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So my current solution to the $1D$ wave equation is (with my given boundary and initial conditions): $$y(x,t) = \sum_{n=1}^\infty C_n\cdot \sin\frac{n \pi x}{2 l}\cdot\cos\frac{n \pi c t}{2 l}$$

However there is one final initial condition that is piecewise, I'm unsure of how to apply this and the solutions expected are of a infinite series (fourier series).

The last initial condition is:

$$y(x,0)= \begin{cases} R\cdot\frac{x}{l} & \quad 0\le x\le 1 \\ R\cdot\left(2 - \frac{x}{l}\right) & \quad l\le x\le 2 l \end{cases}$$

Any help or advice on solving is much appreciated.

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    Please, check if I add correct LaTeX for your formula.2012-11-29
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    I'm going to assume that because there is an $n$ in $y(x,t)$ it isn't just some single fixed $n$ and you should actually sum over them all...also should there really be a $ct$ in the $\sin$ part? I think it should just be $x$.2012-11-29
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    The $x$ was erroneously replaced by $ct$ by an earlier formatting edit. @Sam, you can avoid these sorts of problems by formatting the post yourself. We have a [basic tutorial and quick reference](http://meta.math.stackexchange.com/questions/5020) for that.2012-11-29

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