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What is Doppler effect in sound? Obtain an expression for the observed frequency of sound produced by a source when both the observer and the source are in motion and medium is at rest.

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Doppler effect is a common phenomenon that we observe in our everyday lives. For instance, if you are standing on the footpath, you hear a police vehicle approaching in the distance. First, the sound of the siren is faint and it gets louder as the vehicle reaches closer to you. Once the police car crosses you and goes ahead the sound gradually decreases again. This effect is basically known as the Doppler effect.

Generally, the doppler effect can be defined as the change in wave frequency (whether it is light or sound) during relative motion between the source of the wave and the observer. This effect can be observed every time a source wave is moving in relation to the observer. The Doppler effect was discovered in the year 1842 by an Austrian mathematician and physicist named Christian Johann Doppler. The effect was named after him.

When the source and observer are moving relative to each other, the frequency observed by the observer (fa) is different from the actual frequency produced by the source (f0). This is basically the definition of the Doppler effect in Physics. Here, when the source of waves is moving towards the observer they will have an upward shift in frequency. As for the observers from whom the source is receding, there will be a downward shift in frequency.

However, it should be noted that the effect does not occur as a result of the actual change in the frequency of the wave source. The Doppler effect can be observed in both sound waves and light waves. While we have already described the effect in sound waves, the following is an example of the Doppler effect for light waves.

If we observe the light of a star from earth it usually shifts toward the red end of the spectrum (lower frequency or longer wavelength) when the earth and star are moving away from each other. This is also known as red-shift. On the other hand, it tends to move toward the violet side (higher frequency or shorter wavelength) if both earth and the star are coming close to each other. This is also called the blue shift. As a result of this phenomenon, the doppler effect is used in studying the motion of stars. It is also an integral part of modern theories of the universe.

The main reason that we experience the Doppler effect is that as the wave source moves toward the observer, each new wave crest that is formed from the source is emitted from a location that is closer to the observer. Therefore, as the source moves closer and closer the waves will now take less time to reach the observer or the time between the arrivals of new wave crests is reduced. This further causes an increase in frequency. Similarly, when the source of waves is going away, the waves are emitted from a farther location thus increasing the arrival time between each new wave. This leads to a reduction in frequency.

Nonetheless, from what we have learnt above, we can summarize that the Doppler effect could result from several factors such as;

the motion of the observer

the motion of the source

the motion of the medium.

This is mainly true for sound waves. Whereas, for waves that can travel in any medium, such as light, we need to consider only the relative difference in velocity between the source and the observer.

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