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

In summary, the problem involves finding the time interval between the arrival of wave fronts at observer C', given that the train is 1.0km long and moving at 150km/h. The solution involves using the formula Δt=t(back)-t(front)= 500/(c-(150/3.6m/s))-500/(c+(150/3.6m/s))=4.6*10^-13, which takes into account the distance the train has moved while the wave is moving. However, since the speed of the train is a tiny fraction of the speed of light, special relativity is not needed in this problem. It is important to understand how the formula is derived.
  • #1
Breadsticks
16
1

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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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?
 
  • #6
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!)
 

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

1. What is the meaning of "wave fronts" in S and S'?

"Wave fronts" refer to the imaginary surfaces that represent the crest or peak of a wave as it propagates through a medium.

2. How is the time interval between wave fronts in S and S' measured?

The time interval between wave fronts in S and S' can be measured using a stopwatch or a timer. The observer can start the timer when the wave front passes a specific point and stop it when the next wave front reaches the same point.

3. What is the significance of measuring the time interval between wave fronts in S and S'?

Measuring the time interval between wave fronts in S and S' can help determine the speed of the wave and the distance it has traveled. This information is important in understanding the properties of the medium through which the wave is traveling.

4. How does the time interval between wave fronts in S and S' relate to the frequency of the wave?

The time interval between wave fronts in S and S' is inversely related to the frequency of the wave. This means that as the frequency increases, the time interval between wave fronts decreases and vice versa.

5. Can the time interval between wave fronts in S and S' be different for different types of waves?

Yes, the time interval between wave fronts in S and S' can vary depending on the type of wave. For example, electromagnetic waves and sound waves have different speeds and frequencies, resulting in different time intervals between their wave fronts.

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