Question- Consider a 'standing wave' represented by a superposition of travelling wave amplitude functions A (x) = AoExp[i k x] - AoExp[-i k x] where the parameter "k" now is allowed to be any positive real number (that is k has the same magnitude in each component of the superposition, but different direction). (A) Show that the intensity vanishes at x = (n)\[Pi]/k, n is an integer. (B) Now imagine that we place this superposition amplitude function in a reflective "box" of length L so that A(x) = 0 at x = 0 and x = L. Find the "allowed" values of k that satisfy the boundary conditions.
I want you to elucidate the chemistry in this above problem.