Pipes and Horns

  • Thomas D. Rossing
  • Neville H. Fletcher


The wave propagation phenomena in fluids that we have examined in previous chapters have referred to waves in infinite or semi-infinite spaces generated by the vibrational motion of some small object or surface in that space. We now turn to the very different problem of studying the sound field inside the tube of a wind instrument. Ultimately, we shall join together the two discussions by considering the sound radiated from the open end or finger holes of the instrument, but for the moment our concern is with the internal field. We begin with the very simplest cases and then add complications until we have a reasonably complete representation of an actual instrument. At this stage, we will find it necessary to make a digression, for a wind instrument is not excited by a simple source, such as a loudspeaker, but is coupled to a complex pressure-controlled or velocity-controlled generator—the reed or air jet—and we must understand the functioning of this before we can proceed. Finally, we go on to treat the strongly coupled pipe and generator system that makes up the instrument as played.


Input Impedance Characteristic Impedance Musical Instrument Pipe Axis Wall Loss 
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  1. Ayers, R.D., Eliason, L.J., and Mahgerefteh, D. (1985). The conical bore in musical acoustics. Am. J. Phys. 53, 528–537.ADSCrossRefGoogle Scholar
  2. Benade, A.H. (1959). On woodwind instrument bores. J. Acoust. Soc. Am. 31, 137–146.ADSCrossRefGoogle Scholar
  3. Benade, A.H. (1968). On the propagation of sound waves in a cylindrical conduit. J. Acoust. Soc. Am. 44, 616–623.ADSCrossRefGoogle Scholar
  4. Benade, A.H., and Jansson, E.V. (1974). On plane and spherical waves in horns with nonuniform flare. Acustica 31, 80–98.Google Scholar
  5. Beranek, L.L. (1954). “Acoustics,” pp. 91–115. McGraw-Hill, New York; reprinted 1986, Acoustical Society Am., Woodbury, New York.Google Scholar
  6. Eisner, E. (1967). Complete solutions of the “Webster” horn equation. J. Acoust. Soc. Am. 41, 1126–1146.ADSzbMATHCrossRefGoogle Scholar
  7. Fletcher, N.H., and Thwaites, S. (1988). Response of obliquely truncated simple horns: Idealized models for vertebrate pinnae. Acustica 65, 194–204.Google Scholar
  8. Jahnke, E. and Emde, F. (1938). “Tables of Functions,” p. 146. Teubner, Leipzig, Reprinted 1945, Dover, New York.Google Scholar
  9. Kergomard, J. (1981). Ondes quasi-stationnaires dans les pavillons avec partis viscothermiques aux parois: Calcul de l’impedance. Acustica 48, 31–43.zbMATHGoogle Scholar
  10. Levine, H., and Schwinger, J. (1948). On the radiation of sound from an unflanged pipe. Phys. Rev. 73, 383–406.MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. McIntyre, M.E., Schumacher, R.T., and Woodhouse, J. (1983). On the oscillation of musical instruments. J. Acoust. Soc. Am. 74, 1325–1345.ADSCrossRefGoogle Scholar
  12. Morse, P.M. (1948). “Vibration and Sound,” 2nd ed pp. 233–288. McGraw-Hill, New York; reprinted 1976, Acoustical Society of Am., Woodbury, New York.Google Scholar
  13. Morse, P.M., and Feshbach, H. (1953). “Methods of Mathematical Physics,” Vol. 1, pp. 494–523, 655–666. McGraw-Hill, New York.Google Scholar
  14. Morse, P.M., and Ingard, K.U. (1968). “Theoretical Acoustics,” pp. 467–553. McGrawHill, New York. Reprinted 1986, Princeton Univ. Press, Princeton, New Jersey.Google Scholar
  15. Olson, H.F. (1957). “Acoustical Engineering,” pp. 88–123. Van Nostrand-Reinhold, Princeton, New Jersey.Google Scholar
  16. Pyle, R.W. (1975). Effective length of horns. J. Acoust. Soc. Am. 57, 1309–1317.ADSCrossRefGoogle Scholar
  17. Rayleigh, Lord (1894). “The Theory of Sound,” 2 vols. Macmillan, London. Reprinted 1945. Dover, New York.Google Scholar
  18. Salmon, V. (1946a). Generalized plane wave horn theory. J. Acoust. Soc. Am. 17, 199–211.ADSCrossRefGoogle Scholar
  19. Salmon, V. (1946b). A new family of horns. J. Acoust. Soc. Am. 17, 212–218. Schumacher, R.T. (1981). Ab initio calculations of the oscillations of a clarinet. Acustica 48, 71–85.Google Scholar
  20. Webster, A.G. (1919). Acoustical impedance, and the theory of horns and of the phonograph. Proc. Nat. Acad. Sci. (US) 5, 275–282.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Thomas D. Rossing
    • 1
  • Neville H. Fletcher
    • 2
  1. 1.Physics DepartmentNorthern Illinois UniversityDeKalbUSA
  2. 2.Department of Physical Sciences Research School of Physical Sciences and EngineeringAustralian National UniversityCanberraAustralia

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