Doppler Effect IIT JEE

My sister is doing preparation for IIT JEE Entrance Exam. She wants notes on ‘Doppler Effect’ topic. So is there anybody who will provide important notes based on ‘Doppler Effect’ for IIT JEE Exam?

[sumit]

As you are searching for important notes on ‘Doppler Effect’ Topic for IIT JEE Entrance Exam, so here I am providing notes:

IIT JEE ‘Doppler Effect’ Notes:

The whistle of a fast moving train appears to increase in pitch as it approaches a stationary observer and it appears to decrease as the train moves away from the observer. This apparent change in frequency was first observed and explained by Doppler in 1845.

The phenomenon of the apparent change in the frequency of sound due to the relative motion between the source of sound and the observer is called Doppler effect.

The apparent frequency due to Doppler effect for different cases can be deduced as follows.

(i) Both source and observer at rest
Both Source and Observer at Rest

Suppose S and O are the positions of the source and the observer respectively. Let n be the frequency of the sound and v be the velocity of sound. In one second, n waves produced by the source travel a distance SO = v (Fig. 7.19a).

The wavelength is λ = n

(ii) When the source moves towards the stationary observer
If the source moves with a velocity vs towards the stationary observer, then after one second, the source will reach S’, such that SS’ = vs. Now n waves emitted by the source will occupy a distance of (v – vs) only as shown in figure.

Therefore the apparent wavelength of the sound is

λ’ = v – vs/n

The apparent frequency

Source Moves Towards Observer at Rest

n’ = v/λ’ = (v/v – vs)n

As n′ > n, the pitch of the sound appears to increase.

When the source moves away from the stationary observer

If the source moves away from the stationary observer with velocity vs, the apparent frequency will be given by

n’ = [v/v – (-vs)]n = [v/v + vs] n

As n′ < n, the pitch of the sound appears to decrease.

(iii) Source is at rest and observer in motion
Observer is Moving Towards a Source at Rest

S and O represent the positions of source and observer respectively.

The source S emits n waves per second having a wavelength λ = v/n

Consider a point A such that OA contains n waves which crosses the ear of the observer in one second (Fig. 7.20a). (i.e) when the first wave is at the point A, the nth wave will be at O, where the observer is situated.

When the observer moves towards the stationary source,

Suppose the observer is moving towards the stationary source with velocity vo. After one second the observer will reach the point O′ such that OO′ = vo. The number of waves crossing the observer will be n waves in the distance OA in addition to the number of waves in the distance OO′ which is equal to v0/λ as shown in Fig. 7.20b. Therefore, the apparent frequency of sound is

n’ = n + v0/λ = n + (v0/v) n