Question

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

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

Answer 1

The correct option is D 17.3 GHz

Doppler effect in light ( speed of observer is not very small compared to speed of light )

$f^1=\sqrt{\frac{1+V/C}{1-V/C}}{f}_{source}=\sqrt{\frac{1+1/2}{1-1/2}}\left(10GHz\right)$

$=17.3GHz$