Answer to Question #105465 in Classical Mechanics for Ahmad Raza

Question

In Doppler's effect the observed frequency of waves in case when observer is in motion, depends upon the relative relative velocity between source and observer. But from Michealson Morley experiment speed of light is independent of relative motion between source and observer.Why is it so?

Answer 1

Because the sped of light $c$ is a constant value. If something moves with some speed and emits light, the resulting speed of light will be $c$. The speed of light is independent of the frame of reference. That experiment consequently led to the development of special relativity.

Doppler's effect and red shift particularly, however, do not deal only with the speed of light. They deal with frequency and wavelength. We know that

$$c=\lambda\nu.$$

The electromagnetic waves emitted by a body move toward us/away from us with the speed of light. However, their own speed change the wavelength, not the speed of the electromagnetic waves. The degree of that wavelength change depends on the source's speed:

$$\lambda=\frac{c\pm v}{\nu}.$$