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

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