The Doppler effect in sound wave

The Doppler effect is a phenomenon observed in waves, including sound waves, where there is a perceived change in frequency or wavelength of a wave due to the relative motion between the source of the wave and the observer. In the context of sound waves, it refers to the change in pitch or frequency of a sound as the source of the sound moves relative to the listener.

Here's how it works:

1. Approaching Source: If the source of the sound is moving towards the observer, the sound waves bunch up, resulting in a higher frequency or pitch being perceived by the observer. This is because each successive wave crest is emitted from a position closer to the observer than the previous one, leading to a shorter wavelength and a higher frequency.
2. Receding Source: Conversely, if the source of the sound is moving away from the observer, the sound waves spread out, resulting in a lower frequency or pitch being perceived by the observer. In this case, each successive wave crest is emitted from a position farther away from the observer than the previous one, leading to a longer wavelength and a lower frequency.

The formula to calculate the observed frequency (f') due to the Doppler effect in sound waves is given by:

fobs=fs(vv∓vs) f obs = f s ( v v ∓ v s )

Where:

• f' is the observed frequency.
• f is the emitted frequency by the source.
• v is the speed of sound in the medium.
• v_o is the velocity of the observer relative to the medium (positive if moving towards the source, negative if moving away).
• v_s is the velocity of the source relative to the medium (positive if moving away from the observer, negative if moving towards).

This equation tells us that the observed frequency depends on the relative velocities of the source, observer, and the speed of sound in the medium.