Answer to Question #206545 in Mechanics | Relativity for Safi Ullah

Question

light source moves in a circular orbit with a speed of 0.5c. What is the

displacement, due to the Doppler effect, of the sodium yellow line, as observed at

the center of the circle? The line has a wavelength of 589 nm in the laboratory.

Ans.: Dk ¼ 91 nm

Answer 1

Frequency at observer:

$f_r=f_s\sqrt{1-v^2/c^2}$

where f_s is frequency at source,

v is speed of light source.

Then:

$\lambda_r=\lambda_s/\sqrt{1-v^2/c^2}=589/\sqrt{1-0.25}=680\ nm$

Displacement:

$\Delta=\lambda_r-\lambda_s=680-589=91\ nm$