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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?

12.1GHz

17.3GHz

15.3GHz

10.1GHz

Solution:

According to Doppler's law, when source or observer is in relative motion, apparent frequency is slightly different from real one;
ν′ = ν√(c+v)/(c-v)
Here, ν′ = 10√(1 + 1/2)/(1 - 1/2)
ν′ = 10 × √3 GHz
ν′ = 17.3GHz