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Determine the solution of the wave equation on a semi-infinite interval $u_{tt}=c^2u_{xx},$ $0<x<\infty,$ $t>0,$ where $u(0,t)=0$ and the initial conditions:

$\begin{aligned} & u(x,0)=\left\{ \begin{align}

& 0,\text{ }0<x<2 \\

& 1,\text{ }2<x<3 \\

& 0,\text{ }x>3 \\

\end{align} \right. \\

& {{u}_{t}}(x,0)=0. \\

\end{aligned}$