What is a Doppler Shift?
Doppler shift is also known as the Doppler effect is characterized as a change in wavelength or wave frequency with respect to the observer who is in motion relative to the wave source. The phenomenon was described by the Austrian physicist Christian Doppler in the year 1842.
What happens when an ambulance has passed you? Why does the siren 's tone change? It gets louder as it approaches, but another characteristic of sound changes as well. The pitch is higher when it moves towards you (think of a whining noise) and lower when it moves away (think of a deep voice). This change in pitch has to do with the frequency of waves, or how many waves pass through an area per unit of time.
In the case of an ambulance, you 're still standing and the ambulance is approaching you. As the sound waves move towards you, they are compressed and the frequency increases, so you hear a higher pitch. However, when the ambulance moves away from you, the sound waves spread further apart and the frequency gets lower, so you hear a lower pitch. This change in the frequency of sound waves due to movement is called the Doppler shift, also known as the Doppler effect.
The Doppler effect is observed whenever the wave source moves with respect to the observer. The Doppler effect can be defined as the effect created by a moving wave source in which there is an apparent upward shift in frequency for observers to whom the source is approaching and a clear downward shift in frequency for observers from whom the source is receding. It is important to remember that the effect is not due to a real shift in the frequency of the source.
The Doppler effect can be observed for any wave type-water wave, sound wave, lightwave, etc. Because of our experiences with sound waves, we are most familiar with the Doppler effect. You may remember an incident in which a police car or emergency vehicle was driving to you on the highway. As the car approached with its siren blast, the pitch of the siren sound (a measure of the siren 's frequency) was high; and then, unexpectedly, after the car passed by, the pitch of the siren sound was low. That was the Doppler effect-an an apparent shift in the frequency of a sound wave produced by a moving source.
What is Doppler Shift Formula?
\[f = (\frac{c \pm vr}{c \pm vs})fo\]
Where,
C is the amplitude of the wave in the medium;
vr is the speed of the receiver relative to the medium (positive if the receiver moves towards the source and negative if it moves in the opposite direction)
vs is the velocity of the source relative to the medium (positive if the source moves away from the receiver and negative if it moves in the opposite direction)
f is the frequency observed
f0 is the frequency emitted.
Above is the Doppler shift or Doppler effect formula which explains the relationship between the observed frequency and the emitted frequency where the velocity of the source and receiver is lower than the velocity of the waves in the medium. The following is the formula when the receiver and source speeds are relatively smaller than the wave velocity:
Observed Frequency:
\[F =(1 + \frac{\triangle v}{c})f_{0}\]
Change in Frequency:
\[\triangle f = \frac{\triangle v}{cf_{0}}\]
Where, Δf = f − f0, Δv = vr − vs velocity of the receiver relative to the source (positive when the source and the receiver moving towards each other).
Application of Doppler effect
Sirens
The concept behind siren is that it starts at a pitch higher than its stationary pitch as it travels down from the observer, and again as it recedes from the observer, it continues from a lower pitch than its stationary pitch. It is used in emergency vehicles. The velocity of Siren is given as:
Vradial = v s.cosፀ
where ፀ is the angle between the object’s line of sight and the forward velocity.
The Doppler Effect in Astronomy
The Doppler effect is of considerable interest to astronomers who use information on the change in the frequency of electromagnetic waves generated by moving stars in our galaxy and beyond to gain information about these stars and galaxies. The assumption that the universe is expanding is, in part, based on measurements of electromagnetic waves produced by stars in distant galaxies. In addition, the application of the Doppler effect will assess the precise details of stars within galaxies.
Galaxies are clusters of stars that typically rotate around a center of mass. Electromagnetic radiation released by these stars in a distant galaxy will appear to be moving downwards in frequency (red shift) if the star rotates in its cluster in a direction away from Earth. At the other hand, there is an upward change in the frequency (blue change) of the detected radiation as the star rotates in a direction to the Moon.
Velocity Profile Measurement
Ultrasonic Doppler Velocimeter is used to calculate the real-time performance velocity profile of any liquid containing suspended particles, such as dust, emulsions and gas bubbles. The flow can be pulsating, laminar or turbulent, oscillating or steady.
