1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Intensity of 2 waves

  1. May 9, 2010 #1

    fluidistic

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    Show that the maximum intensity of 2 waves is worth [tex](E_{01}+E_{02})^2[/tex] while for 2 waves out of phase by pi rad, it's worth [tex](E_{01}-E_{02})^2[/tex].


    2. Relevant equations
    Not sure about intensity. According to my notes it's worth [tex](U_1+U_2)(U_1+U_2)*[/tex] where * denotes the complex conjugate. And [tex]U(x)=\sqrt{\frac{2}{\eta}}E(x)[/tex].
    Also [tex]\eta=\frac{\sqrt{\frac{\mu _0}{\varepsilon _0}}}{n}[/tex] where n is the refractive index of the medium. Is there some easier formula for the intensity that I could use?

    3. The attempt at a solution
    As they don't say anything if the 2 waves have the same frequency, I think that indeed they have the same frequency otherwise it's senseless to talk of a phase. Am I right?
     
  2. jcsd
  3. May 10, 2010 #2
    If we talk of superposition of waves a phasor treatment provides
    Ar2 = A12 + A22 + 2A1A2cosT
    where T is the phase difference. Now knowing that intensity is proportional to amplitude squared and using conditions for constructive and destructive interference you can easily show the required results.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook