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Wave interference

  1. Mar 19, 2009 #1
    1. The problem statement, all variables and given/known data
    2 sources emitting radio waves of the same frequency are placed at x=0 meters and x = 1.2 meters. There are nodes at x= 0.344m, x= 0.719m, and x=1.094m. What is the frequency of the 2 sources and the difference in their phase constant


    2. Relevant equations



    3. The attempt at a solution
    Well i know that maximum destructive interference occurs for every 2pi increase in the difference in phase of the waves
    The difference in phase is:
    dФ = 2Pi (dr)/wavelength + dФ0

    where dr is r2 - r1 = difference in radial distance between each source and the point in question
    now here is my problem:
    since dФ0 stays the same, it means that there will be a node for every increase in dr equal to one wavelength
    however, if i use those points mentioned above to find the radial difference for each point, i get
    dr1 = 0.512
    dr2 = 0.238
    dr3 = 0.988

    so each one of these nodes has an increase in phase difference of 2Pi from the previous
    so taking the 2 with lower drs :
    dФ1 = 2Pi (0.238)/wavelength + dФ0
    dФ2 = 2Pi (0.512)/wavelength + dФ0 = dФо+ 2Pi
    dФ2 - dФ1 = 2 pi = 2pi (0.512)/wavelength - 2Pi (0.238)/wavelength
    wavelength = 0.512 - 0.238

    so the difference between 2 consecutive nodes should give me the wavelength
    ...but these are not evenly spaced, so if i use the 2nd set of points instead i get a different result (0.988 - 0.512 = 0.476) so I don't get it, where is my thinking going wrong?
     
  2. jcsd
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