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Homework Help: Electromagnetic waves

  1. Mar 6, 2010 #1
    1. The problem statement, all variables and given/known data

    The electric components E1 and E2 of two coherent electromagnetic waves are given as follows :

    [tex]E_1=E_o\sin (\omega t-kx)[/tex]

    [tex]E_2=E_o\sin (\omega t-k(x+\delta))[/tex]

    These two waves superpose each other at a certain point . Derive the amplitude of the resultant wave in terms of k and delta .

    2. Relevant equations



    3. The attempt at a solution

    I tried adding them using the sin formulas , but i failed to express it in the form of

    [tex]A \cos \theta \sin \omega t [/tex]
     
  2. jcsd
  3. Mar 6, 2010 #2

    ehild

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    Homework Helper

    The sum of the two waves can be substituted by a single one of the same angular frequency w and wavenumber k, that is

    [tex]
    E_o\sin (\omega t-kx)+E_o\sin (\omega t-k(x+\delta))= A\sin (\omega t-k(x+\alpha))
    [/tex].

    You have to find the expression of A in terms of E0 and delta.

    ehild
     
  4. Mar 6, 2010 #3
    thanks ehild , but i don really get it , i don see where is the alpha coming from ..
     
  5. Mar 6, 2010 #4

    ehild

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    Homework Helper

    Alpha is a phase constant for the new wave. You can determine both alpha and the amplitude A by using the identity for the sine of the difference of angles. Have you learnt how to do it?

    ehild
     
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