FAQs on Doppler Shift
1. What is the Doppler effect in simple terms?
The Doppler effect, also known as the Doppler shift, describes the change in the frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. In simpler terms, it's why the pitch of an ambulance siren sounds higher as it approaches you and lower as it moves away. The actual frequency of the siren doesn't change, but its motion relative to you compresses or stretches the sound waves, causing you to perceive a different pitch.
2. What is the general formula to calculate the apparent frequency in the Doppler effect for sound?
The general formula to find the apparent frequency (f') due to the Doppler effect for sound is:
f' = f ( (v ± v₀) / (v ± vₛ) )
Where:
- f' is the apparent frequency heard by the observer.
- f is the actual frequency emitted by the source.
- v is the velocity of sound in the medium.
- v₀ is the velocity of the observer.
- vₛ is the velocity of the source.
The signs for v₀ and vₛ depend on their direction of motion relative to each other. Typically, the sign is positive for movement towards each other and negative for movement away.
3. What are some important real-world applications of the Doppler effect?
The Doppler effect has numerous practical applications across various fields. Some key examples include:
- Astronomy: Astronomers use the 'red shift' (decrease in frequency) and 'blue shift' (increase in frequency) of light from distant stars and galaxies to determine if they are moving away from or towards Earth, which is a cornerstone of the expanding universe theory.
- Medical Imaging: In medicine, Doppler ultrasound uses this effect to measure the velocity of blood flow in arteries and veins, helping diagnose conditions like clots or blockages.
- Weather Forecasting: Doppler radar is used to detect the motion of precipitation, allowing meteorologists to track storms, determine their rotation, and issue timely warnings for events like tornadoes.
- Police Radar: Law enforcement uses radar guns that bounce radio waves off a moving vehicle. The change in frequency of the reflected waves is used to calculate the vehicle's speed accurately.
4. How does the Doppler effect for light waves differ from the Doppler effect for sound waves?
While the underlying principle is the same (relative motion changing perceived frequency), there are key differences:
- Medium Dependency: The Doppler effect in sound requires a medium (like air) to travel. Its formula depends on the velocities of the source and observer relative to this medium. Light, being an electromagnetic wave, does not require a medium and can travel in a vacuum.
- Symmetry: For sound, it matters whether the source is moving or the observer is moving; the results are not symmetrical. For light, due to the principles of special relativity, only the relative velocity between the source and observer matters.
- Formula: The classical Doppler formula works for sound at speeds much less than the speed of sound. The Doppler effect for light requires the use of the relativistic Doppler effect formula, especially as speeds approach the speed of light.
5. Why does the actual frequency of a source, like a siren, remain constant while the observed pitch changes?
This is the core concept of the Doppler effect. The source of the sound (the siren) is always vibrating at the same, constant rate, which defines its actual frequency. The change in pitch is a perceptual phenomenon experienced by the observer. When the siren moves towards you, it is 'catching up' to the sound waves it just emitted, effectively compressing them into a smaller space. This means more wave crests reach your ear per second, which you perceive as a higher frequency or pitch. Conversely, as it moves away, it is 'outrunning' its sound waves, stretching them out and causing fewer crests to reach your ear per second, which you perceive as a lower frequency or pitch.
6. How do astronomers use the concepts of 'red shift' and 'blue shift' to understand the universe?
In astronomy, the Doppler effect for light is a critical tool. 'Red shift' and 'blue shift' refer to how the light from celestial objects changes.
- Red Shift: When a star or galaxy is moving away from Earth, its light waves are stretched. This increases the wavelength, shifting its spectral lines towards the red end of the electromagnetic spectrum. The observation that almost all distant galaxies exhibit a red shift is the primary evidence for the expansion of the universe.
- Blue Shift: When an object is moving towards Earth, its light waves are compressed. This decreases the wavelength, shifting its spectral lines towards the blue end of the spectrum. The Andromeda Galaxy, for instance, exhibits a blue shift, indicating it is on a collision course with our Milky Way galaxy.
7. Is the Doppler effect limited only to sound and light waves?
No, the Doppler effect is a fundamental property of all types of waves. It applies whenever there is relative motion between a wave source and an observer. Besides sound and light, it can be observed in:
- Water waves: The frequency of waves hitting a boat changes if the boat is moving towards or away from the source of the waves.
- Radio waves: Used in satellite communication and radar systems.
- Ultrasound waves: Used in medical diagnostics to measure flow.
The specific mathematical formulas may differ based on the wave type and the medium, but the principle of an apparent shift in frequency due to relative motion remains the same.
