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

[Breadsticks]

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?

[/B]

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.

 

[Doc Al]

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.

 

[Breadsticks]

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?

 

[Doc Al]

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.

 

[Breadsticks]

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?

 

[Doc Al]

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!)