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 1.3% 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

The speed of galaxy relative to the earth is
`3.9 * 10^(6)`
`(m)/(s)`

Step-by-step explanation:

Given :

Observed frequency
`f_(obs) = 1.013 f`

Actual frequency
`f_(act) = f`

For finding the speed of galaxy relative to the earth.

From the doppler effect of light,

`f_(obs) = (c+v)/(c) f _(act)`

Where
`c = 3 * 10^(8) (m)/(s)`,
`v=` relative speed

`1.013 f= (c+v)/(c) f`

`0.013c = v`

`v = 0.013 * 3 * 10^(8)`

`v = 3.9 * 10^(6) (m)/(s)`

Therefore, the speed of galaxy relative to the earth is
`3.9 * 10^(6)`
`(m)/(s)`