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A boy standing near a railway track found that the pitch of the siren of a train increases as it approaches him

1. State the phenomenon behind it?

2. List any two applications of the same Phenomenon

3. Obtain an expression for the apparent frequency of the siren as heard by the boy.

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1. Doppler effect.

2. Doppler effect can be used to find the speed of moving object. Dopplar effect in light is used to find speed of galaxies.

3. The apparent change in the frequency of sound wave due to the relative motion of source or listener or both is called Doppler effect. It was proposed by John Christian Doppler and it was experimentally tested by Buys Ballot.

Considers source is producing sound of frequency v. Let V be the velocity of sound in the medium and λ the wavelength of sound when the source and the listener are at rest.

The frequency of sound heard by the listener is ν = vλ. Let the source and listener be moving with velocities vs and vl in the direction of propogation of sound from source to listener. (The direction S to L is taken as positive).

The relative velocity of sound wave with respect to the source = V – Vs
Apparent wavelength of sound,

λ1 = \(\frac{V−V_s}{v}\)  _____(1)

Since the listener is moving with velocity v^, the relative velocity of sound with respect to the listener,

V1 = V – Vl  ______(2)

Apparent frequency of sound as heard by the listener is given by

ν = \(\frac{v_1}{λ_1}\)  ______(3)

Sub (1) and (2) in eq.(3) we get

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