Two traveling waves moving on a string are identical except for opposite velocities. They obey the equation y(x, t) = Asin (kx + wt), where the plus-or-minus sign in the argument Depends on the direction the wave is traveling.
(a) Show that the vibrating string is described by the equation Ynet(x, t) = 2Asinkxcoscut. (Hint: Use the trigonometric formulas for sin (a + b).)
(b) Show that the string never moves at the places along it for which x = nA/2, where n is a nonnegative integer.