DOPPLER EFFECT -

The apparent change in the observed frequency of a wave due to the relative motion between the source of waves and the observer is called the Doppler effect.

Case 1:- When the source is at rest and the observer is in motion.

Here the source is at rest and emits waves continuous with the speed of sound $\dpi{120} \fn_cm v$ . Let $\dpi{120} \fn_cm \lambda$ is the wavelength of sound.

The frequency of the sound is given by

$\dpi{120} \fn_cm f_s=\frac{v}{\lambda}............(1)$

Consider the observer approaches the source with a speed $\dpi{120} \fn_cm v_0$ .

Then the speed of sound w.r.t observer is given by $\dpi{120} \fn_cm (v+v_0)$

Here wavelength of sound does not change w.r.t observer but frequency changed because wave (crest) reaches very fastly to the observer.

i.e. The apparent frequency observed by the observer is

$\dpi{120} \fn_cm f_0=\frac{v+v_0}{\lambda}$

from (1)

$\dpi{120} \fn_cm \left [ f_0=\left ( \frac{v+v_0}{v} \right )f_s \right ]$

If the observer moving away from the source, then

$\dpi{120} \fn_cm \left [ f_0=\left ( \frac{v-v_0}{v} \right )f_s \right ]$

Case 2:- When the observer is at rest and source is in motion:-

Let $\dpi{120} \fn_cm v$ is the speed of sound and $\dpi{120} \fn_cm v_s$ is the speed of source towards the observer.

In this case, the wavelength of sound is changed (reduced) as shown in fig.

Since the observer is at rest, i.e. speed of sound w.r.t observer is $\dpi{120} \fn_cm v \;(not\;\;v+v_s)$ , because the velocity of sound depends upon medium, not source.