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2D Interference Problem

  1. Mar 23, 2010 #1
    1. The problem statement, all variables and given/known data

    Two radio frequency sources broadcast waves of the same frequency. They are placed 1.0 m apart. Let the x-axis be the line from one source to the other, and let x = 0 be at one of the sources.

    Nodes are observed at x = 0.24 m, x = 0.49 m, x = 0.74 m.

    1) What is the frequency of the two sources?

    2) What is the difference between their phase constants?

    3. The attempt at a solution

    I've simplified the numbers from the original problem to hopefully make things easier. Other than that, the wording is the same.

    1) The frequency of the two sources:

    I know that the distance d1between two nodes is

    d1 = 0.49 m - 0.24 m = 0.25 m .

    And the wavelength is twice the distance between nodes.

    wavelength = 2d1 = 2(0.25 m) = 0.50 m .

    Does this mean that the frequency f is the speed of light divided by wavelength?

    f = c/wavelength = 3.00E8 / 0.25 m = 1.2E9 Hz

    Not sure if that makes sense...

    2) I am really confused about this part.

    We can calculate the wave number k,

    k = 2pi / wavelength = 2pi / 0.50 m = 4pi rad/m .

    And we are given nodes, so we want to use an equation for destructive interference?

    (m + 1/2)2pi = k(delta)r + (delta)phi0 = pi when m = 0

    But how do I find out what (delta)r is?

    A push in the right direction would be appreciated!
  2. jcsd
  3. Mar 24, 2010 #2


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    Homework Helper

    The first wave starts from x=0 with a phase constant phi and travels in the +x direction. The other wave starts at x=1 m, with zero phase constant and travels in the - x direction. What will be the phase of both waves at one of the nodes?

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