Doppler Effect

Introduction

The Doppler Effect is a change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who proposed it in 1842.

Basic Formulas

The Doppler Effect can be described by the following formulas. For waves, such as light or sound, moving towards an observer, the frequency increases (a shift to higher frequencies) and is given by:

and for waves moving away from the observer, the frequency decreases (a shift to lower frequencies) and is given by:

where is the observed frequency, is the source frequency, is the speed of the wave, and is the speed of the observer.

Doppler Shift in Light: Redshift and Blueshift

When the source of light is moving away from the observer, there is an increase in the wavelength (or decrease in frequency) of the light, a phenomenon known as redshift. When the source of light is moving towards the observer, there is a decrease in the wavelength (or increase in frequency), known as blueshift.

The Doppler Effect for light is given by:

where , is the velocity of the source, and is the speed of light.

Applications

The Doppler Effect has many practical applications. It is used in radar and sonar systems to determine the speed of a target. In medicine, it is used in ultrasound imaging. In astrophysics, it is used to determine the velocity and distance of distant galaxies, providing key evidence for the expansion of the universe.

Conclusion

The Doppler Effect is a fundamental concept in wave physics. It describes the changes in frequencies of waves as observed in a moving frame of reference, and it has widespread applications in various fields of science and technology.

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