Show that u(x, t) = f(x−ct)+g(x+ct), where c is a constant and f and g have continuous second derivatives, is a solution of the wave equation in
one dimension, ie (∂t)^2 u = c^2 ∂x^2 u. Note that this solution to the wave equation consists of two functions who keep the same shape but travel to the left and right with speed c.