978)
  320. Kraus, E. B., 1977, The Upper Layers of the Ocean (Oxford University, New York)
  321. Labonte, B. J., and R. Howard, 1982, "Torsional waves on the sun and the activity cycle," Solar Phys. 75, 161
  322. Lagrange, J. L., 1760, "Nouvelles recherches sur la nature et la propagation du son," Misc. Turin. 2, 11 (Oeuvres, Gauthier-Villars, Paris, Vol. 1, p. 151)
  323. Lamb, H., 1879, Hydrodynamics (Cambridge University, Cambridge, England, 6th ed., 1932)
  324. Lamb, H., 1910, "On the theory of waves propagated vertically in the atmosphere," Proc. London Math. Soc. 7, 122
  325. Lambert, R. F., 1954, "Acoustical studies of the tractrix horn," J. Acoust. Soc. Am. 26, 1024
  326. Landau, L. D., and E. F. Lifshitz, 1949, Mechanics (Pergamon, London)
  327. Landau, L. D., and E. F. Lifshitz, 1953, Fluid Mechanics (Pergamon, London)
  328. Landau, L. D., and E. F. Lifshitz, 1956, Electrodynamics of Continuous Media (Pergamon, London)
  329. Landau, L. D., and E. F. Lifshitz, 1966, Quantum Mechanics (Pergamon, New York)
  330. Landau, L. D., and E. F. Lifshitz, 1967a, Theory of Elasticity (Pergamon, New York)
  331. Landau, L. D., and E. F. Lifshitz, 1967b, Statistical Physics (Pergamon, New York)
  332. Laufer, J. and T. Yen, 1983, "Noise generation by a low Mach number jet," J. Fluid Mech. 134, 1
  333. Lavoie, J. L., T. J. Osler, and R. Tremblay, 1976, "Fractional derivatives and special functions," SIAM Rev. 18, 240
  334. Lehnert, B., 1954, "Magnetohydrodynamic waves under the action of the Coriolis force. I," Astrophys. J. 119, 647
  335. Lehnert, B., 1955, "Magnetohydrodynamic waves under the action of the Coriolis force. II," Astrophys. J. 120, 481
  336. Leppington, F. G., 1972, "Scattering of quadrupole sources near the end of a rigid semi-infinite circular pipe," Aeron. Res. Council CP-1195, Chap. 5
  337. Leppington, F. G., E. G. Broadbent, and K. H. Heron, 1984, "Acoustic radiation from rectangular panels with constrained edges," Proc. R. Soc. London, Ser. A 393, 67
  338. Leppington, F. G., and H. Levine, 1980, "Acoustics of a blocked duct with flow," J. Sound. Vib. 72, 303
  339. Leroy, B., 1980, "Propagation of waves in an atmosphere in the presence of a magnetic field: II. The reflection of Alfvén waves," Astron. Astrophys. 91, 136
  340. Leroy, B., 1982, "Propagation of waves in an atmosphere in the presence of a magnetic field: III. Alfvén waves in the solar atmosphere," Astron. Astrophys. 97, 245
  341. Lesser, M. B., and D. G. Crighton, 1975, "Physical acoustics and the method of matched asymptotic expansions," in Physical Acoustics: Principles and Methods, edited by W. P. Mason (Academic, New York), Vol. 11, p. 1
  342. Levine, A. H., 1975, "Acoustical diffraction radiation," Philips Res. Rep. 30, 240, 276
  343. Levine, A. H., 1978, Unidirectional Wave Motions (North-Holland, Amsterdam)
  344. Lighthill, M. J., 1952, "On sound generated aerodynamically: I. General theory," Proc. R. Soc. London, Ser. A 211, 564
  345. Lighthill, M. J., 1953, "On the energy scattered from the interaction of turbulence with sound and shock waves," Proc. Cambridge Philos. Soc. 44, 531
  346. Lighthill, M. J., 1954, "On sound generated aerodynamically. II: Turbulence as a source of sound," Proc. R. Soc. London, Ser. A 222, 1
  347. Lighthill, M. J., 1956, "Viscosity effects in sound waves of finite amplitude," in Surveys in Mechanics, edited by G. K. Batchelor and R. M. Davies (Cambridge University, Cambridge, England), p. 250
  348. Lighthill, M. J., 1958, Fourier Series and Generalized Functions (Cambridge University, Cambridge, England)
  349. Lighthill, M. J., 1960, "Studies in magnetohydrodynamic waves and other anisotropic wave motions," Philos. Trans. R. Soc. London, Ser. A 252, 397
  350. Lighthill, M. J., 1961, "Bakerian lecture: sound generated aerodynamically," Proc. R. Soc. London 267, 147
  351. Lighthill, M. J., 1963, "Jet noise," Am. Inst. Aeron. Astron. J. 1, 1587
  352. Lighthill, M. J., 1964, "Group velocity," J. Inst. Math. Appl. 1, 1
  353. Lighthill, M. J., 1969, "Dynamic response of the Indian ocean to the onset of the southwest monsoon," Philos. Trans. R. Soc. London, Ser. A 265, 45
  354. Lighthill, M. J., 1972, "Fourth annual Fairey lecture: the propagation of sound through moving fluids," J. Sound Vib. 24, 471
  355. Lighthill, M. J., 1975, Mathematical Biofluidmechanics (Society for Industrial and Applied Mathematics, Philadelphia)
  356. Lighthill, M. J., 1978a, Waves in Fluids (Cambridge University, Cambridge, England)
  357. Lighthill, M. J., 1978b, "Acoustic Streaming," J. Sound Vib. 61, 391
  358. Lighthill, M. J., 1981, "Energy flow in the cochlea," J. Fluid Mech. 106, 149
  359. Lilley, G. M., 1973, "On the noise from jets," AGARD Conference Proceedings CP-131, 13.1
