An electric bulb, linked to a make and break power supply, turns off and on every second in its rest frame. Determine the frequency of its switching off and on as observed from a spaceship travelling at a speed of 0.8c .

Step-by-step solution

The proper time interval between two consecutive switching events in the rest frame of the bulb is t₀ = 1 s . The spaceship is moving with a speed v = 0.8c relative to the bulb. According to the time dilation formula, the time interval t observed from the spaceship is given by: t = t₀ 1 - v^2 c^2 Substituting v = 0.8c and t₀ = 1 s : t = 1 1 - (0.8)^2 = 1 1 - 0.64 = 1 0.36 = 1 0.6 s The observed frequency f is the reciprocal of the observed time interval: f = 1 t = 0.6 Hz