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Homework Help: Wave interferance and determining an unknown height

  1. Nov 30, 2009 #1
    1. The problem statement, all variables and given/known data

    Radio waves from a star, of wavelength 231 m, reach a radio telescope by two separate paths. One is a direct path to the receiver, which is situated on the edge of a cliff by the ocean. The second is by reflection off the water. The first minimum of destructive interference occurs when the star is 23.7° above the horizon. Calculate the height of the cliff. (Assume no phase change on reflection.)

    The attempt at a solution

    Since its destructive interference, the difference between the two lengths is half a wavelength (=115.5 m).
    So lets say L-D=115.5 m.
    D = Lsin(90-23.7) = Lsin(66.3)
    L - (0.916)L = 115.5 m
    0.0843L = 115.5 m
    L = 1370 m

    Height = Lsin(23.7)
    = 550.7 m

    Any idea what I'm doing wrong? Thanks :)
  2. jcsd
  3. Nov 30, 2009 #2


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    Staff Emeritus
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    Homework Helper

    I don't think 23.7 is the angle to use here. Did you draw a figure to show what is going on?

    The rest of it looks okay:
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