# Doppler Shift

## What is Doppler Shift?

Doppler shift is also known as the Doppler effect is defined as the change in the wavelength or frequency of the waves with respect to the observer who is in motion relative to wave source. The phenomenon was described in the year 1842 by the Austrian physicist Christian Doppler.

## What is Doppler Shift Formula?

 $f=(\frac{c\pm v_{r}}{c\pm v_{s}})f_{0}$

Where,

• c is the velocity of waves in the medium
• vis the velocity of the receiver relative to the medium (positive if the receiver is moving towards the source and negative if in the opposite direction)
• vis the velocity of the source relative to the medium (positive if the source is moving away from the receiver and negative if in the opposite direction)
• f is the observed frequency
• fis the emitted frequency

Above is the Doppler shift or Doppler effect formula explaining the relationship between observed frequency and the emitted frequency where the speed of source and receiver are lower than the velocity of the waves in the medium.

Following is the formula when the speeds of receiver and source are comparatively smaller than the speed of the wave:

Observed frequency:

 $f=(1+\frac{\Delta v}{c})f_{0}$

Change in frequency:

 $\Delta f=\frac{\Delta v}{c}f_{0}$

Where,

$\Delta f=f-f_{0}$ $\Delta v=v_{r}-v_{s}$ velocity of the receiver relative to the source (positive when the source and the receiver moving towards each other)

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## Application of Doppler effect

### Sirens

The principle behind siren is that it starts out at a higher pitch than its stationary pitch when it slides down from the observer and again when it recedes from the observer it continues from the lower pitch than its stationary pitch. It is used in emergency vehicles. Siren’s velocity is given as: $v_{radial}=v_{s}.cos\Theta$ where Ө is the angle between the object’s line of sight and the forward velocity.

### Astronomy

In astronomy, Doppler effect for electromagnetic waves of light results in either red-shift or blue-shift. With the help of Doppler effect and radial velocity, one can measure the speed at which stars or galaxies are receding or approaching from us.

### Velocity profile measurement

Ultrasonic Doppler Velocimetry is used to measure the real-time completion velocity profile of any liquids containing suspended particles like dust, emulsions and gas bubbles. The flow can be pulsating, laminar or turbulent, oscillating or stationary.