I got a little confused with the derivation of doppler effect for light as showed on wikipedia. The derivation states that when the source of light and the receiver are moving away from one another, the wavelength as observed by the receiver equals to the wavelength as emitted by the source plus the distance the receiver moved whilst the wave moved one wavelength (as emitted by the source) towards it.
Suppose one wavefront arrives at the receiver. The next wavefront is then at a distance $\lambda_s = c / f_s$ away from the receiver (where $\lambda_s$ is the wavelength, $f_s$ is the frequency of the waves that the source emits, and $c$ is the speed of light).
The wavefront moves with speed $c$, but at the same time the receiver moves away with speed $v$ during a time $t_s = 1/f_s = \lambda_s/c$, so $$\lambda + v t_s=ct_{r,s} \Longleftrightarrow (1 + v/c) \lambda_s = c t_{r,s} \Longleftrightarrow t_{r,s} = (1 + \beta) \frac{1}{f_s}$$
I don't understand why as when the wavefront will complete the distance the receiver moved away from it previously, the receiver will already have moved again so they won't meet. Could anyone please explain that to me? Thanks a lot!
