An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GhHz. What is the frequency of the microwave measured by the observer? (speed of light=`3xx10^(8)ms`)

Options

A. `17.3GHz`
B. `15.3GHz`
C. `10.1GHz`
D. `12.1GHz`

Answer

A

Explanation

Here, `v=10GHz, v^(')=?`
`upsilon=(c)/(2)` and `c=3xx10^(8)m//s`
As speed of observer is not very much less than the speed of light , therefore,
`v^(')=sqrt((1+upsilon//c)/(1-upsilon//c))xxv=sqrt((1+1//2)/(1-1//2))xxv`
`=sqrt(3)xx10GHz=17.3GHz`