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Homework Help: Special Theory of Relativity! Need help, Urgent?

  1. Jan 27, 2010 #1
    1. The problem statement, all variables and given/known data
    An observer in frame S standing at the origin observes two flashes of coloredlight separated spatially by delta x=2400 m. A blue flash occurs first, followed by a red flash 5 microseconds later. An observer in S' moving along x axis at speed v relative to S also observes the flashes 5 microseconds apart and with a separation of 2400m, but the red flash is observed first. Find the magnitude and direction of v.

    This is the only prob. on the hw that i seem to have no clue where to start.





    3. The attempt at a solution
    I know that the fact that the blue and red light switch places in terms of appearance (1st, 2nd) is the key factor in figuring out how to solve this problem, but i don't really know what this is telling me(i.e. what information it is providing me with). Any help/hint would be greately appreciated.
     
  2. jcsd
  3. Jan 27, 2010 #2

    gabbagabbahey

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    Hmmm... there may be an easier method, but when in doubt I recommend just labeling all events (assigning space and time coordinates to them in both reference frames) and using Lorentz transformations to solve for the unknowns.

    In this case, there are 6 events to consider:

    (1)blue flash occurs
    (2)red flash occurs
    (3)light from blue flash reaches origin in frame S
    (4)light from red flash reaches origin in frame S
    (5)light from blue flash reaches observer in frame S'
    (6)light from red flash reaches origin in frame S'

    I haven't worked the problem out myself, but I suspect that this could be a bit of a trick question. After all, assuming the sources of the flashes are stationary in frame S, they will be in relative motion to the observer in S' and hence doppler shifted.
     
  4. Jan 27, 2010 #3
    thanks for the hints, i will try to use them. Meanwhile, it occurred to me that the following might work, but it looks too simple to be true:

    In general, in frame S, if event 1 occurs at location x1 at time t1 and event two at location x2 at time t2, then the time interval in reference frame S' is given by:

    t'2-t'1=gama(t2-t1)-gamma*v/c^2(x2-x1). But like i said, this might not work at all, but i am not sure, since from here i can readily solve for v.

    do you think this approach works? if not why not?
     
    Last edited: Jan 27, 2010
  5. Jan 27, 2010 #4

    gabbagabbahey

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    I don't know how much that really helps you here. You are only given (using the event numbering from the list in my previous post) that [itex]|x_2-x1|=|x_2'-x_1'|=2400\text{m}[/itex], [itex]t_2-t_1=5\mu\text{s}[/itex] and [itex]|t_2'-t_1'|=5\mu\text{s}[/itex]

    The absolute values in the first equation are necessary because you aren't given the positions of the sources in either frame (you aren't even told which source is on the left and which is on the right), just the spatial separation between them.

    And the absolute values in the last equation are there because it is possible that the flash that was originally blue appears red to the moving observer (lots of Doppler shifting) and vice versa In which case [itex]t_2'-t_1'=5\mu\text{s}[/itex]. Or that when the questioner says that the "red flash is observed first", they mean that the light from the red flash is observed first, regardless of which color it actually appears to the moving observer (in other words, the observer already used the doppler formula to determine that the flash he observed was originally red), in which case [itex]t_1'-t_2'=5\mu\text{s}[/itex]

    Hopefully your calculations will show that only one of these scenarios is possible, otherwise your answer may depend on how you interpret the question.
     
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