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Homework Help: Wave addition

  1. May 7, 2010 #1

    fluidistic

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    1. The problem statement, all variables and given/known data
    Describe the sum of two EM waves that have the same initial phase and same amplitude but different frequencies such that [tex]\omega _1 >> \omega _2[/tex].


    2. Relevant equations
    [tex]E=E_0 \cos (kx -\omega t + \alpha)[/tex].


    3. The attempt at a solution
    I summed them up and reached, after an approximation, that [tex]E_1+E_2 \approx 2 E_0 \cos \left (kx -\frac{\omega _1t}{2} + \alpha \right ) \cos \left ( \frac{\omega _ 1 t}{2} \right )[/tex]. I don't know how to simplify further. It seems that the amplitude is the sum of both amplitudes and I'm not sure yet what is the frequency. It should be almost [tex]\omega _1[/tex], intuitively. I just don't know how to show it.
    Any help is appreciated.
     
  2. jcsd
  3. May 8, 2010 #2

    physicsworks

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    Did you consider the fact that
    [tex]k=\frac{\omega}{c}[/tex]
    and that's why k is different for the two plane waves with two different frequencies?
     
  4. May 8, 2010 #3

    fluidistic

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    Thanks, actually I didn't consider this. I will redo the exercise.
     
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