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Waves & Interference

  1. Oct 8, 2007 #1
    1. The problem statement, all variables and given/known data
    There are 2 in-phase radio wave generators at x = 100 and x = 200. The frequency of each wave is 3.2 MHz. Find spot closest to x = 200 such that the interference at that point is maximum.

    2. Relevant equations
    [tex]\Delta\Phi = \frac{2\pi}{\lambda} \Delta x + \Phi_{0}[/tex]
    [tex]v = c = f\lambda[/tex] c = speed of light

    3. The attempt at a solution

    I assumed that point d was close to x = 300. So that
    [tex]\Delta x = (100-d) - d[/tex]
    [tex]\Delta x = (100 - 2d)[/tex]

    [tex] 2\pi m = \frac{2\pi}{c/f} (100 - 2d) + 0 [/tex] for some integer m; \Phi_{0} = 0 since the waves are in-phase

    [tex] m = \frac{1}{c/f} (100 - 2d)[/tex] cancel out 2 * pi

    [tex]c/f * m = (100 - 2d)[/tex]

    [tex](c/f * m ) - 100= 2d[/tex]

    [tex] d = \frac{(c/f * m) - 100}{2} [/tex]


    Ignoring d, I solved for m such that [tex]\frac{(c/f * m) - 100}{2} [/tex] was equal to 300. Using the m i found (rounding it to nearest integer), i plugged it back into [tex] d = \frac{(c/f * m) - 100}{2} [/tex] to find d.

    Is the method I used correct? What did I do wrong? (Could you please provide me the correct answer & method...i have an exam in 5 hours).

    Thanks!
     
    Last edited: Oct 8, 2007
  2. jcsd
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