220 SOLUTIONSSecond solution: We solve the equation of motion for the wire (see deriva-
tion in Problem 1.46, Part I). For the boundary conditions
we have modes:
with for where is the phase velocity,
Taking for simplicitywe can find the average kinetic and potential energy in each mode:
The total energy in each mode is
The fluctuation of the wire is given by
where we have used For