Find in closed form (similar to d'Alembert's formula) the solution u(x, t) of the one-dimensional semi-infinite wave equation. U_tt = c^2 u_xx, x, t > 0, u(0, t) = 0, t greaterthanorequalto 0, u(x,0) = f(x), u_t(x,0) = g(x) x > 0. Find conditions on f and g so that the solution has two continuous derivatives, even on the characteristic x = ct. What happens when a wave traveling towards x = 0 hits the boundary at x = 0