Question

For frequency displacement in sound waves, Doppler's formula is slightly Different in the following two situations -

(i) the source is at rest and the observer is in motion, and
(ii) the source is in motion, but the audience is in restlessness.
While the Doppler formula for light is definitely the same in vacuum, in both of these situations. Why is this ? Make clear Do you think that these formulas will be completely identical in both situations even for light motion in some medium?​

Answer 1

You hear the high pitch of the horn of the approaching train, and notice that its pitch drops suddenly as the train passes you. This is called Doppler Effect.

Doppler Effect definition

Doppler Effect is the increase or decrease in the frequency of light, sound or other waves as the source and observer move towards each other or moves away from each other.

or

Doppler Effect is the change in the frequency of sound wave or light wave received by an observer compared with the frequency with which it was emitted by the source.

or

When there is a relative motion between the source of sound and observer, the frequency of sound heard by the observer is different from the actual frequency of sound emitted by the source.

Doppler Effect is the increase or decrease in the frequency of light, sound or other waves as the source and observer moves towards each other or moves away from each other.

Example:

Assume that you are standing on the platform at a railway station; you hear a high pitch sound when the train is approaching you. However, when the train passes you, the pitch suddenly becomes low. This is because when the train is approaching, you hear a high frequency sound but when the train passes, you hear a low frequency sound.

Observer at rest and source at rest

If an observer is at rest and source of sound is at rest, separated by some distance, the frequency of sound heard by the observer is same as the frequency of sound emitted by the source.

If observer is at rest and source of sound is at rest, separated by some distance, the frequency of sound heard by the observer is same as the frequency of sound emitted by the source.

In other words, if both observer and source are at rest position, the observer receives the same number of wave cycles per sec as emitted by the source.

Source at rest and observer moving towards source

If the source is at rest and observer is moving towards the source, then the distance between the source and observer decreases. As a result, the frequency of sound increases for the observer.

If the source is at rest position and observer is moving towards the source, then the distance between the source and observer decreases.

In the above diagram, the observer is traveling in the opposite direction to the sound waves at faster speed. As a result, more wave cycles will pass through the observer per second than the waves sent by the source per second. For example, if the source sends two wave cycles (2 Hz) to pass through a given point in one second, the observer receives four wave cycles (4 Hz) per second.

Therefore, the observer hears a high frequency sound than the original frequency sound emitted by the source.

The formula for the frequency that the observer will detect when the observer is moving towards source will be:

The formula for the frequency that the observer will detect when the observer is moving towards source will be:

Where,

fobserved = frequency received by the observer

fsource = original frequency

Vwave = speed of wave

Vobserver = speed of observer

hope it helps you dear✌✌✌✌

Answer 2

$\bold{\huge{\underline{Answer-}}}$

The Doppler effect for the moving light in the vacuum is similar to the virtual frequency of light taken by the observer in both the conditions. Even if the viewer is moving towards a constant source or the source is moving towards the viewer with the same moves.

Thus Doppler effect is symmetrical in light. . Sound waves are required on the other hand to run the medium, so even if the same relative positions between observers and sources in both the above situations seem to be similar, but they are not identical.

This is because of the reason that the velocity relative to the observer's medium in both directions is different;

Therefore, the virtual instances of the sound heard in both the conditions can not be the same. If there is talk of the speed of light in any medium then both the positions will be different as there will vary velocity between the observer's medium in both the situations.

Therefore, different doppler formulas of the frequency of light taken by the observer should be expected in this condition.