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Derive Phase difference between clocks with distance

  1. Aug 31, 2014 #1
    Phase difference between clocks with distance

    1. The problem statement, all variables and given/known data

    Derive Phase difference between clocks with distance

    2. Relevant equations

    I honestly don't understand how this equation ΔT = vD/c2 is derived/figured out.

    3. The attempt at a solution

    We haven't covered Lorentz Transformations yet so is there a way to explain this to me without using it? I understand the concept of simultaneity, time dilation, and length contraction. This problem deals with the first two. The situation is a rectangular box with two detectors on either end marked with the left as A and the right as B. The box is centered along vertical axis where a flash of light in the center of the box flashes, and the light moves towards left and right towards the detectors. Now the box is moving at a constant velocity to the right.

    A picture is attached because it's hard to explain. L is the length of the box, D is the distance between panel 2 and panel 3. Tr is the time it takes for the light to travel to the left detector (Event 1) and Tf is the time it takes for the light to travel to the right detector (Event 2).

    I have equations from panel 1 to panel 2: cTr = L/2 - vTr
    And from panel 1 to 3: cTf = L/2 + vTf

    I just don't understand how to get to the phase difference between them with these equations.

    unnamed.jpg
     
    Last edited: Aug 31, 2014
  2. jcsd
  3. Aug 31, 2014 #2

    nrqed

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    Your two expressions for panels 1 and 2 to 3, look right. Are you sure that D is defined as is shown in your figure?

    Your next step is to get an expression for D (in terms of T_f, T_d and L).

    By the way, a time interval is usually not called a "phase difference" so it is a confusing term to use here.
     
  4. Sep 18, 2014 #3
    I figured I needed that relationship already. I was just unsure how to visualize it and needed explaining of the problem. The relationship was c = v(deltaT).

    Simple enough but I just needed to understand the problem first.
     
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