1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Wave addition

  1. May 7, 2010 #1

    fluidistic

    User Avatar
    Gold Member

    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

    User Avatar
    Gold Member

    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

    User Avatar
    Gold Member

    Thanks, actually I didn't consider this. I will redo the exercise.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook