A spaceship is going away from Earth with a speed 0.28c. A passenger in the spaceship measures his heartbeat as 72 beats per minute. How many beats per minute are observed in the telemetry radio signals received on Earth? Note that, in addition to time dilation, one must take into account that the signals of successive heartbeats have to travel longer distances because the spaceship is moving away (Doppler Effect).
A) 75
B) 96
C) 54
D) 69
E) 100

Question

Quizplus · Accepted Answer

The relativistic Doppler effect must be considered. The time dilation factor is given by the Lorentz factor, which is approximately 1.038 for 0.28c. However, due to the Doppler effect, the observed frequency is reduced further. The formula for the relativistic Doppler effect for a receding source is f' = f * sqrt((1 - β) / (1 + β)), where β = v/c. Substituting the values, the observed frequency is approximately 54 beats per minute.

A Spaceship Is Going Away from Earth with a Speed