10. (II) Show that for a standing wave on a string (Eq. 16.11) the average kinetic energy per unit length and the potential energy per unit length are given by dK du dx lav = H(WA)- sin' kx; dx / av = F(KA)2 cos2 kx 1 (II) (a) Consider the ath standing wave on a string of length L fixed at both ends in the form given in Eq. 16.11. Show that the total energy is En = p(w, A ) L where u is the linear mass density and w is the angular frequency. (b) Show that the energy in one loop of a stand- ing wave is E = 21 HA? fu (Try Problem 10 first.)