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Expressing waves in complex form

  1. Sep 23, 2007 #1
    Question:
    Two waves have the same amplitude, speed, frequency moving in the same region of space. The resultant wave can be expressed like the sum of two waves: psy(y,t) = Asin(ky+wt) + Asin(ky-wt+pi).

    Express each wave individually using the complex representation. Demonstrate, using this representation, that the resultant wave can be expressed such as: psy(y,t)=2Acos(ky)sin(wt).

    What is the amplitude at y=0, y=pi/k?


    Attempt to answer:

    I've tried breaking this problem into pieces. I'm having quite a bit of difficulty converting the wave equations into complex form.

    I started by splitting the equation in two.

    psi1(y,t) = (ky + wt)
    psi2(y,t) = (ky - wt + pi)

    From there, I'm not sure what to do. I know that I have to convert it into a form of Ae^i(wt-kx+epsilon).

    Would simply be: psy1(y,t) = Ae^i(wt+ky) and psy2(y,t) = Ae^i(-wt+ky) ?

    I'm pretty confused about this. I don't know where to go from here or even if what I did has sense to it. Hopefully someone can help me out!
     
    Last edited: Sep 24, 2007
  2. jcsd
  3. Sep 24, 2007 #2
    Anyone?
     
  4. Sep 24, 2007 #3

    robphy

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    Can you write [tex] \sin(\theta) [/tex] in terms of the exponential function?
     
  5. Sep 24, 2007 #4
    I think (not sure) that its: 1/2i(e^i[tex] (\theta) [/tex] - e^(-i[tex] (\theta) [/tex]))
     
  6. Sep 25, 2007 #5
    Would anyone know any websites that could explain the idea behind this because my book is limited when describing this concept?
     
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