  360. Lin, C. C., 1955, Theory of Hydrodynamic Stability (Cambridge University, Cambridge, England)
  361. Lindeberg, J. W., 1922, "Eine neue Erleitung der Exponential Gezetses in der Wahrscheinlichtkeitrechnung," Math. Z. 15, 211
  362. Lindzen, R. S., 1970, "Internal gravity waves in atmospheres with realistic dissipation and temperature," Geophys. Fluid Mech. 1, 303
  363. Liu, C. H., and L. Maestrello, 1975, "Propagation of sound through a real jet flowfield," Am. Inst. Aeron. Astron. J. 13, 66
  364. Long, D. F., and R. E. A. Arndt, 1984, "Jet noise at low Reynolds number," Am. Inst. Aeron. Astron. J. 22, 187
  365. Longuet-Higgins, M. S., 1964, "Planetary waves on a rotating sphere," Proc. R. Soc. London, Ser. A 279, 446
  366. Longuet-Higgins, M. S., 1968, "On the trapping of waves along a discontinuity of depth in a rotating ocean," J. Fluid Mech. 31, 417
  367. Love, A. E. H., 1927, Theory of Elasticity, 4th ed. (Cambridge University, Cambridge; reprinted, Dover, New York, 1944)
  368. Lumsdaine, E., and S. Ragab, 1977, "Effect of flow on quasi-one-dimensional acoustic wave propagation in a variable duct of finite length," J. Sound Vib. 53, 47
  369. Lundquist, S., 1949, "Experimental investigation of magnetohydrodynamic waves," Phys. Rev. 76, 1805
  370. Lynden-Bell, D., and J. Katz, 1981, "Isocirculational flows and their Lagrangian and energy principles," Proc. R. Soc. London, Ser. A 378, 179
  371. Lyons, P., and M. Yanowitch, 1974, "Vertical oscillations in a viscous and thermally conducting isothermal atmosphere," J. Fluid Mech. 66, 273
  372. Macaskill, C. C., and B. J. Uscinski, 1981, "Propagation in waveguides containing random irregularities: second moment equation," Proc. R. Soc. London, Ser. A 377, 73
  373. MacGregor, G. R., H. S. Ribner, and H. Lam, 1973, "Basic jet noise patterns after deletion of convection and rarefaction effects: experiment vs theory," J. Sound Vib. 27, 437
  374. Mach, E., 1926, The Principles of Physical Optics (Methuen, London; reprinted, Dover, New York, 1953)
  375. Mani, R., 1976a, "The influence of jet flow on jet noise. Part 1. The noise of unheated jets," J. Fluid Mech. 80, 321
  376. Mani, R., 1976b, "The influence of jet flow on jet noise. Part 2. The noise of heated jets," J. Fluid Mech. 73, 779
  377. Mani, R., 1980, "Sound propagation in parallel sheared flows in ducts: the mode estimation problem," Proc. R. Soc. London, Ser. A 371, 393
  378. Mani, R., 1981, "Low-frequency sound propagation in quasione-dimensional flow," J. Fluid Mech. 104, 81
  379. Marble, F. E., and S. M. Candel, 1977, "Acoustic disturbance from gas nonuniformities convected through a nozzle," J. Sound Vib. 55, 225
  380. Marble, F. E.S. M. CandelMason, W. P., 1964-1973, Ed., Physical Acoustics: Principles and Methods, 12 vols. (Academic, New York)
  381. Marble, F. E.S. M. CandelMassey, H., 1980, Ed., "The middle atmosphere as observed from balloons, rockets and satellites," Philos. Trans. R. Soc. London, Ser. A 296, 1
  382. Mawardi, O. K., 1949, "Generalized solutions of Webster horn theory," J. Acoust. Soc. Am. 57, 1030
  383. Maxwell, J. C., 1873, Treatise on Electricity and Magnetism, 2 vols. (Clarendon, Oxford; 3rd ed. 1891; reprinted, Dover, New York, 1954)
  384. McGowan, R. S., and R. S. Larson, 1984, "Relationship between static, flight and simulated flight jet noise measurements," Am. Inst. Aeron. Astron. J. 22, 460
  385. McIntyre, M. E., and T. N. Palmer, 1983, "Breaking planetary waves in the stratosphere," Nature (London) 305, 593
  386. McLachlan, N. W., 1934a, Bessel Functions for Engineers (Oxford University, London; 2nd ed. 1955)
  387. McLachlan, N. W., 1934b, Loudspeakers: Theory, Performance, Testing and Design (Oxford University, London)
  388. McLachlan, N. W., 1935, Elements of Loudspeakers Practice (Oxford University, London)
  389. McLachlan, N. W., 1936, The New Acoustics (Oxford University, London)
  390. McLachlan, N. W., and T. M. McKay, 1936, "Transient oscillations in a loud-speaker horn," Proc. Cambridge Philos. Soc. 32, 265
  391. Meecham, W. C., 1983, "Aerosound from corner flow and flap flow," Am. Inst. Aeron. Astron. J. 21, 228
  392. Melville, W. K., 1980, "On the Mach reflexion of a solitary wave," J. Fluid Mech. 98, 285
  393. Merkulov, L. G., 1957, "Design ultrasonic concentrators," Akust. Zh. 3, 230
  394. Merkulov, L. G., and A. V. Kharitonov, 1959, "Theory and analysis of sectional concentrators," Akust. Zh. 5, 183 (1959)
  395. Mermelstein, P., 1966, "Determination of the vocal tract shape from measured formant frequencies," J. Acoust. Soc. Am. 40, 1283
  396. Michalke, A., and U. Michel, 1979, "Prediction of jet noise in flight from static tests," J. Sound Vib. 67, 341
  397. Mihalas, D., and B. W. Mihalas, 1983, "On the propagation of acoustic waves in a radiating fluid," Astrophys. J. 273, 355
