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Young's double slit and radio antennas

  1. Mar 3, 2015 #1
    1. The problem statement, all variables and given/known data
    antennas can both receive and emit electromagnetic radiation depending on wetter their connecting cicuit is monitored for, or driven by a current. the pattern of emitted radiation is identical to the pattern for absorbed incident radiation.

    As shown in the notes, far-field radiation pattern of two antennas emitting in phase is the same as that of a double split experiment.

    Consider spy in a secret government building which has a footprint of 10x20m rectangle. The surveillance technician of the installation has installed two antenna 2m apart along the external wall at the end of one building, in order to detect any signals that potential spies would broadcast. The spy is at the other end of the building, 20m away.

    A) where should the spy stand to avoid detection if the spy is to transmit on a 500MHz frequency?
    B) if the spy instead has three channels of 50MHz, 4GHz and 2THz to choose from, which should the spy choose in order to avoid detection?
    C) what assumption of the double slit experiment is being violated in this problem?

    2. Relevant equations
    dsin (theta) = (m + 1/2)wavelength
    Wavelength = c/ frequency

    3. The attempt at a solution
    A) for the spy not be detected, he must be standing in the destructive interference fringe. That would mean that in dsin(theta)=(m+1/2)wavelength, where m=0 [the first destructive band from the centre]. So now it's just a case of solving for theta and using trig, solve to find the distance from the Centre line on the wall the spy is against. Is this correct?
    B) not quite sure how to choose between the channels. My guess would be that the higher the frequency, the shorter the wavelength so it's more likely to be out of phase with the antenna??
    C) again, no idea but taking a stab at it I'd say that the assumption that the radio antennas are coherent. Pretty sure I'm wrong though...
     
  2. jcsd
  3. Mar 3, 2015 #2
    Did you draw a diagram?
     
  4. Mar 5, 2015 #3
    Yeah I drew what I think was happening in this question. We have to determine where the dark fringe is.
     

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