What is Doppler Shift?

What is Doppler Effect? How do the Doppler effect and Doppler shift relate to each other? Explain the Applications and Limitations of the Doppler Effect?

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- GoPhotonics

Feb 10, 2023

The Doppler shift is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the source of the wave. The Doppler effect is the phenomenon that causes this change in frequency or wavelength. It is named after Austrian physicist Christian Doppler, who first described it in 1842. The effect can be observed with sound waves, light waves, or any other type of wave.

The Doppler effect: A moving source emits a wave

Einstein's theory of special relativity incorporates the Doppler effect into its description of the behaviour of light. In special relativity, the Doppler effect is not limited to just sound waves but also applies to electromagnetic waves such as light.

Einstein showed that the frequency and wavelength of a light wave change as a result of the relative motion between the source of the light and the observer. This effect is known as the relativistic Doppler effect and is consistent with both the special theory of relativity and the principles of classical physics.

Blue shift and Red Shift

In the context of Einstein's special relativity, the most important Doppler effect is that for light waves, and the shift can be observed as a blue shift and a red shift.

A blue shift occurs when the source of the wave is moving towards the observer and the frequency of the wave appears to be higher than its actual frequency. On the other hand, a red shift occurs when the source of the wave is moving away from the observer and the frequency of the wave appears to be lower than the actual frequency.

Doppler Shift in Light Waves

Doppler shift applies to the entire electromagnetic spectrum, but light in particular is significant on all physical scales, from the atomic scales to the cosmic scales. On the atomic scale, we are concerned with the dispersion in frequency of spectral lines caused by the thermal velocities of atoms or molecules in a gas. On the cosmic scale, we observe the redshift of spectral lines from galaxies receding, with velocities comparable with the velocity of light.

Astronomers use this shift to determine the speed at which different objects in the universe are moving with respect to us. Other galaxies are moving away from ours due to the expansion of the universe. This causes a downward shift in the frequency of the light the galaxies emit. The light that we observe as red has a lower frequency within the visible spectrum than the light that we perceive as blue. Thus, the light that we perceive from other sources is shifted towards the red end of the visible spectrum and is referred to as the red shift.

Equations of Doppler shift

From the perspective of a stationary observer, a source releasing ๐›Ž0 waves in a second while moving away from the observer with velocity ν will cause the ๐›Ž0 waves to spread out to a distance of (c + ν) where c is the velocity of the waves. The frequency seen by the observer is given as:

Similarly, an observer travelling away from a stationary source at velocity ν will experience a frequency that is lowered by the rate at which the observer travels wavelengths of distance. The observed frequency is given as:

When compared to small velocities, these two equations are virtually identical, but when applied to large velocities, they start to diverge.

For light, there cannot be a difference between the motion of the source and the motion of the observer, which produces the Doppler shift.

According to special relativity, the observed frequency for any oscillator at frequency ๐›Ž0 that is travelling with velocity ν in relation to a stationary observer is given as:

Same equation is obtained for the moving observer. 

In terms of wavelength,

This formula is essential in the context of astronomical measurements of distant galaxies. It has been noted that the spectral lines wavelengths λobs are redshifted from their original wavelength λ0 by a factor of more than 7 that corresponds to a velocity 0.96 = ๐›Ž0.

Applications

The Doppler shift is used in many fields, including astronomy, meteorology, medicine, and telecommunications, to gather information about the movement of objects or to study the properties of waves. It is used to study the large-scale structure of the universe and to determine the properties of stars and galaxies by determining the velocity of stars and galaxies. 

The Doppler Shift is used in weather radar to determine the speed and direction of winds in the atmosphere. In the field of medicine, this shift is employed in medical imaging, such as ultrasound, to measure blood flow in the body.

It can also be used in telecommunications and radar systems to correct for the frequency shift.