  398. Miles, J. H., 1981, "Acoustic transmission matrix of a variablearea duct or nozzle carrying a compressible mean flow," J. Acoust. Soc. Am. 64, 1186
  399. Miles, J. W., 1954, "Reflection of sound due to a change in cross section of a tube," J. Sound Vib. 26, 14
  400. Miles, J. W., 1957, "On the reflection of sound at an interface of relative motion," J. Acoust. Soc. Am. 29, 226
  401. Miles, J. W., 1958, "On the disturbed motion of a vortex sheet," J. Fluid Mech. 4, 538
  402. Miles, J. W., 1959, The Potential Theory of Unsteady Supersonic Flow (Cambridge University, Cambridge, England)
  403. Miles, J. W., 1972, "Kelvin waves on oceanic boundaries," J. Fluid Mech. 55, 113
  404. Miles, J. W., 1981, "The Korteweg—de Vries equation: a historical essay," J. Fluid Mech. 106, 131
  405. Milne-Thomson, L. M., 1938, Theoretical Hydrodynamics (Mac-Millan, London; 5th ed. 1968)
  406. Milne-Thomson, L. M., 1958, Theoretical Aerodynamics (Mac-Millan, London; reprinted, Dover, New York, 1966)
  407. Misner, C. W., K. S. Thorne, and J. A. Wheeler, 1973, Gravitation (Freeman, San Francisco)
  408. Mobbs, S. D., 1982, "Variational principles for perfect and dissipative fluid systems," Proc. R. Soc. London, Ser. A 381, 457
  409. Moffat, H. K., 1976, "Generation of magnetic fields by fluid motion," Adv. Appl. Mech. 16, 119
  410. Moffatt, H. K., 1978, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University, Cambridge, England)
  411. Moffatt, H. K.Moffatt, H. K., and M. R. E. Proctor, 1982, Eds., Metallurgical Applications of Magnetohydrodynamics, proceedings of the International Union of Theoretical and Applied Mechanics Symposium, Cambridge (Metals Society, London, 1984)
  412. Möhring, W., 1971, "Energy flux in duct flow," J. Sound Vib. 18, 101
  413. Möhring, W., 1978a, "On vortex sound at low Mach number," J. Fluid Mech. 85, 685
  414. Möhring, W., 1978b, "Acoustic energy flux in non-homogeneous ducts," J. Acoust. Soc. Am. 64, 1186
  415. Möhring, W., 1980, "Acoustic momentum and energy theorems for piecewise uniform ducts," J. Acoust. Soc. Am. 67, 1463
  416. Möhring, W., E. A. Müller, and F. Obermeier, 1983, "Problems in flow acoustics," Rev. Mod. Phys. 55, 707
  417. Möhring, W., and S. Rahman, 1976, "The influence of perturbations of the velocity and speed of sound on the propagation of sound waves in ducts," Am. Inst. Aeron. Astron. Paper 76-493
  418. Moir, J., 1961, High-Quality Sound Reproduction (Chapman and Hall, London)
  419. Møller, C., 1952, The Theory of Relativity (Oxford University, London; 2nd ed. 1972)
  420. Molloy, C., 1975, "N-parameter ducts," J. Acoust. Soc. Am. 57, 1030
  421. Moore, C. J., 1979, "The role of shear-instability waves in jet exhaust noise," J. Fluid Mech. 80, 321
  422. Moore, D. W., and E. A. Spiegel, 1964, "The generation and propagation of waves in a compressible atmosphere," Astrophys. J. 139, 48
  423. Moorhem, W. K., and G. K. Landheim, 1984, "Propagation of plane waves in a thermally stratified atmosphere," J. Acoust. Soc. Am. 76, 867
  424. Morfey, C. L., 1971, "Sound transmission and generation in ducts with flow," J. Sound Vib. 14, 37
  425. Morfey, C. L., 1973, "Amplification of aerodynamic noise by convected flow inhomogeneities," J. Sound Vib. 31, 391
  426. Morse, P. M., and H. Feshbach, 1953, Methods of Theoretical Physics (McGraw-Hill, New York)
  427. Morse, P. M., and K. U. Ingard, 1968, Theoretical Acoustics (McGraw-Hill, New York)
  428. Mortell, M. P., and B. R. Seymour, 1979, "Non-linear forced oscillations in a closed tube: continuous solutions of a functional equation," Proc. R. Soc. London, Ser. A 367, 253
  429. Mowbray, D. E., and B. S. H. Rarity, 1967, "A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified fluid," J. Fluid Mech. 28, 1
  430. Mungur, P., and H. E. Plumblee, 1969, "Propagation and attenuation of sound in a soft-walled annular duct containing a sheared flow," NASA SP-207, p. 305
  431. Munt, R. M., 1977, "The interaction of sound with a subsonic jet issuing from a semi-infinite pipe," J. Fluid Mech. 83, 609
  432. Myers, M. K., 1980, "On the acoustic boundary condition in the presence of flow," J. Sound Vib. 71, 429
  433. Myers, M. K., and A. J. Callegari, 1972, "On the singular behavior of linear acoustic theory in near-sonic flows," J. Sound Vib. 51, 517
  434. Myers, M. K., and S. L. Chuang, 1984, "Uniform asymptotic expansions for duct acoustic modes in a thin boundary-layer flow," Am. Inst. Aeron. Astron. J. 22, 1234
  435. Nagarkar, B. N., and R. D. Finch, 1971, "Sinusoidal horns," J. Acoust. Soc. Am. 50, 23
  436. Nagel, R. T., J. W. Denham, and A. G. Papathanasiou, 1983 "Supersonic jet screech tone cancellation," Am. Inst. Aeron. Astron. J. 21, 1541
