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Phase change from mass in middle of a string

  1. Apr 11, 2012 #1
    1. The problem statement, all variables and given/known data

    There is a mass M in the middle of an infinite string, of the same linear density on both sides. The reflection coefficient is [itex] r=-ip/(1+ip) [/itex] where [itex] p=ω^2 M/2Tk [/itex]
    How does the phase change on reflection vary with M, for fixed ω and T?

    2. Relevant equations

    Phase change = Im(r)/Re(r)

    3. The attempt at a solution

    I got the expression [itex] \varphi =arctan(1/p) [/itex], which I can't see how it could be right, as it implies that a phase change of [itex] \pi/2 [/itex] occurs when the mass is 0. I know that when the mass is 0, there should be no phase change, and it should tend to [itex] \pi [/itex] as the mass tends to infinity (but the arctan function has a maximum value of [itex] \pi/2 [/itex]). How can I resolve this to get an equation for the phase change that works?
     
  2. jcsd
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