# Solving the wave equation numerically using the Fast Fourier Transform

#### tjackson3

1. The problem statement, all variables and given/known data

According to the website, the statement is as follows:

Write a program which will calculate the evolution of the Wave Equation,
in the case of a bound string. Test this program on the base eigenfunctions,
i.e. the sinusoids, and on more interesting combinations. You should use
matlab’s fft to do this.

2. Relevant equations

The only really relevant equation here is the wave equation, $$u_{tt} = a^2u_{xx}$$

3. The attempt at a solution

Specifically, I'm trying to numerically solve the wave equation for a bound string of length L using a fast Fourier transform. The only thing is, I have absolutely no idea what I'm supposed to be FFT'ing. According to the instructions on my project, I'm supposed to try it on the "base eigenfunctions; i.e., the sinusoids." Where do I start with this? Nothing I can find really gives me a clue as to where to start; that's all I'm looking for.

Last edited:
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