Question

Intelligent beings in a distant galaxy send a signal to earth in the form of an electromagnetic wave. The frequency of the signal observed on earth is 1.1% greater than the frequency emitted by the source in the distant galaxy. What is the speed vrel of the galaxy relative to the earth?

Answer 1

Answer:

3900000 m/s

Explanation:

c = Speed of light = $3\times 10^8\ m/s$

v = Speed of the galaxy relative to the earth

Observed frequency is

$f'=(1+0.013)f\\\Rightarrow \dfrac{f'}{f}=1.013$

Here the Doppler relation must be used.

So, observed frequency is given by

$f'=f\dfrac{v+c}{c}\\\Rightarrow \dfrac{f'}{f}=\dfrac{v+c}{c}\\\Rightarrow v=\dfrac{f'c}{f}-c\\\Rightarrow v=(1.013\times 3\times 10^8)-3\times 10^8\\\Rightarrow v=3900000\ m/s$

The speed of the galaxy relative to the earth is 3900000 m/s