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Destructive Interference problem

  1. Jul 13, 2008 #1
    The problem states:

    Waves broadcast by a 1152 kHz radio sta-
    tion arrive at a home receiver by two paths.
    One is a direct path, and the second is from
    re°ection o® an airplane directly above the re-
    ceiver. The airplane is approximately 137 m
    above the receiver, and the direct distance
    from station to home is 18:7 km.
    What is the height (within 1% error) of the
    airplane if destructive interference occurrs?
    Assume no phase change on reflection.
    Answer in units of m.

    First of all I am kind of confused as to where the receiver is...on the house or the radio station. I was thinking it should be on the house, but 137 meters seems very low for an airplane to be flying above a house.

    What I know/tried:
    I know that since it's destructive interference, it is out of phase, so we use ∆L=(lamda/2). and we can find L1 and L2 with the values given, but I have no idea how to include frequency...maybe using v=lamda/f? I tried applying the small angle approximation (where sinө~tanө), but the trigonometry is really confusing and I wasn't having much success. Could someone help?
     
  2. jcsd
  3. Jul 14, 2008 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi jhoffma4! :smile:
    It doesn't matter, does it? :wink:
    Yes, v=lamda/f should do fine.

    And just use Pythagoras. :smile:
     
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