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Homework Help: Relfected wave equation for free and fixed end

  1. Apr 21, 2012 #1
    1. The problem statement, all variables and given/known data
    I have problems with expressing a reflected wave mathematically.
    In my printed notes I found the following formulas for reflected waves:
    a) For a fixed end: incoming wave: [tex]y_1(x,t)=e^{-i(kx+ωt)}[/tex]
    reflected wave: [tex]y_2(x,t)=re^{i(kx-ωt)}[/tex] where r is the reflection coefficient.
    I understand the - in front of ωt is because the wave has changed its direction, and the - in front of the whole power (before i) is because the wave is reflected.
    Now for a free end: [tex]y_1(x,t)=e^{i(kx-ωt)}[/tex] it is said that [tex]y_2(x,t)=re^{i(-kx-ωt)}[/tex]
    2. Relevant equations
    Shouldn't the reflected wave for a free end in this case be:
    [tex]y_2(x,t)=re^{i(kx+ωt)}[/tex] because the wave is not inverted, but it changes its direction?

    Any help appreciated!
    Last edited: Apr 21, 2012
  2. jcsd
  3. Apr 22, 2012 #2
    Could anyone please have a look at this problem? I thought it was quite straightforward :(
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