Answer to Question #206543 in Mechanics | Relativity for Safi Ullah

Question

Show that the light from a source which is moving away from us with a speed of

0.6c has twice the wavelength it has in the frame of reference of the source.

Answer 1

We can use the relativistic Doppler Effect equation in this problem.

For a source of light moving away from the observer, the wavelength of light measured by the observer will be:

$λ=λ_0 \sqrt{ \frac{1+β}{1-β} }$

λ₀ is the wavelength of light in frame of reference of the source

We can compute the β value as

$β = \frac{v}{c} \\ β = \frac{0.6c}{c} \\ β =0.6$

Substitute the β value:

$λ=λ_0 \sqrt{ \frac{1+0.6}{1-0.6} } \\ λ=λ_0 \sqrt{4} \\ λ=2λ_0$

The light from a source which is moving away from us with a speed of 0.6c has twice the wavelength it has in the frame of reference of the source.