An observer is moving in space toward a distant star at 200 km/s while the star is moving toward the observer at 400 km/s;the relative velocity being 600 km/s of approach.What relative change in frequency of the light from the star as seen by the observer? (The speed of light in space is 3.00 × 10⁵ km/s). A) 0.067% increase B) 0.20% decrease C) 0.20% increase D) 0.033% decrease

Question

Quizplus · Accepted Answer

The formula for calculating the relative change in frequency due to Doppler effect is:

Δf/f = (v/c) / (1 ± v/c)

where Δf is the change in frequency, f is the original frequency, v is the relative velocity, and c is the speed of light.

In this case, the observer and the star are moving towards each other, so we use the positive sign:

Δf/f = (200+400)/(3.00 × 10^5) / (1 + (200+400)/(3.00 × 10^5))
     = 600/3.00 × 10^5 / (1 + 600/3.00 × 10^5)
     = 0.002

So the relative change in frequency is 0.2%, which means a 0.2% increase in frequency, since the observer is moving towards the source of the light. Therefore, the answer is C.

An Observer Is Moving in Space Toward a Distant Star