  437. Namba, M., and K. Fukushige, 1980, "The application of the equivalent source method to the acoustics of duct systems with non-uniform wall impedance," J. Sound Vib. 73, 125
  438. Namba, M., T. Notomi, and T. Fujimoto, 1984, "Analysis of sound attenuation in a duct with a solid or porous splitter," J. Sound Vib. 92, 47
  439. Nayfeh, A. H., 1973, Perturbation Methods (Wiley, New York; 2nd ed. 1982)
  440. Nayfeh, A. H., 1975a, "Acoustic waves in a duct with sinusoidally perturbed walls and mean flow," J. Acoust. Soc. Am. 57, 1036
  441. Nayfeh, A. H., 1975b, "Finite-amplitude plane waves in ducts with varying properties," J. Acoust. Soc. Am. 57, 1413
  442. Nayfeh, A. H., J. E. Kaiser, R. L. Marshall, and C. J. Hurst, 1980, "A comparison of experiment and theory for sound propagation in variable-area ducts," J. Sound Vib. 71, 241
  443. Nayfeh, A. H., J. E. Kaiser, and D. P. Telionis, 1975a, "Acoustics of aircraft engine-duct systems," Am. Inst. Aeron. Astron. J. 13, 130
  444. Nayfeh, A. H., J. E. Kaiser, and D. P. Telionis, 1975b, "Transmission of sound through annular ducts of varying cross sections," Am. Inst. Aeron. Astron. J. 13, 60
  445. Nayfeh, A. H., J. J. Kelly, and L. T. Watson, 1982, "Propagation of spinning acoustic modes in partially-chocked converging ducts," J. Acoust. Soc. Am. 71, 796
  446. Nayfeh, A. H., B. S. Shaker, and J. E. Kaiser, 1980, "Transmission of sound through non-uniform circular ducts with compressible mean flows," Am. Inst. Aeron. Astron. J. 18, 515
  447. Newton, I., 1686, Principia (Pepys, London; reprinted, Dover, New York, 1934), 2 vols
  448. Noble, B., 1958, The Wiener-Hopf Technique (Oxford University, London)
  449. Norum, T. D., 1984, "Screech suppression in supersonic jets," Am. Inst. Aeron. Astron. J. 21, 235
  450. Ockendon, H., and D. A. Spence, 1969, "Non-linear wave propagation in a relaxing gas," J. Fluid Mech. 39, 329
  451. Oldham, K. B., and J. Spanier, 1974, The Fractional Calculus (Academic, New York)
  452. Olson, H. F., 1938, "A horn consisting of manifold exponential sections," J. Soc. Motion Pict. Eng. 30, 511
  453. Olson, H. F., 1940, Elements of Acoustic Engineering (Van Nostrand, Princeton)
  454. Olson, H. F., 1952, Music, Physics and Engineering (Dover, New York; 2nd ed. 1967)
  455. Olson, H. F., 1972, Modern Sound Production (Van Nostrand, Princeton)
  456. Olson, H. F., and I. Wolff, 1930, "A sound concentrator for microphones," J. Acoust. Soc. Am. 1, 410
  457. Olson, H. F., and F. Massa, 1934, Applied Acoustics (Blakiston, Philadelphia)
  458. Ono, H., 1975, "Algebraic solitary waves in stratified fluids," J. Phys. Soc. Jpn. 39, 1082
  459. Orr, W. M., 1907, "The stability or instability of steady motions of a perfect liquid and a viscous liquid," Proc. R. Irish Acad., Sec. A 27, 9
  460. Osborne, A. R., and T. L. Burch, 1980, "Internal solitons in the Andaman sea," Science 208, 451
  461. Page, N. W., and D. J. Mee, 1984, "Wall effects on sound propagation in tubes," J. Sound Vib. 93, 473
  462. Page, N. W.D. J. MeePao, Y. H., and A. Goldburg, 1969, Eds., Clear Air Turbulence and its Detection (Plenum, New York)
  463. Parker, E. N., 1979, Cosmical Magnetic Fields (Clarendon, London)
  464. Parodi, M., 1945, "Propagation sur une ligne électrique sans pertes, dont les paramètres lineiques sont des fonctions exponentielles du carré de l'espace," J. Phys. (Paris) 6, 331
  465. Pars, L. A., 1960, Calculus of Variations (Heinemann, London)
  466. Pauling, L., and E. B. Wilson, 1935, Introduction to Quantum Mechanics (McGraw-Hill, New York)
  467. Paynter, H. M., and F. D. Ezekiel, 1958, "Water hammer in non-uniform pipes as an example of wave propagation in gradually varying media," Trans. Am. Soc. Mech. Eng. 80, 1585
  468. Péclet, E., 1843, Traité de la Chaleur Considerée dans ses Applications, 3 vols. (Hachette, Paris)
  469. Pedley, T. J., 1980, The Fluid Mechanics of Large Blood Vessels (Cambridge University, Cambridge, England)
  470. Pedlosky, J., 1960, Geophysical Fluid Dynamics (Springer, Berlin; 2nd ed. 1979)
  471. Peixoto, J. P., and A. H. Oort, 1984, "Physics of climate," Rev. Mod. Phys. 56, 365
  472. Peregrine, D. H., and R. Smith, 1979, "Non-linear effects of waves near caustics," Philos. Trans. R. Soc. London, Ser. A 292, 341
  473. Perulli, M., 1979, "Propagation acoustique dans les conduits," AGARD Report 686, Chap. 6
  474. Peube, T. L., and J. Chasseriaux, 1973, "Non-linear acoustics in ducts with varying cross section," J. Sound Vib. 27, 533
  475. Philips, O. M., 1960a, The Dynamics of the Upper Ocean (Cambridge University, Cambridge, England; 2nd ed. 1976)
  476. Philips, O. M., 1960b, "On the generation of sound by supersonic turbulent shear layers," J. Fluid Mech. 9, 1
  477. Pickering, W. M., and C. Sozou, 1982, "The axisymmetric flow field induced by a point force in the presence of a plane wall," Proc. R. Soc. London, Ser. A 380, 349
