Spherical Waves, Sources, and Multipoles

  • Eugen Skudrzyk


Sound rays, sound beams, plane waves, and cylindrical waves are possible only near a sound source. According to Huygen’s principle, every point in a wave front acts as a secondary source and propagates energy in all directions. This spreading out of the sound energy leads to a divergence of the sound waves so that, eventually, at great distances from the source, all sound waves become spherical waves. From a great distance, every sound source appears as the center of outgoing spherical waves.


Volume Flow Sound Pressure Sound Source Radiation Resistance Sound Field 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bies, D. A.: Effect of a reflecting plane on an arbitrarily oriented multipole. J.A.S.A. 33 (1961) 286.MathSciNetGoogle Scholar
  2. Brekhovskikh, L.: Reflection of spherical waves on the plane separation of two media. J. Tech. Phys. (U.S.S.R.) 18 (1948) 455–482 (in Russian).Google Scholar
  3. Horton, C. W., Sobey, A. E., Jr.: Studies on the near fields of monopole and dipole acoustic sources. J.A.S.A. 30 (1958) 1088.Google Scholar
  4. Ingard, U.: On the theory and design of acoustic resonators. J.A.S.A. 25 (1953) 1037.Google Scholar
  5. Ingard, U., Lamb, G. L., JR.: Effect of a reflecting plane on the power output of sound sources. J.A.S.A. 29 (1957) 743.Google Scholar
  6. Ingard, U., Lyon, R. H.: Impedance of a resistance loaded Helmholtz resonator. J.A.S.A. 25 (1953) 854.Google Scholar
  7. Karnovskh, M. I.: Interaction acoustical impedances of spherical radiators and resonators. Comptes Rendus (Doklady) de l’Académie des Sciences de l’URSS 32 (1941) 40–43.Google Scholar
  8. Mclachlan, N. W.: Loudspeakers. Oxford: Clarendon Press. 1934.Google Scholar
  9. Mcleroy, E. G.: Complex image theory of low-frequency sound propagation in shallow water. J.A.S.A. 33 (1961) 1120.Google Scholar
  10. Morse, P. M., Ingard, U.: Theoretical acoustics. New York, N. Y.: McGraw-Hill. 1968;Google Scholar
  11. Morse, P. M., Ingard, U.: Linear acoustic theory, p. 1–127 (in Handbuch der Physik, Vol. XI ). Berlin Göttingen—Heidelberg: Springer. 1962.Google Scholar
  12. Paul, D. I.: Acoustical radiation from a point source in the presence of two media. J.A.S.A. 29 (1957) 1102.Google Scholar
  13. Rayleigh, Lord: The theory of sound, Vol. I. London: Macmillan. 1894.MATHGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1971

Authors and Affiliations

  • Eugen Skudrzyk
    • 1
  1. 1.Ordnance Research Laboratory and Physics DepartmentThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations