Kirchhoff–Helmholtz integral

The Kirchhoff–Helmholtz integral combines the Helmholtz equation with the Kirchhoff integral theorem[1] to produce a method applicable to acoustics,[2] seismology[3] 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.

[math]\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' }[/math]

## See also

* Kirchhoff integral

## References

1. ↑ Kurt Heutschi (2013-01-25), Acoustics I: sound field calculations, https://people.ee.ethz.ch/~isistaff/courses/ak1/acoustics-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, https://asa.scitation.org/doi/abs/10.1121/1.415524
3. ↑ Scott, Patricia; Helmberger, Don (1983), Applications of the Kirchhoff-Helmholtz integral to problems in seismology

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/Kirchhoff–Helmholtz integral. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Physics:Kirchhoff–Helmholtz_integral&oldid=2978640"