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What is doppler effect. How doppler effect is used to calculate the relative velocity
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Doppler Effect:

• Doppler effect is used to measure speed in RADAR sensors. When the fixed-frequency radio wave sent from the sender continuously strikes an object that is moving towards or away from the sender, the frequency of the reflected radio wave will be changed. This frequency shift is known as Doppler effect.

• The Doppler effect causes the received frequency of a source to differ from the sent frequency if there is motion that is increasing or decreasing the distance between the source and the receiver. This effect is readily observable as variation in the pitch of sound between a moving source and a stationary observer.

• The main reason for the Doppler effect is that when the source of the waves is moving towards the observer, each successive wave crest is emitted from a position closer to the observer than the crest of the previous wave. Therefore, each wave takes slightly less time to reach the observer than the previous wave. Hence, the time between the arrivals of successive wave crests at the observer is reduced, causing an increase in the frequency. While they are traveling, the distance between successive wave fronts is reduced, so the waves "bunch together". Conversely, if the source of waves is moving away from the observer, each wave is emitted from a position farther from the observer than the previous wave, so the arrival time between successive waves is increased, reducing the frequency. The distance between successive wave fronts is then increased, so the waves spread out.

In Doppler effect, the relationship between the received frequency f and the transmitted frequency f0 is given by:- where c is the velocity of radio waves in the medium, vT is the velocity of the receiver with respect to the medium and vs is the velocity of the source with respect to the medium.

How doppler effect is used to calculate the relative velocity:-

If a source moving toward the observer raises the frequency heard by the observer by decreasing the wavelength of the sound in the denominator which is given by:-

But if an observer moves toward the source, it increases the frequency heard by increasing the relative velocity between him and the sound wave in the numerator. Where v` is relative velocity.

(U is negative because it's towards the source).