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Question

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10GHz. What is the frequency of the microwave measured by the observer?
(speed of light =3×108 ms1)

A
15.3GHz
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B
10.1GHz
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C
12.1GHz
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D
17.3GHz
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Solution

The correct option is D 17.3GHz
Speed of observer, v=C2

where speed of microwave is C.

Original frequency of source is given as f0=10 GHz

Using relativistic Doppler effect in case observer moves towards the stationary source.

Apparent frequency measured by observer f=f0C+vCv

f=10C+(C/2)C(C/2)

=10(3/2)C(1/2)C

=10×1.73 GHz

=17.3 GHz

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