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Reflected and Transmitted Waves Phase changes

  1. Apr 20, 2007 #1
    1. The problem statement, all variables and given/known data

    Consider an infinitely long continuous string with tension [tex]\tau[/tex]. A mass M is attached to the string at x=0. If a wave train with velocity [tex]\frac{\omega}{k}[/tex] is incident from the left, show that reflection and transmission occur at x=0 and that the coefficients R and T are given.
    Consider carefully the boundary condition on the derivatives of the wave functions at x=0. What are the phase changes for the reflected and transmitted waves?


    3. The attempt at a solution

    I got the first part of the problem using a boundary condition derived from Newton's second law. And showed that Sin[theta]^2 = R and Cos[theta]^2 = T, where Tan[theta] = m*(omega)/(2*tau*k). I don't know where to start to find the phase changes. I think it has something to do with the ratio of the complex to the real part of the solution that I found in the first part, but again not sure how to go about this.
     
    Last edited: Apr 20, 2007
  2. jcsd
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