Starting in Toronto, Canada, a spaceship flies down Yonge Street(reportedly the

Question

Starting in Toronto, Canada, a spaceship flies down Yonge Street(reportedly the longest street in the world) at a velocity of0.450c. An astronaut on board measures herpulse rate at 50.0 beats per minute. (a) What is the time intervalbetween heartbeats according to her? (b) What is the time intervalbetween beats according to observers who are standing by the sideof the road? Now, the astronaut is attached to a machine that sendsa brief radio pulse for each beat of her heart back toward amonitoring device at her starting point. (c) What is the timeinterval measured by the monitor between consecutive radio pulses?

Explanation / Answer

f = 50 / 60 sec = .833 / sec a) t = 1 / f = 1.2 sec b) t' = t / (1 - v2 /c2) = 1.2 / (1 - .452) = 1.34sec for observer by road     t is the proper time (events occur ata single place) c) f' = f * (1 - v / c) / (1 - v2 /c2)     the formula for therelativistic Doppler effect    f' = .833 * (1 - .45) / .893 = .513 t' = 1 / f' = 1 / .513 = 1.95 sec

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