Doppler Shift: Formula & Applications

The Doppler shift, also known as the Doppler effect, is described as a change in the wavelength or frequency of waves as a function of the observer's position in relation to the wave source. 

• Christian Doppler, an Austrian physicist, proposed the shift theory in 1842. 
• It involves the increase or decrease in the frequency of sound or other waves when the source and observer change positions.
• Doppler shift will experience an upward shift in frequency when observers are facing the source caused by a moving wave source. 
• However, the result is the opposite when observers are facing away from the source.
• The most common example is a change of pitch when you hear a vehicle approaching, sounding a horn, and receding from an observer. 
• In this article, we will discuss the Doppler shift phenomenon, its formula, application, and effects.

Key Terms: Doppler Shift, Doppler Effect, Doppler Shift Formula, Pitch, Frequency, Sound Waves, Wavelength, Velocity

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What is Doppler Shift?

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Doppler Shift refers to the movement of the observer or the source with respect to the medium. It's vital to understand that the effect isn't caused by a change in the source's frequency.

• The Doppler shift can be seen in any type of wave, including water waves, sound waves, and light waves.
• It is a shift caused by a moving wave source that causes an apparent upward frequency shift for observers approaching the source.
• The Doppler shift depends on the velocity of the medium, the velocity of the source, and the velocity of the observer. 
• Researchers and astronomers use the concept for numerous scientific experiments. 
• Red shift and blue shift are two types of doppler shift.
• The blue shift occurs when the source is moving toward the observer, whereas the red shift occurs when the source is moving away from the observer.

Doppler Shift

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Doppler Shift Formula

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Doppler shift formula explain the link between perceived frequency and emitted frequency when the speed of the source and receiver is slower than the speed of wave.

• The apparent frequency in Doppler Effect can be calculated using the following formula:

\(f = \frac{(V \pm v_r)}{(V \pm v_s)} f_0\)

• where V refers to the velocity of the sound waves;
• vr refers to the receiver's speed with relation to the respective medium (positive if the receiver moves towards the source and vice-versa)
• vs denotes the source's velocity in relation to the medium (positive if the source moves away from the receiver and vice-versa)
• f denotes the observed frequency;
• fo is the emitted frequency

Perceived Frequency

The perceived frequency is given as:

△f=1+△v/ vf0

Emitted Frequency

The emitted frequency is given by:

\(\bigtriangleup f = \frac{ \bigtriangleup v}{v} f_0\)

• where, Δf = f - f₀  and Δv= v_r-v_s is the receiver's velocity in relation to the source.
• In various situations, the formula can be written as:

1. When the source moves towards an observer who is at rest, in this case, the velocity of the observer is zero. Hence,

\(f = \frac{V}{(V - v_s)}f_0\)

2. When the source moves away from an observer who is at rest, in this case, the velocity of the observer is zero, and since the source moves away from the observer, its velocity is taken as negative. Hence,

\(f = \frac{V}{(V - (-v_s))}f_0\)

100. When the observer moves towards a source at rest, in this case the velocity of the source is zero. Hence,

\(f = \frac{(V + v_r)}{V} f_0\)

500. When the observer moves away from a source that is stationary, in this case the velocity of the observer is zero and since the source moves away, its velocity is taken as negative. Hence,

\(f = \frac{(V - v_r)}{V} f_0\)

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Application of Doppler Shift

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Various applications of doppler shift are as follows:

Measurement of Velocity Profiles

Ultrasonic Doppler Velocimetry is a technique for determining the real-time completion velocity profile of liquids containing suspended particles such as dust, emulsions, and gas bubbles. Pulsating, laminar, or turbulent flow might be oscillating or stationary.

Sirens

When it passes by the spectator, the siren begins at a higher pitch than its stationary pitch, and when it recedes from the observer, it transforms into a lower pitch.

• It is employed in emergency vehicles.
• The velocity of the siren is denoted as vradial = vs.cosθ where θ is the angle formed by the line of sight of the item and its forward velocity.

Doppler Shift with Sirens

Astronomy 

Astronomers use the information about the shift in frequency of electromagnetic waves created by moving stars in our galaxy and beyond to learn about the stars and galaxies.

• Measurements of electromagnetic waves emitted by stars in distant galaxies are used to support the idea that the universe is expanding.
• Furthermore, the Doppler effect will be used to examine the fine features of stars within galaxies.

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Things to Remember

• Doppler shift indicates a change in the frequency or wavelength with respect to the observer's position relative to the wave source. 
• It solely depends on the relative speed of the source and the observer for light travelling in a vacuum. 
• The Doppler shift can only be noticed when the absorption lines are away from the required frequencies. 
• Different stars have different absorption lines at different frequencies.
• For the Doppler shift to be applicable, the motion of both the observer and the source should be along the same straight line.