The Helmholtz Huygens Integral

  • Eugen Skudrzyk


The sound intensity inside a given volume is determined by the power of the sound sources inside this volume and by the sound intensity that enters the volume from outside. It is apparent that the expression for the sound field will be determined by the contributions of the sources and by boundary terms, which represent whatever is reflected at the boundaries or enters through the boundaries from outside. In deriving a formal solution, Green’s formula and Gauss’ theorem are of particular importance.


Sound Source Velocity Potential Sound Field Sound Intensity Field Point 


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  1. Baker, B. B., Corson, E. T.: The mathematical theory of Huygens’ principle. Oxford: Clarendon Press. 1950.MATHGoogle Scholar
  2. Bladel, J. V.: Low-frequency scattering by hard and soft bodies. J.A.S.A. 44 (1968) 1069.Google Scholar
  3. Bouwkamp, C. J.: A contribution to the theory of acoustic radiation. Philips Res. Rep. 1 (1945/46) 251 277.Google Scholar
  4. Chertock, G.: Sound radiation from vibrating surfaces. J.A.S.A. 36 (1964) 1305.Google Scholar
  5. Copley, L. G.: Integral equation method for radiation from vibrating bodies. J.A.S.A. 41 (1967) 807.Google Scholar
  6. Ferris, H. G.: Computation of farfield radiation patterns by use of a general integral solution to the time-dependent scalar wave equation. J.A.S.A. 41 (1967) 394MATHGoogle Scholar
  7. Greenspon, J. E.: Far-field sound radiation from randomly vibrating structures.J.A.S.A. 41 (1967) 1201.Google Scholar
  8. King, L. V.: On the radiation field of a perfectly conducting base insulated cylindrical antenna over a perfectly conducting plane earth, and the calculation of radiation resistance and reactance. Phil. Trans. Roy. Soc. (London) A, 218 (1919) 211–293;ADSCrossRefGoogle Scholar
  9. King, L. V.: On the acoustic radiation field of the piezoelectric oscillator and the effect of viscosity on the transmission. Canad. J. Research 11 (1934) 135–155, 484–488.CrossRefGoogle Scholar
  10. Kuo, E. Y. T.: Acoustic field generated by a vibrating boundary. I. General formulation and sonar-dome noise loading. J.A.S.A. 43 (1968) 25;MATHGoogle Scholar
  11. Kuo, E. Y. T.: Acoustic field produced by an arbitrary body in good vibration. I. Theory and three-dimensional synthesis. J.A.S.A. 46 (1969) 623.MATHGoogle Scholar
  12. Mitziter, K. M.: Numerical solution for transient scattering from a hard surface shape—retarded potential technique. J.A.S.A. 42 (1967) 391.Google Scholar
  13. Morse, P. M., Feshbach, H.: Methods of theoretical physics, Part I, Chapters 1 to 8. New York, N. Y.: McGraw-Hill. 1953.Google Scholar
  14. Morse, P. M., Ingard, K. U.: Theoretical acoustics. New York, N. Y.: McGraw-Hill. 1968.Google Scholar
  15. Rubinowicz, A.: Die Beugungswelle in der Kirchhoffschen Theorie der Beugung. Wien—New York: Springer. 1966.Google Scholar
  16. Schmidt, H • Einführung in die Theorie der Wellenbeugung. Leipzig: Barth. 1931.Google 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

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