A string has its endpoints fixed at (0, 0) and (L, 0). If its height at a and time t is (x, t) then (to a good approximation) its total kinetic energy is E($) = " So didx and its total potential energy (coming from stretching tension) is T($) = ? So didx. The string moves to minimise the integral (E($) - T($)) dt. Show that the string obeys the wave equation 1 020 C2 at 2 where c = VT/ P