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166. Problem 21.17 (RHK) An experimenter arranges to trigger two flashbulbs
simultaneously, a blue flash located at the origin of his reference frame and a
red flash at
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. A
second observer, moving at a speed of 0.247 c in the direction of
increasing x also observes the flashes. (a) We have to find the time
difference between the flashes measured by the moving observer; (b) we
have to answer which flash is observed first.|
Solution: Click For PDF Version (a) In the frame of reference of the experimenter the space-time co-ordinates of the two synchronous events are: blue flash,
red flash,
A second observer moving with speed
Using the Lorentz transformation the times of the two events measured by the moving observer will be: blue flash,
red flash,
The time interval between the two simultaneous flashes in the experimenter’s
frame as observed by the moving observer will be
(b) And, according to the moving observer the red flash occurs earlier than the blue flash and will be Doppler shifted.
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in the
direction of increasing x observes these events. The space-time
co-ordinates of the events as observed by the moving observer will be related to
those of the experimenter by the Lorentz transformation:
.