Green Functions and the Helmholtz Integral Equation
The Helmholtz integral equation and Green functions are important to the study of acoustics. Though it is not strictly in the realm of Fourier acoustics, it is crucial for the extension of NAH to arbitrary geometries. There is much work in many fields of acoustics today which relies heavily on the Helmholtz integral equation. In particular, the field of boundary elements has as its starting point this important equation. It is very relevant to nearfield acoustical holography applied to arbitrary geometries, and instead of being based in Fourier acoustics, the singular value decomposition becomes the medium for the eigenfunctions of the problem.
We will derive the ...