Problem 2. Suppose u solves the following initial value problem
\begin{cases}
u_{tt} - u_{xx} = 0 & x \in \mathbb{R}, t > 0, \\
u|_{t=0} = \mathbb{1}_{[-2,-1]}(x) + \mathbb{1}_{[1,2]}(x) & x \in \mathbb{R}, \\
u_t|_{t=0} = 0 & x \in \mathbb{R},
\end{cases}
(3)
where
\mathbb{1}_{[-2,-1]}(x) = \begin{cases} 1 & x \in [-2, -1] \\ 0 & \text{otherwise} \end{cases} and \mathbb{1}_{[1,2]}(x) = \begin{cases} 1 & x \in [1, 2] \\ 0 & \text{otherwise} \end{cases} (4)
Sketch the region on the $xt$-plane where $u(x, t) = 0.$
