Derive Phase difference between clocks with distance

[Shiz]

Phase difference between clocks with distance

Homework Statement

Derive Phase difference between clocks with distance

Homework Equations

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

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. T_r is the time it takes for the light to travel to the left detector (Event 1) and T_f 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: cT_r = L/2 - vT_r
And from panel 1 to 3: cT_f = L/2 + vT_f

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

 

[nrqed]

Homework Statement

Derive Phase difference between clocks with distance

Homework Equations

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

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. T_r is the time it takes for the light to travel to the left detector (Event 1) and T_f 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: cT_r = L/2 - vT_r
And from panel 1 to 3: cT_f = L/2 + vT_f

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

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.

 

[Shiz]

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.