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Question

An observer is moving with one-third of the speed of light towards a stationary microwave source emitting waves at frequency 8 GHz. What is the frequency of the microwave measured by the observer?

A
8 GHz
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B
83 GHz
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C
82 GHz
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D
83 GHz
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Solution

The correct option is C 82 GHz
As the observer is moving towards a stationary source with relativistic velocity, distance between the light source and observer is decreasing, then the apparent frequency of the source will be given by
f=f0   1+vc1vc

From the data given in the question,

v=c3 and f0=8 GHz
f observer frequency
So
f=8⎢ ⎢ ⎢1+13113⎥ ⎥ ⎥12=8(42)12=82 GHz

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