Hi, I want to know how to get rid of the time part of the homogeneous wave equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\newcommand{\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } }

\nabla^2\psi-c^{-2}\pd{\psi}{t}{2} = 0[/tex]

I've read that this can be done using a Fourier transform, with the following given as the "frequency-time Fourier transform pair" that is apparently used for this (according to a document I found on the internet, anyway):

[tex]f(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}f(\omega)e^{-i\omega t}d\omega[/tex]

[tex]f(\omega)=\int_{-\infty}^{\infty}f(t)e^{i\omega t}dt[/tex]

Now, I've never used Fourier transforms before and all the references I've come across say to use a Fourier transform to get the Helmholtz equation, but don't explain the steps.

Can anyone explain to me step-by-step how one applies a Fourier transform to the above wave equation to get the Helmholtz equation, or provide a good reference for beginners that explains it in reasonable detail?

Also, if there is another way it can be done (without using a Fourier transform) I'd appreciate any explanation. Thanks.

This isn't so much a homework question as me trying to understand some things that I've glossed over in the past (accepting the results without really understanding how they were reached). Should this question be in the maths forum instead, or is it okay to post it here?

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# Using a Fourier transform on the wave equation

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