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Interference of waves - 2 point source Question

  1. May 11, 2008 #1
    [SOLVED] Interference of waves - 2 point source Question

    1. The problem statement, all variables and given/known data
    Two towers of a radio station are 400 m apart along an east-west line. The towers act essentially as point sources, radiating in phase at a frequency of 1.00 x 10^6 Hz.

    a) In what directions is the intensity of the radio signal at a maximum for listeners 20 km north of the transmitter (but not necessarily directly north of it)?

    b) In which directions would you find the intensity at a minimum, north of the transmitter, if the towers were to start transmitting in opposite phase?


    2. Relevant equations
    (n-1/2)lamda = sin theta
    d
    where n - the number of nodes
    theta - the angle between nodes
    d - distance between 2 point sources


    velocity= lamda x frequency

    3. The attempt at a solution

    I thought that I want to figure out the angle between the central max, and the first node - where the radio signal would be at a minimum (due to destructive interference) and then divide it by 2 to get the angle at the maximum (constructive interference).

    lamda= 3.00 x 10^8 m/s = 300 m
    1.00 x 10 ^ 6 Hz

    ( 300m) (1-1/2)= sin theta
    400 m

    theta = 22 degrees / 2
    = 11 degrees

    My answer was N 11 E or N 11 W, whereas the real answer should be N 49 E or N 49 W.
    Help please!
    Thanks!
     
    Last edited: May 11, 2008
  2. jcsd
  3. May 12, 2008 #2

    alphysicist

    User Avatar
    Homework Helper

    Hi anachronautic,

    You did find the first minimum; however, there is no maximum between that and the central maximum. Starting at the center and going out, you have :

    central maximum (at zero degrees), 1st minimum, 1st maximum, 2nd minimum,...

    But you can find the first maximum directly from the constructive condition:

    [tex]
    d \sin\theta= m \lambda
    [/tex]
     
  4. May 12, 2008 #3
    Thanks alphysicist!
    It all makes sense now! :)
     
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