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

3900000 m/s

Step-by-step explanation:

c = Speed of light =
`3* 10^8\ m/s`

v = Speed of the galaxy relative to the earth

Observed frequency is

`f'=(1+0.013)f\\\Rightarrow (f')/(f)=1.013`

Here the Doppler relation must be used.

So, observed frequency is given by

`f'=f(v+c)/(c)\\\Rightarrow (f')/(f)=(v+c)/(c)\\\Rightarrow v=(f'c)/(f)-c\\\Rightarrow v=(1.013* 3* 10^8)-3* 10^8\\\Rightarrow v=3900000\ m/s`

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