# Solving the wave equation numerically using the Fast Fourier Transform

## Homework Statement

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.

## Homework Equations

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

## 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.

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