JEE Main 2017 · 2 Apr · Shift 1 · Physics Q13

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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 = $3\times10^8$ ms $^{-1}$ )

10.1 GHz

12.1 GHz

17.3 GHz

15.3 GHz

Answer and worked solution

Official answer: C

For light the relativistic Doppler formula applies, with $\beta=\frac12$ :
$f=f_0\sqrt{\frac{1+\beta}{1-\beta}}=10\sqrt3\approx17.3\text{ GHz}.$

Topics:Doppler effect

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JEE Main 2017 · 2 Apr · Shift 1, Physics question 13