- #1

Mark Zhu

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- Homework Statement
- Consider a source of light (for example, a star) and a receiver (an astronomer) approaching one another with a relative velocity v. First we consider the

receiver fixed (Figure 2.27a) in system K and the light source in system K moving toward the receiver with velocity v. The source emits n waves during the time

interval T. Because the speed of light is always c and the source is moving with

velocity v, the total distance between the front and rear of the wave train emitted

during the time interval T is

- Relevant Equations
- Length of wave train = cT - vT

I am confused about how to find the length of a wave train emitted within a time interval T and that is moving with speed c relative to a moving frame that is itself moving with velocity v. Apparently the answer is that the wave train's length is cT - vT, but I tried to plug in variables into the Lorentz velocity transformation equation in the x direction and didn't get the right answer. I also tried to use the time dilation and length contraction equations but to no avail. Please see attachment for the figure.

Also, I am unsure whether the textbook is trying to find the proper length or is trying to find the length with respect to the stationary frame.

Also, I am unsure whether the textbook is trying to find the proper length or is trying to find the length with respect to the stationary frame.

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