Consider the wave equation for the infinite string on the entire real line    utt − uxx = 0 x ∈ R, t > 0 u(x, 0) = 0 ut(x, 0) = ψ(x) with ψ(x) = ( 0, x ≤ 4 1, 4 < x. Find the values of u(t, x) for all (t, x) and write down the answers on the regions of the (t, x)-plane. (4 pts) Draw the profile of the string at times t = 2 and t = 4. (2 pts)