Question

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency $10\, GHz$. What is the frequency of the microwave measured by the observer ? (speed of light $= 3 \times 10^8 \, ms^{-1}$)

• A. 10.1 GHz
• B. 12.1 GHz
• C. 17.3 GHz
• D. 15.3 GHz

Answer 1

Answer: (C)

17.3 GHz

Answer 2

For relativistic motion
$f = f_{0 } \sqrt{\frac{c+v}{c-v}}$ ; v = relative speed of approach
$f = 10\sqrt{\frac{c+\frac{c}{2}}{c-\frac{c}{2}} } = 10\sqrt{3} = 17.3\, GHz$