You\'ve entered the Great Space Race. Your engines are hearty enough to keep you

Question

You've entered the Great Space Race. Your engines are hearty enough to keep you in second place. While racing, the person in front of you begins to have engine troubles and turns on his emergency lights that emit at a frequency of 5.510 1014 Hz. If the person in front of you is traveling 2658 km/s faster than you when he turns on his lights, what is the frequency of the emergency lights that you observe when it reaches you in your spaceship? (Enter your answer to four significant figures.)

answer is not 5.41E14 or 5.46E14

Explanation / Answer

here the observer is approaching the source and hence the observed frequency is higher than the source frequency du to relativistic doppler effect

relative speed v = 2658 km/s = 2.658e+6 m/s = 0.00886c

obsreved frequency   fo   = (sqrt(1+v/c)/sqrt(1-v/c) ) *fs

                                           = sqrt(1.00886/0.99114) *5.51e+14

                                           = 5.559e+14 Hz

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