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Harmonic traveling wave physics

  1. May 4, 2010 #1

    bon

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    1. The problem statement, all variables and given/known data

    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


    2. Relevant equations



    3. 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
     
  2. jcsd
  3. May 6, 2010 #2

    bon

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    Re: Waves

    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
     
  4. May 6, 2010 #3

    ehild

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    Homework Helper
    Gold Member

    Re: Waves

    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:

    [tex]\sin(x) =\frac{e^{ix}-e^{-ix}}{2i} [/tex]

    or

    [tex]\cos(x) =\frac{e^{ix}+e^{-ix}}{2} [/tex]

    ehild
     
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