(a) Show that the function y(x, t) = x2 + v2t2 is a solution to the wave equation.
(b) Show that the function in part (a) can be written as f (x # vt) # g(x " vt), and determine the functional forms for f and g.
(c) What If? Repeat parts (a) and (b) for the function y(x, t) = sin (x) cos (vt).