Q

# Stuck here, help me understand: 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

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)

• Option 1)

10.1 GHz

• Option 2)

12.1 GHz

• Option 3)

17.3 GHz

• Option 4)

15.3 GHz

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As we learnt in

Doppler Effect -

When a source of sound and a listener are in motion relative to each other, the frequency of the sound heard by the listener is not the same as the source frequency.

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Doppler effect in light

$\upsilon'=\sqrt{\frac{1+v/c}{1-v/c}}\ \; \Rightarrow\ \; \sqrt{\frac{1+1/2}{1-1/2}}\ (10)$

$\upsilon'=17.3\ GHz$

Correct option is 3.

Option 1)

10.1 GHz

This is an incorrect option.

Option 2)

12.1 GHz

This is an incorrect option.

Option 3)

17.3 GHz

This is the correct option.

Option 4)

15.3 GHz

This is an incorrect option.

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