# Fourier analysis for waves [closed]

If we have 1D wave equation:

$$\frac{\partial^2 \psi}{\partial x^2}=\frac{1}{c^2}\frac{\partial^2 \psi}{\partial t^2}$$

we say that it's always possible to decompose the generic solution $f(x+ct)+g(x-ct)$ using Fourier Transforms.

But

$$\frac{1}{2\pi} \int_R f(\omega)e^{i\omega t}d\omega$$

and we have two variables, $x$ and $t$, how can we use the FT with

$$\int_R f(\omega)e^{i(k(\omega)x\mp\omega t)}d\omega \; ?$$

We have two different types of evolution, $+ct$ and $-ct$... I have seen situations with no dispersion law, where we consider only the $x+ct$ wave and use the point $x=0$ to find the spectrum of waves $f(\omega)$, but can someone explain me the general method?

In 2D or 3D I haven't any idea about how I can do all this. Someone can explain me this too?

Thank you very much!

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This question seems rather incomplete still, please edit. – Noldorin Dec 11 '10 at 22:04
I concur. Also, I have a feeling this really belongs to math.SE as it is a standard mathematical topic of PDE and Fourier analysis. No actual physics in this. – Marek Dec 11 '10 at 22:22

## closed as off topic by David Zaslavsky♦, Marek, NoldorinDec 12 '10 at 1:24

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