# Wave question

1. Feb 25, 2008

### joker_900

1. The problem statement, all variables and given/known data
Two transverse waves are on the same piece of string. The first has displacement y non-zero only for kx + wt between pi and 2pi, when it is equal to Asin(kx + wt). The second has y = Asin(kx - wt) for kx - wt between -2pi and -pi, and is zero otherwise. When t=0, the displacement is such that there is a positive sinusoidal displacement between -2pi/k and -pi/k and a negative displacement between pi/k and 2pi/k. Calculate the energy of the two waves.

What is the displacement of the string at t=3pi/2w? Calculate the energy at this time.

2. Relevant equations

3. The attempt at a solution

OK so I did a kinda standard derivation for the energy in the string - for each wave, I did dKE = o.5pdx (dy/dt)^2 where the differential is a partial differential and p is the linear density of the string. I then integrated this over the lengths stated (pi/k to 2pi/k for the second wave). I did a similar thing for potential energy and got the total energy to be

(pi/k)A^2 w^2 p

First up I'm not sure if this is right, as there was no p stated in the question.

For the next part, I think that at the time 3pi/2w, the two waves are about the origin and superimpose to produce a net displacement of zero - so what is the energy now? I assume it must be the same as I found no time or position dependence in the energy (and conservation of energy), but then where is the energy - surely there's no potential energy?