Question

An electric bulb, connected to a make and break power supply, switches off and on every second in its rest frame. What is the frequency of its switching off and on as seen from a spaceship travelling at a speed 0.8c?

Answer 1

Given:
Speed of spaceship, v = 0.8 c
Proper frequency of bulb, f = 1 Hz

Let the frequency of bulb as seen from a spaceship be f'.

$$\begin{gathered} f\text{'}=f\sqrt{1-v^2/c^2} \\ f\text{'}=\sqrt{\frac{1-0.64c^2}{c^2}} \\ =\sqrt{0.36}=0.6\mathrm{Hz} \end{gathered}$$