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Homework Statement
I'm given that the motion of an infinite string is described by the wave equation:
(let D be partial d)
D^2 y /Dx^2 - p/T D^2/Dt^2 = 0
I'm asked for what value of c is Ae^[-(x-ct)^2] a solution (where A is constant)
Then I am asked to show that the potential and KE of the wave packet are equal..
Homework Equations
The Attempt at a Solution
So I am guessing the value of c is root(T/p)?since the solution is a function of (x-ct) so this corresponds to D'Alembert..But then PE and KE don't seem equal...
KE = integral from -infinity to + infinity of 1/2 p A^2 e^[4c^2(x-ct)] while PE = integral from - inf to + inf of 1/2 p A^2 c^2 e^[-(4x-ct)]..and these don't seem equal..
any help?
thanks!