What is the Doppler effect in waves?

The Doppler effect in waves is the change in frequency or wavelength due to the relative motion of the source and observer.

The Doppler effect is observed in all types of waves, including sound waves, light waves, and water waves. When a wave source moves towards an observer, the frequency of the wave appears to increase, resulting in a higher pitch or shorter wavelength. Conversely, when a wave source moves away from an observer, the frequency appears to decrease, resulting in a lower pitch or longer wavelength.

The Doppler effect is used in various applications, such as in radar and sonar systems, where it is used to determine the speed and direction of moving objects. It is also used in astronomy to determine the motion of stars and galaxies.

The Doppler effect can be expressed mathematically using the equation:

f' = f (v ± v₀) / (v ± vᵒ)

where f is the frequency of the wave, v is the speed of the wave in the medium, v₀ is the speed of the observer, vᵒ is the speed of the source, and the plus or minus sign depends on whether the source is moving towards or away from the observer.

Overall, the Doppler effect is an important concept in wave physics and has many practical applications in various fields.