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How would I find the magnitude of this wave.(complex numbers/quanties)

  1. Jan 16, 2006 #1
    ψ(y,t)=2*e^(iky)*e^(iωt) + 4*e^(iky)*e^(-iωt)
    Here is my work for the problem
    2e^(iky)*(e^(iωt)+2e^(-iωt)); 2e^(iky)*(cos(ωt)+i*sin(ωt)+2cos(ωt)-2i*sin(ωt));
    2e^(iky)*(3cos(ωt)-isin(ωt))
    How would you continue this problem?
     
  2. jcsd
  3. Jan 17, 2006 #2

    Galileo

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    You are asked for the absolute value (or magnitude) of [itex]2e^{iky}(3\cos(\omega t)-i\sin(\omega t))[/itex].
    I'm sure you know how to calculate the magnitude of a complex number.
    The magnitude will depend on time.
     
  4. Jan 17, 2006 #3

    cepheid

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    My advice would be to rewrite the wave in the form:

    [tex] \Psi(y,t) = 2e^{i(ky + \omega t)} + 4e^{i(ky - \omega t)} [/tex]

    and it should be obvious from this form that you have the sum of two sinusoidal waves, one travelling to the left (er, negative y-direction) with amplitude 2, and the other to the right (+ y-direction) with amplitude 4. If that is not obvious, then consider that if this is really a physical wave propagating along the y-axis, then the physical wave is given by:

    [tex] Re[\Psi(y,t)] = 2\cos{(ky + \omega t)} + 4\cos{(ky - \omega t)} [/tex]

    To be honest, I'm not sure how/don't feel like putting in the effort at this hour to calculate the combined amplitude of the two waves, and whether that corresponds to the magnitude of the complex number psi.

    Edit, just saw Galileo's post, so maybe I was way off on this one/answering the wrong question.
     
  5. Jan 17, 2006 #4
    How do you edit posts?
    Anyway I end up getting (20+16cos(wt))^1/2 for my magnitude.
     
  6. Jan 18, 2006 #5

    Galileo

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    The magnitude of [itex]2e^{iky}(3\cos(\omega t)-i\sin(\omega t))[/itex] is not [itex]\sqrt{20+16\cos(\omega t)}[/itex].
    Try again.

    Click the edit button at the bottom of your post to edit.
     
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