Journal of Engineering Mathematics

, Volume 87, Issue 1, pp 99–109 | Cite as

Pulsed acoustic field radiation in a laterally bounded layered fluid

  • Martin Štumpf
  • Börje Nilsson


The acoustic field radiation from an impulsive source located in a discretely layered and laterally bounded fluid is investigated with the aid of the generalized-ray theory. The main ingredient of the presented approach is the Cagniard–de Hoop technique in combination with the method of images that provide exact space–time expressions for the activated acoustic wavefield components. Illustrative numerical examples are presented.


Cagniard–de Hoop method Generalized ray theory Layered fluid Time domain 



The research leading to the results reported in the manuscript was sponsored by the ESF project CZ.1.07/2.3.00/ 30.0005 and the SIX project CZ.1.05/2.1.00/03.0072 of the Brno University of Technology.


  1. 1.
    Piercy JE, Embleton TFW, Sutherland LC (1977) Review of noise propagation in the atmosphere. J Acoust Soc Am 61:1403–1418ADSCrossRefGoogle Scholar
  2. 2.
    Cotté B, Blanc-Benon P (2009) Time-domain simulations of sound propagation in a stratified atmosphere over an impedance ground. J Acoust Soc Am 125:EL202–EL207ADSGoogle Scholar
  3. 3.
    Morse PM, Bolt RH (1944) Sound waves in rooms. Rev Mod Phys 16:69–150ADSCrossRefGoogle Scholar
  4. 4.
    Visentin V, Prodi N, Valeau V, Picaut J (2012) A numerical investigation of the Fick’s law of diffusion in room acoustics. J Acoust Soc Am 132:3180–3189ADSCrossRefGoogle Scholar
  5. 5.
    Albert DG (2003) Observations of acoustic surface waves in outdoor sound propagation. J Acoust Soc Am 113:2495–2500ADSCrossRefGoogle Scholar
  6. 6.
    Brekhovskikh LM (1980) Waves in layered media. Academic Press, New YorkMATHGoogle Scholar
  7. 7.
    de Hoop AT (1960) A modification of Cagniard’s method for solving seismic pulse problems. Appl Sci Res B8:349–356CrossRefGoogle Scholar
  8. 8.
    de Hoop AT, van der Hijden JHMT (1983) Generation of acoustic waves by an impulsive line source in a fluid/solid configuration with a plane boundary. J Acoust Soc Am 74:333–342ADSCrossRefMATHGoogle Scholar
  9. 9.
    de Hoop AT, van der Hijden JHMT (1984) Generation of acoustic waves by an impulsive point source in a fluid/solid configuration with a plane boundary. J Acoust Soc Am 75:1709–1715ADSCrossRefGoogle Scholar
  10. 10.
    van der Hijden JHMT (1987) Propagation of transient elastic waves in stratified anisotropic media. Dissertation, Delft University of TechnologyGoogle Scholar
  11. 11.
    de Hoop AT (1988) Acoustic radiation from impulsive sources in a layered fluid. Nieuw Arch Wis 6:111–129MATHGoogle Scholar
  12. 12.
    de Hoop AT (1990) Acoustic radiation from an impulsive point source in a continuously layered fluid—an analysis based on the Cagniard method. J Acoust Soc Am 88:2376–2388ADSCrossRefGoogle Scholar
  13. 13.
    Verweij MD (1992) Transient acoustic waves in continuously layered media. Dissertation, Delft University of TechnologyGoogle Scholar
  14. 14.
    Verweij MD (1992) Transient acoustic wave modeling: higher-order Wentzel–Kramers–Brillouin–Jeffreys asymptotics and symbolic manipulation. J Acoust Soc Am 92:2223–2238ADSCrossRefMathSciNetGoogle Scholar
  15. 15.
    Xia M-Y, Chan CH, Xu Y, Chew WC (2004) Time-domain Green’s functions for microstrip structures using Cagniard–de Hoop method. IEEE Trans Antennas Propag 52(6):1578–1585ADSCrossRefGoogle Scholar
  16. 16.
    Štumpf M, de Hoop AT, Vandenbosch GAE (2013) Generalized ray theory for time-domain electromagnetic fields in horizontally layered media. IEEE Trans Antennas Propag 61(5):2676–2687ADSCrossRefGoogle Scholar
  17. 17.
    Buckingham MJ (1992) Ocean-acoustic propagation models. J Acoustique 43(30):223–287Google Scholar
  18. 18.
    Berman JM (1975) Behavior of sound in a bounded space. J Acoust Soc Am 57:1275–1291ADSCrossRefGoogle Scholar
  19. 19.
    Bullen R, Fricke F (1976) Sound propagation in a street. J Sound Vib 46:33–42ADSCrossRefMATHGoogle Scholar
  20. 20.
    Iu KK, Li KM (2002) The propagation of sound in narrow street canyons. J Acoust Soc Am 112:537–550ADSCrossRefGoogle Scholar
  21. 21.
    Lager IE, de Hoop AT (2011) Time-domain receiving properties of a multimode cylindrical waveguide antenna. In: Proceedings of 5th European Conference on Antennas and Propagation, Rome, Italy, 11–15 April 2011Google Scholar
  22. 22.
    Porter MB (1990) The time-marched fast-field program (FFP) for modeling acoustic pulse propagation. J Acoust Soc Am 87:2013–2023ADSCrossRefGoogle Scholar
  23. 23.
    Sturm F (2005) Numerical study of broadband sound pulse propagation in three-dimensional oceanic waveguides. J Acoust Soc Am 117:1058–1079ADSCrossRefGoogle Scholar
  24. 24.
    Herman GC, van den Berg PM (1982) A least-square iterative technique for solving time-domain scattering techniques. J Acoust Soc Am 72:1947–1953ADSCrossRefMATHGoogle Scholar
  25. 25.
    Bluck MJ, Walker SP (1996) Analysis of three-dimensional transient acoustic wave propagation using the boundary integral equation method. Int J Numer Methods Eng 39:1419–1431CrossRefMATHGoogle Scholar
  26. 26.
    Hargreaves JA, Cox TJ (2008) A transient boundary element method model of Schroeder diffuser scattering using well mouth impedance. J Acoust Soc Am 124:2942–2951ADSCrossRefGoogle Scholar
  27. 27.
    de Hoop AT (1995) Handbook of radiation and scattering of waves. Academic Press, LondonGoogle Scholar
  28. 28.
    Doetsch G (1974) Introduction to the theory and application of the Laplace transformation. Springer, BerlinCrossRefMATHGoogle Scholar
  29. 29.
    Zauderer E (1989) Partial differential equations of applied mathematics, 2nd edn. Wiley, New YorkMATHGoogle Scholar
  30. 30.
    Quak D (2001) Analysis of transient radiation of a (traveling) current pulse on a straight wire segment. In: Proceedings of the IEEE EMC International Symposium, Montreal, Canada, August 2001, pp 13–17Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.ESAT-TELEMICKatholieke Universiteit LeuvenHeverlee, LeuvenBelgium
  2. 2.Department of MathematicsLinnæus UniversityVäxjöSweden

Personalised recommendations