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tourjete
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Homework Statement
Suppose that A', B' and C' are at rest in frame S', which moves with respect to S at speed v in the +x direction. Let B' be located exactly midway between A' and C'. At t'=0, a light flash occurs at B' and expands outward as a spherical wave.
1. According to an observer in S', do the wave fronts arrive at A' and C' simultaneously? What about an observer in S?
2. If you answered no, what is the difference in their arrival times and at which point did the front arrive first?
Homework Equations
None, just Einstein's postulates of special relativity.
The Attempt at a Solution
Alright, so I *think* that the flashes would not arrive at A' and C' simultaneously according to an observer in S'. Because S' is moving in the +x direction, from the instant the flash occurs it has to travel a little further to get to C' than to A'. However, when I did out the math it told me that it would arrive at C' first.
This is what I tried. (I'm not sure if its right, should I be using a Lorentz transformation instead?)
t(b'-> c') = L/(c+v)
t(b' -> a') = L(c-v)
[tex]\Delta[/tex]t = L/(c-v) - L/(c+v)
[tex]\Delta[/tex]t = 2Lv/(c[tex]^{2}[/tex] - v[tex]^{2}[/tex])
I feel like I'm not understanding something about the fact that the speed of light always being a constant.
Furthermore, the observer in S would see the flash reach A' and B' simultaneously, right?