Harmonic traveling wave physics

[bon]

Homework Statement

Two semi infinite strings are attached at x=0 and stretched to a tension T. They have linear densities p1 and p2 respectively. A harmonic traveling wave, given in complex form as

Ae^[iw(t-x/v1)] travels along string 1 towards the boundary.

1) Determine the amplitudes of reflected and transmitted waves
2) Check the amplitudes are such that energy conservation is obeyed in the region x approx = 0

Homework Equations

The Attempt at a Solution

So I've done part 1)

I got that A' (amp of refl. wave) = (v2-v1)/(v1+v2) A

and A'' (amp of trans. wave) = 2v2/(v1+v2) A

Just don't see how to do part 2). How do I show energy is conserved in region x approx = 0?

thanks

 

[bon]

Any one able to offer help on this? I'm also having trouble understanding what it means for the equation to be y = Ae^[iw(t-x/v1)] since this includes complex terms..what is the physical interpretation?

Thanks

 

[ehild]

The solution of the wave equation can be written in exponential form. When you calculate energy, however, you have to turn to the real functions, sine or cosine:

$$\sin(x) =\frac{e^{ix}-e^{-ix}}{2i}$$

or

$$\cos(x) =\frac{e^{ix}+e^{-ix}}{2}$$

ehild