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.