An observer moves with velocity `v_(1) = (1)/(2) c` along a straight line. In front of him a source of monochromatic light moves with velocity `v_(2) = (3)/(4)c` in the same direction and along the same straight line. The proper frequency of light is equal to `omega_(0)`. Find teh frequency of light registered by the observer.

Explanation

We go to the frame in which the observer is at rest. In this frame the velocity of the source of light is, by relativistic velocity addition formula,
`v = ((3)/(4)c-(1)/(2)c)/(1-((3)/(4)c.(1)/(2)c//c^(2))) = (2c)/(5)`
When this source emits light of proper frequency `omega_(0)`, the frequency recorded by observer will be
`omega = omega_(0) sqrt((1-v//c)/(1+v//c)+v//c) = sqrt((3)/(7)) omega_(0)`
Note that `omega lt omega_(0)` as the sourcee is moving away form the observer (red shift).