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  4. 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 × 108 ms-1)

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Q. 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 $= 3 \times 10^8 \, ms^{-1}$)

JEE MainJEE Main 2017Wave Optics

Solution:

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 $