What time interval between wave fronts in S and S'?

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Homework Help Overview

The problem involves a scenario with a moving train and the measurement of time intervals between wave fronts as perceived by different observers in different reference frames. The context relates to special relativity and wave propagation, specifically examining how the motion of the train affects the timing of wave arrivals.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the use of distances traveled in different frames and question the application of special relativity given the train's speed. There is exploration of how to account for the distance the train moves while the waves propagate.

Discussion Status

The discussion is ongoing, with participants raising questions about the assumptions made in the problem and the implications of using specific distances in different reference frames. Some guidance has been offered regarding the derivation of the formula used, but no consensus has been reached on the necessity of special relativity in this context.

Contextual Notes

Participants note that the speed of the train is a small fraction of the speed of light, which raises questions about the relevance of relativistic effects. There is also mention of length contraction and how it might affect the problem setup.

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Homework Statement



1-9: Assume the train is 1.0km long as measured by the observer at C' and is moving at 150km/h. What time interval between the arrival of the wave fronts at C' is measured by the observer at C in S?
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Homework Equations

The Attempt at a Solution


The solution from the manual is Δt=t(back)-t(front)= 500/(c-(150/3.6m/s))-500/(c+(150/3.6m/s))=4.6*10^-13

How can it use the distance it travels in S'? It doesn't travel that distance in S.
 
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Breadsticks said:
How can it use the distance it travels in S'? It doesn't travel that distance in S.
The speed of the train is a tiny fraction of the speed of light. No need for SR here.
 
Doc Al said:
The speed of the train is a tiny fraction of the speed of light. No need for SR here.

Thanks for the reply. If the train was moving at a non-negligible fraction of the speed of light, I would then simply find where the waves meet to figure distance for each then use the above procedure with the modified distances?
 
Breadsticks said:
If the train was moving at a non-negligible fraction of the speed of light, I would then simply find where the waves meet to figure distance for each then use the above procedure with the modified distances?
I would use the exact procedure with the only difference being the modified distances (the length of the train in frame S).

Be sure you understand how that formula is derived.
 
Doc Al said:
I would use the exact procedure with the only difference being the modified distances (the length of the train in frame S).

Be sure you understand how that formula is derived.
Right, there would be length contraction but what about the distance the train has moved while the wave is moving?
 
Breadsticks said:
Right, there would be length contraction but what about the distance the train has moved while the wave is moving?
That is covered by the formula you quoted. (Understand how it is derived!)
 

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