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Homework Help: Interference at a single wavelength

  1. Jan 11, 2010 #1
    1. The problem statement, all variables and given/known data

    I have a question relating to the interference at a single frequency? Does this statement mean that the intereference has occured between two waves which are completely in phase? I also have a question regarding if two waves which are not in phase but do not cause complete destruction or construction ie they are out of phase by a 1/2 a wavelength for example would the still interact and produce a new wavelength?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jan 11, 2010 #2


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    Welcome to PF!

    Hi physical101! Welcome to PF! :smile:
    I suspect you're thinking of beats, for example in sound waves, when two nearby frequencies are added.

    No, a single frequency stays at that frequency.

    Asinωt + Bsin(ωt+φ) = (A + Bcosφ)sinωt + Bsinφcosωt,

    which is a multiple of sin(ωt+ψ), where tanψ = Bsinφ/(A + Bcosφ) :wink:
  4. Jan 11, 2010 #3
    so would I be correct in thinking that when a journal/literature states that intereference has occured at a single frequency that the resultant wave would be increased in amplitude due to total constructive intereference? What I am trying to clarify is that when they state that interference has occured at a single frequency that the interefering waves were of the same frequency to begin with? Sorry if im not making much sense
  5. Jan 11, 2010 #4


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    Hi physical101! :wink:

    No, you're making complete sense: that's exactly correct.

    Constructive interference starts with the same frequency it finishes with (and so does destructive interference). Only the amplitude (and maybe the phase) changes. :smile:
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