  478. Pierce, A. D., 1981, Acoustics (McGraw-Hill, New York)
  479. Pinker, R. A., and W. D. Bryce, 1976, "The radiation of plane wave duct noise from jet exhausts, statically and in flight," Am. Inst. Aeron. Astron. Paper 76-581
  480. Plumblee, H. E., and P. D. Dean, 1983, "Sound measurements within and in the radiated field of an annular duct with flow," J. Sound Vib. 28, 715
  481. Plumblee, H. E., P. D. Dean, G. A. Wynne, and R. H. Burrin, 1973, "Sound propagation in and radiation from acoustically-lined flow ducts: a comparison of experiment and theory," NASA CR-2306
  482. Pochhammer, L., 1876, "Über die Fortplanzungsgeschwindigkeiten der Schwingungen in einem unbegrentzen isotropen Kreiscylinder," Crelle 81, 324
  483. Poirée, B., 1982, "Équations de perturbations et équations de passage associés: application au dioptre acoustique," thèse doctorale (Université de Paris VI), p. 113
  484. Poisson, S. D., 1807, "Mémoire sur la theorie du son," J. E. Polytech. 7, 367
  485. Poisson, S. D., 1817, "Sur les mouvements des fluides élastiques dans les tuyaux cylindriques, et sur la théorie des instruments à vent," Mem. Acad. Sci. 2, 305
  486. Poole, E. G. C., 1936, Linear Differential Equations (Oxford University, Oxford; reprinted, Dover, New York, 1960)
  487. Powell, A., 1959, "Propagation of a pressure pulse in a compressible flow," J. Acoust. Soc. Am. 31, 1527
  488. Powell, A., 1960, "Theory of sound propagation through ducts carrying high-speed flows," J. Acoust. Soc. Am. 32, 1640
  489. Powell, A., 1961, "Vortex sound," University of California, Los Angeles, Department of Engineering Report 61-70
  490. Powell, A., 1964, "Theory of vortex sound," J. Acoust. Soc. Am. 36, 177
  491. Prandtl, L., and O. G. Tietjens, 1934, Applied Hydro- and Aeromechanics, 2 vols. (McGraw-Hill, New York; reprinted, Dover, New York, 1957)
  492. Prasad, M. G., and M. J. Crocker, 1984, "A note on the propagation of acoustic plane waves in a uniform pipe with mean flow," J. Sound Vib. 92, 284
  493. Prasad, P., 1973, "Non-linear wave propagation on an arbitrary steady transonic flow," J. Fluid Mech. 57, 721
  494. Priest, E. R., 1982, Solar Magnetohydrodynamics (Reidel, Dordrecht)
  495. Pridmore-Brown, D. C., 1959, "Sound propagation in a fluid flowing through an attenuating duct," J. Fluid Mech. 4, 393
  496. Pyle, R. W., 1965, "Duality principle for horns," J. Acoust. Soc. Am. 37, 1187A
  497. Pyle, R. W., 1967, "Solid torsional horns," J. Acoust. Soc. Am. 41, 1147
  498. Quinn, M. C., and M. S. Howe, 1984, "The influence of mean flow on the acoustic properties of a tube bank," Proc. R. Soc. London, Ser. A 396, 383
  499. Quinn, T. J., A. R. Collough, and T. R. D. Chandler, 1976, "A new determination of the gas constant by an acoustical method," Philos. Trans. R. Soc. London, Ser. A 283, 367
  500. Rabinovich, M. I., V. P. Reutov, and G. V. Rybushkina, 1984, "Dipole acoustic radiation from a turbulent boundary layer on a rigid surface with a geometrical irregularity," Akust. Zh. 30, 105
  501. Rae, I. C., and B. Roberts, 1983, "MHD wave motion in magnetically structured atmospheres," Solar Phys. 84, 99
  502. Raiser, Y. P., and Y. B. Zel'dovich, 1966-1967, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, 2 vols. (Academic, New York)
  503. Ramachandra, M. K., and W. C. Strahle, 1983, "Acoustic signature from flames as a combustion diagnostic tool," Am. Inst. Aeron. Astron. J. 21, 1107 [Rayleigh Papers, 6 vols. (Cambridge University, Cambridge, 1899-1920; reprinted, Dover, New York, 1964, 3 vols.), Vol. 1, p. 33]
  504. Rayleigh, J. W. S., 1868, "On the theory of resonance," Philos. Trans. R. Soc. London 159, 77
  505. Rayleigh, J. W. S., 1873, "Note on a natural limit to the sharpness of spectral lines," Nature 8, 474 (Papers, Vol. 1, p. 83)
  506. Rayleigh, J. W. S., 1876, "On waves," Philos. Mag. 1, 257 (Papers, Vol. 1, p. 251)
  507. Rayleigh, J. W. S., 1879, The Theory of Sound, 2 vols. (MacMillan, London; reprinted, Dover, New York, 1945)
  508. Rayleigh, J. W. S., 1880, "On the stability or instability, of certain fluid motions," Proc. London Math. Soc. 11, 57 (Papers, Vol. 1, p. 474)
  509. Rayleigh, J. W. S, 1887, "On the instability of jets II," Proc. London Math. Soc. 19, 67 (Papers, Vol. 3, p. 17)
  510. Rayleigh, J. W. S., 1889, "On the limit to interference when light is emitted from moving molecules," Philos. Mag. 27, 298 (Papers, Vol. 3, p. 258)
  511. Rayleigh, J. W. S., 1890, "On the vibrations of an atmosphere," Philos. Mag. 29, 173 (Papers, Vol. 3, p. 335)
  512. Rayleigh, J. W. S., 1915, "On the widening of spectral lines," Philos. Mag. 29, 274 (Papers, Vol. 6, p. 291)
  513. Rayleigh, J. W. S., 1916, "On the propagation of sound in narrow tubes of variable section," Philos. Mag. 31, 89 (Papers, Vol. 6, p. 376)
  514. Reitz, J. R., and F. J. Milford, 1967, Foundations of Electromagnetic Theory (Addison-Wesley, Reading, Mass.)
  515. Reynolds, O., 1883, "An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and the law of resistance in parallel channels," Philos. Trans. R. Soc. London 156, 935
  516. Ribe, F. L., 1975, "Fusion reactor systems," Rev. Mod. Phys. 46, 325
  517. Ribner, H. S., 1957, "Reflection, transmission and amplification of sound by a moving medium," J. Acoust. Soc. Am. 29, 435
  518. Riemann, B., 1860, "Uber die Fortpflanzung Evener Luftwellen von Endlicher Schwingunsweite," Ges. Werke, p. 156
  519. Rienstra, S. W., 1981, "Sound diffraction at a trailing edge," J. Fluid Mech. 108, 443
  520. Rienstra, S. W., 1984, "Acoustic radiation from a semi-infinite duct," J. Sound Vib. 94, 267
  521. Roberts, B., and A. Mangeney, 1982, "Solitons in a magnetic flux tube," Mon. Not. R. Astron. Soc. 198, 7p
  522. Roberts, P. H., 1971, "Dynamo theory," in Mathematical Problems in the Geophysical Sciences, edited by W. H. Reid (American Mathematical Society, Providence, Rhode Island), p. 126
  523. Roberts, P. H.Ross, B., 1975, Ed., Fractional Calculus and its Applications, Proceedings of the New International Conference, New Haven, June, 1974 (Springer, Berlin), Lecture Notes in Mathematics, Vol. 457
  524. Ross, B., 1981, "Spectral broadening effects in open wind tunnels in relation to noise assessment," Am. Inst. Aeron. Astron. J. 19, 567
  525. Rossby, C. G., 1939, "Relation between variations in the intensity of zonal circulation of the atmosphere and the displacement of semi-permanent centers of action," J. Mar. Res. 2, 38
  526. Rossby, C. G.R. T. BeyerRudenko, O. V., and S. I. Soluyan, 1975, Eds., Theoretical Foundations of Nonlinear Acoustics (Nauka, Moscow) [translation by , Plenum, New York (1977)]
  527. Rudnick, I., 1946, "Acoustic transmission through a fluid lamina," J. Acoust., Soc. Am. 17, 245
  528. Russel, J. S., 1845, "Reports on waves," British Assoc. Rep. 13, 311
  529. Salikuddin, M., and P. Mungur, 1983, "Acoustic radiation impedance of a duct-nozzle system," J. Sound Vib. 86, 497
  530. Salmon, V., 1946a, "A new family of horns," J. Acoust. Soc. Am. 17, 212
  531. Salmon, V., 1946b, "Generalized plane wave horn theory," J. Acoust. Soc. Am. 17, 199
  532. Schiff, L. I., 1949, Quantum Mechanics (McGraw-Hill, New York; 3rd ed. 1968)
  533. Schlichting, H., 1933, "Zur entstehung der Turbulenz bei der platten-stromung," Nachr. Ges. Wiss. Goettingen Math. Phys. K1. 181
  534. Schlichting, H., G. Breun1951, Boundary Layer Theory (G. Braunsche, Karlsruhe) [translation of 7th ed. by , McGraw-Hill, New York (1970)]
  535. Schlichting, H., and E. Truckenbrodt, 1979, Aerodynamics of the Airplane (McGraw-Hill, New York)
  536. Schmidt, D. W., and P. M. Tillmann, 1970, "Experimental study of sound phase fluctuations caused by turbulent wakes," J. Acoust. Soc. Am. 47, 1310
  537. Schroeder, M. R., 1967, "Determination of the shape of the human vocal tract by acoustic measurements," J. Acoust. Soc. Am. 41, 1002
  538. Schulten, J. B. H. M., 1984, "Vane stagger angle and camber effects in fan noise generation," Am. Inst. Aeron. Astron. J. 22, 1071
  539. Schwarzschild, M., 1958, Structure and Evolution of Stars (Princeton University, Princeton, N.J.; reprinted, Dover, New York, 1965)
  540. Schwartz, L., 1949, Théorie des Distributions (Hermann, Paris)
  541. Schwartz, R. F., 1974, "Transformations in the analysis of non-uniform transmission lines," J. Franklin Inst. 278, 163
  542. Scott, J. F., 1981, "Uniform asymptotics for spherical and cylindrical nonlinear acoustic waves generated by a sinusoidal source," Proc. R. Soc. London, Ser. A 375, 211
  543. Scott, J. F., 1982, "The non-linear propagation of acoustic noise," Proc. R. Soc. London, Ser. A 383, 55
  544. Seeliger, R. L., and G. B. Whitham, 1968, "Variational principles in continuum mechanics," Proc. R. Soc. London, Ser. A 305, 1
  545. Seiner, J. M., and J. C. Yu, 1984, "Acoustic near-field properties associated with broadband shock noise," Am. Inst. Aeron. Astron. J. 22, 1207
  546. Seymour, B. R., and M. P. Mortell, 1980, "A finite-rate theory of resonance in a closed tube: discontinuous solutions of a functional equation," J. Fluid Mech. 99, 365
  547. Shapiro, A. H., 1954, The Dynamics and Thermodynamics of Compressible Fluid Flow, 2 vols. (Ronald, New York)
  548. Shaw, E. A. G., 1970, "Acoustic horns with spatially varying density or elasticity," J. Acoust. Soc. Am. 50, 830
  549. Shercliff, J. A., 1965, Textbook of Magnetohydrodynamics (Pergamon, London)
  550. Shermann, A., and G. W. Sutton, 1965, Engineering Magnetohydrodynamics (McGraw-Hill, New York)
  551. Sholnik, M. I., 1962, Introduction to Radar Systems (McGraw-Hill, New York)
  552. Silcox, R. J., 1984, "Geometry and static flow effects on acoustic radiation from ducts," Am. Inst. Aeron. Astron. J. 22, 1087
  553. Silcox, R. J., and H. C. Lester, 1982, "Sound propagation through a variable-area duct: experiment and theory," Am. Inst. Aeron. Astron. J. 20, 1377
