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Kirchhoff–Helmholtz integral

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The Kirchhoff–Helmholtz integral combines the Helmholtz equation with the Kirchhoff integral theorem to produce a method applicable to acoustics, seismology and other disciplines involving wave propagation.

It states that the sound pressure is completely determined within a volume free of sources, if sound pressure and velocity are determined in all points on its surface.

P ( w , z ) = ∬ d A ( G ( w , z | z ′ ) ∂ ∂ n P ( w , z ′ ) − P ( w , z ′ ) ∂ ∂ n G ( w , z | z ′ ) ) d z ′ {\displaystyle {\boldsymbol {P}}(w,z)=\iint _{dA}\left(G(w,z\vert z'){\frac {\partial }{\partial n}}P(w,z')-P(w,z'){\frac {\partial }{\partial n}}G(w,z\vert z')\right)dz'}

See also

References

  1. Kurt Heutschi (2013-01-25), Acoustics I: sound field calculations (PDF)
  2. Oleg A. Godin (August 1998), "The Kirchhoff–Helmholtz integral theorem and related identities for waves in an inhomogeneous moving fluid", Journal of the Acoustical Society of America, 99 (4): 2468–2500, doi:10.1121/1.415524
  3. Scott, Patricia; Helmberger, Don (1983), Applications of the Kirchhoff-Helmholtz integral to problems in seismology


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