A source of light moves with velocity `v` relative to a receiver. Demonstrate that for `vlt lt c` the fractional variation of frequency of light is defined by Eq.

Explanation

When `v lt lt c` time dilation effect of relativity can be neglected (i.e `t' ~~t)` and we can use time in the reference frame fixed to the observer. Suppose the source emits short pulses with intervals `T_(0)`. Then in the reference frame fixed to the receiver the disatnce between two seccessive pulses is `lambda = cT_(0)-v_(r)T_(0)` when measured along the observation line.
Here `v_(r)=v cos theta `is the projection of the source velocity on the observation line. The frequency of the pulses received by the observer is
`v =(c)/(lambda) = (v_(0))/(1-(v)/(c)) ~~v_(0)(1+(v_(r))/(c))`
(The formula is accurate to first order only)
Thus `(v-v_(0))/(v_(0)) = (v_(r))/(c) = (v cos theta)/(c)`
The frequecny increases when the source is moving towards the observer.