  554. Sinai, Y. L., 1981, "Two-dimensional acoustic wave propagation in elastic ducts," J. Sound Vib. 74, 519
  555. Sneddon, I. N., 1972, The Use of Integral Transforms (McGraw-Hill, New York)
  556. Sobolev, A. F., 1982, "Sound radiation from a cylindrical duct with impedance walls," Sov. Phys. Acoust. 29, 310
  557. Sommerfeld, A., 1896, "Mathematical theorie der Diffraction," Math. Ann. 67, 317
  558. Sommerfeld, A., 1908, "Eine Beitrag zur hydrodynamischen Erklaerung der turbulenten Fluessigkeits bewegungen," in Atti del IV Congresso Internazionali dei Matematici, edited by G. Castelnuovo (Tipografia della Reale Academia dei Lincei, Roma, 1909), Vol. 3, p. 116
  559. Sornette, D., and M. Lagier, 1984, "Nature monopolaire du rayonnement acoustique engendré par les écoulements instables," Acustica 55, 255
  560. Spitzer, L., 1956, Physics of Fully Ionized Gases (Interscience, New York)
  561. Spruit, H. C., and B. Roberts, 1984, "Magnetic flux tubes on the sun," Nature 304, 401
  562. Stein, R. F., 1967, "The generation of acoustic and acoustic-gravity waves by turbulence in an isothermal stratified atmosphere," Solar Phys. 2, 385
  563. Stein, R. F.Stenflo, J. O., 1982, Ed., Solar and Stellar Magnetic Fields: Origins and Coronal Effects (Reidel, Dordrecht)
  564. Stevenson, A. F., 1951a, "General theory of electromagnetic horns," J. Appl. Phys. 22, 1447
  565. Stevenson, A. F., 1951b, "Exact and approximate solutions for wave propagation in acoustic horns," J. Appl. Phys. 21, 1461
  566. Stevin, G. O., 1984, "A computational model of the ear reflex," Acustica 55, 277
  567. Stewart, G. W., 1920, "The performance of conical horns," Phys. Rev. 16, 313
  568. Stix, T. H., 1962, The Theory of Plasma Waves (McGraw-Hill, New York)
  569. Stoker, J. J. 1953, Water Waves (Interscience, New York)
  570. Stollery, J. L., A. G. Gaydon, and P. R. Owen, 1971, Shock Tube Research (Chapman and Hall, London)
  571. Stone, J. R., D. E. Groesbeck, and C. L. Zola, 1983, "Conventional profile coaxial jet noise prediction," Am. Inst. Aeron. Astron. J. 21, 336
  572. Stratton, J. A., 1941, Electromagnetic Theory (McGraw-Hill, New York)
  573. Strouhal, V., 1878, "Reibungstöne," Ann. Phys. Chem. (Wied. Ann.) 5, 216
  574. Sunyach, M., D. Juvé, and G. Comte-Bellot, 1982, "Acoustics of turbulent flows: a report on Euromech 142," J. Fluid Mech. 122, 511
  575. Swinbanks, M. A., 1973, "The active control of sound propagation in long ducts," J. Sound Vib. 27, 441
  576. Swinbanks, M. A., 1975, "Sound field generated by a source distribution in a long duct carrying sheared flow," J. Sound Vib. 40, 51
  577. Synge, J. L., 1960, Relativity: The General Theory (North-Holland, Amsterdam)
  578. Tatarski, V. I., 1971, Wave Propagation in a Turbulent Medium (Dover, New York)
  579. Taylor, G. I., 1910, "The conditions necessary for discontinuous motions in gases," Proc. R. Soc. London, Ser. A 84, 371
  580. Taylor, K., 1978, "A transformation of the acoustic equation with implications for wind-tunnel and low-speed flight tests," Proc. R. Soc. London, Ser. A 363, 271
  581. Tester, B. J., 1973a, "The optimization for modal sound attenuation in ducts, in the absence of mean flow," J. Sound Vib. 27, 477
  582. Tester, B. J., 1973b, "Ray models for sound propagation and attenuation in ducts, in the absence of mean flow," J. Sound. Vib. 27, 515
  583. Tester, B. J., and R. H. Burrin, 1974, "On sound radiation from sources in parallel sheared jet flows," Air Force Aero Propulsion Lab. Technical Report No. TR-74-24, p. 59
  584. Thiessen, G. J., 1950, "Resonance characteristics of a finite sinusoidal horn," J. Acoust. Soc. Am. 75, 346
  585. Thomas, J. H., 1983, "Magneto-atmospheric waves," Annu. Rev. Fluid Mech. 15, 321
  586. Thomson, C., 1984, "Linear inviscid wave propagation in a waveguide having a single boundary discontinuity," J. Acoust. Soc. Am. 75, 346
  587. Thorpe, S. A., 1968, "On the shape of progressive internal waves," Philos. Trans. R. Soc. London, Ser. A 263, 563
  588. Titchmarsch, E. C., 1937, Theory of Fourier Integrals (Clarendon, London; 2nd ed. 1948)
  589. Tollmien, W., 1929, "Uber die Entstehung der Turbulenz," Nachr. Ges. Wiss. Goettingen Math. Phys. K1. 21, 44 [N.A.C.A. TM-609 (1931)]
  590. Tolman, R. C., 1934, Relativity, Thermodynamics and Cosmology (Clarendon, London)
  591. Tolstoy, I., 1963, "The theory of waves in stratified fluids including the effects of gravity and rotation," Rev. Mod. Phys. 35, 207
  592. Townsend, A. A., 1956, Structure of Turbulent Shear Flow (Cambridge University, Cambridge, England)
  593. Trevena, D. H., 1984, "Cavitation and the generation of tension in liquids," J. Phys. D 17, 2139
  594. Truesdell, C. A., 1955, "Theory of aerial sound 1687-1788," in Euleri Opera Omnia (O. Füssli, Lausanne), Vol. 3, 13b, p. 19
  595. Truesdell, C. A., 1960, "The rational mechanics of flexible or elastic bodies 1638-1788," in Euleri Opera Omnia (O. Füssli, Turin), Vol. 2, 116, p. 15
  596. Tsien, H. S., 1952, "The transfer functions of rocket nozzles," J. Am. Rocket Soc. 22, 139
