Consider a solution of the wave equation with c = 1 on
Chapter 5, Problem 18(choose chapter or problem)
Consider a solution of the wave equation with c = 1 on [0,l] with homogeneous Dirichlet or Neumann boundary conditions. (a) Show that its energy E = 1 2l 0 (u2 t +u2 x)dx is a constant. (b) Let En(t) be the energy of its nth harmonic (the nth term in the expansion).Showthat E = En.(Hint:Usetheorthogonality.Assume that you can integrate term by term.)
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