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

1. Mar 2, 2016

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

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?

2. Relevant equations

3. 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.

2. Mar 2, 2016

### Staff: Mentor

The speed of the train is a tiny fraction of the speed of light. No need for SR here.

3. Mar 2, 2016

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?

4. Mar 2, 2016

### Staff: Mentor

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.

5. Mar 2, 2016

Right, there would be length contraction but what about the distance the train has moved while the wave is moving?

6. Mar 2, 2016

### Staff: Mentor

That is covered by the formula you quoted. (Understand how it is derived!)