  597. Tsien, H. S., 1958, "The equations of gas dynamics," in Fundamentals of gas dynamics, 8 vols., edited by H. W. Emmons (Princeton University, Princeton), Vol. 3, p. 3
  598. Turner, J. S., 1973, Buoyancy Effects in Fluids (Cambridge University, Cambridge, England)
  599. Uenishi, K., and M. K. Myers, 1984, "Two-dimensional acoustic field in a non-uniform duct carrying compressible flow," Am. Inst. Aeron. Astron. J. 22, 1242
  600. Uscinski, B. J., 1977, Elements of Wave Propagation in Random Media (McGraw-Hill, New York)
  601. Uscinski, B. J., 1980, "Parabolic moment equations and acoustic propagation through internal waves," Proc. R. Soc. London, Ser. A 372, 117
  602. Vaidya, P. G., 1984, "Multiple pure tone generation in aeroengine fans at subsonic and supersonic relative tip speeds," Am. Inst. Aeron. Astron. J. 22, 1366
  603. Van Dyke, 1964, Perturbation Methods in Fluid Mechanics (Academic, New York)
  604. Van Dyke, M., 1972, An Album of Fluid Motion (Parabolic, Stanford)
  605. Varley, E., and E. Cumberbatch, 1970, "Large-amplitude waves in stratified media: acoustic pulses," J. Fluid Mech. 43, 513
  606. Varley, E., J. Y. Kazakya, and P. A. Blythe, 1977, "The interactions of large-amplitude barotropic waves with ambient shear flow: critical flows," Philos. Trans. R. Soc. London, Ser. A 287, 24
  607. Viergeuer, M., 1980, Mechanics of the Inner Ear (Delft University, Delft, Netherlands)
  608. Von Mises, R., 1958, Mathematical Theory of Compressible Fluid Flow (Academic, New York)
  609. Von Mises, R., 1964, Mathematical Theory of Probability and Statistics (Academic, New York)
  610. Wang, K. S., and T. G. Tszeng, 1984, "Propagation and radiation of sound in a finite length duct," J. Sound Vib. 93, 71
  611. Waterhouse, R. V., and R. D. Berendt, 1958, "Reverberation chamber study of sound power output from subsonic air jets," J. Aeron. Sci. 30, 114
  612. Watson, G. N., 1944, Bessel Functions (Cambridge University, Cambridge, England)
  613. Watson, J. G., and J. B. Keller, 1984, "Rough surface scattering via the smoothing method," J. Acoust. Soc. Am. 75, 1705
  614. Watson, W. B., 1984, "An acoustic evaluation of circumferentially segmented duct liners," Am. Inst. Aeron. Astron. J. 22, 1229
  615. Webster, A. G., 1919, "Acoustical impedance and the theory of horns and the phonograph," Proc. Natl. Acad. Sci. U.S.A. 5, 275
  616. Weibel, E. S., 1955, "On Webster's horn equation," J. Acoust. Soc. Am. 75, 1705
  617. Welsh, M. C., A. N. Stokes, and R. Parker, 1984, "Flow-resonant interaction in a duct containing a plate," J. Sound Vib. 95, 395
  618. Wentzel, A. R., 1980, "Spectral broadening of waves propagating in a random medium," J. Math. Phys. 21, 2131
  619. Wentzel, G., 1926, "Eine Varallgemeinerung der Qiarterbedomgiger für die Zwecke der Wellenmechanik," Z. Phys. 38, 518
  620. Westervelt, P. J., 1963, "A parametric acoustic array," J. Acoust. Soc. Am. 25, 60
  621. Wever, E. G., and M. Lawrence, 1954, Physiological Acoustics (Princeton University, Princeton, N.J.)
  622. Whitfield, O. J., and M. S. Howe, 1976, "The generation of sound by two-phase nozzle flows and its relevance to excess jet noise of jet engines," J. Fluid Mech. 75, 353
  623. Whitham, G. B., 1974, Linear and Non-Linear Waves (Wiley, New York)
  624. Whittaker, E. T., 1904, Analytical Dynamics of Particles and Rigid Bodies (Cambridge University, Cambridge, England; 4th ed. 1937)
  625. Whittaker, K. W., and G. L. Morrison, 1984, "Acoustic measurements of high-speed subsonic jets," Inst. Aeron. Astron. J. 22, 756
  626. Wiener, N., 1933, The Fourier Integral and Certain of its Applications (Cambridge University, Cambridge; reprinted, Dover, New York, 1958)
  627. Woods, A., 1944, The Physics of Music (Chapman and Hall, London, 7th ed. 1975)
  628. Yanowitch, M., 1967a, "Effect of viscosity on the vertical oscillations of an isothermal atmosphere," Can. J. Phys. 45, 2003
  629. Yanowitch, M., 1967b, "Effect of viscosity on gravity waves and the upper boundary condition," J. Fluid Mech. 29, 209
  630. Yanowitch, M., 1969, "A numerical study of vertically propagating waves in a viscous, isothermal atmosphere," J. Comput. Phys. 4, 531
  631. Yeh, K. C., and C. H. Liu, 1974, "Acoustic-gravity waves in the upper atmosphere," Rev. Geophys. Space Sci. 12, 193
  632. Yeow, K. W., 1974, "Webster wave equation in two dimensions," J. Acoust. Soc. Am. 56, 19
  633. Yeow, K. W., 1984, "Variation with distance of aircraft noise impact parameters," J. Sound Vib. 95, 127
  634. Yih, C. S., 1965, Dynamics of Non-Homogeneous Fluids (MacMillan, London)
  635. Yoshida, H., 1981, "Sound wave propagation in ducts whose walls are lined with a porous layer backed by cellular cavities," J. Sound Vib. 74, 519
  636. Zamorski, T., and R. Wyrzykowski, 1981, "Approximate methods for the solution of the equation of acoustic wave propagation in horns," Arch. Acoust. 6, 237
  637. Zhugzhda, Y. D., and N. S. Dzhalilov, 1981, "Conversion of magnetogravitational waves in the solar atmosphere," Astron. Zh. 58, 838

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation