An illustration of the Doppler Effect and how relative motion affects the perceived frequency. Various different flypast cases are animated and put together. The Doppler effect occurs not only for sound, but for any wave when there is relative motion between the observer and the source. Doppler shifts occur in the frequency of sound, light, and water waves, for example. Doppler shifts can be used to determine velocity, such as when ultrasound is reflected from blood in a medical diagnostic. Step 4: Calculate the unknown by substituting from the Doppler effect equation. WORKED EXAMPLES 1. A sound source, moving at a constant speed of 240 m∙s-1 towards a detector, emits sound at a constant frequency. The detector records a frequency of 5 100 Hz. Take the speed of sound in air as 340 m∙s-1.
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The Doppler effect can be observed for any type of wave - water wave, sound wave, light wave, etc. We are most familiar with the Doppler effect because of our experiences with sound waves. Perhaps you recall an instance in which a police car or emergency vehicle was traveling towards you on the highway. Doppler Effect - Definition, Formulas, Solved Examples, Uses Doppler effect or Doppler shift is the change in frequency of a wave produced by a moving source with respect to an observer. Doppler effect is useful in a variety of different scientific disciplines, including planetary science.
Learning Objectives
By the end of this section, you will be able to:
- Explain the origin of the shift in frequency and wavelength of the observed wavelength when observer and source moved toward or away from each other
- Derive an expression for the relativistic Doppler shift
- Apply the Doppler shift equations to real-world examples
As discussed in the chapter on sound, if a source of sound and a listener are moving farther apart, the listener encounters fewer cycles of a wave in each second, and therefore lower frequency, than if their separation remains constant. For the same reason, the listener detects a higher frequency if the source and listener are getting closer. The resulting Doppler shift in detected frequency occurs for any form of wave. For sound waves, however, the equations for the Doppler shift differ markedly depending on whether it is the source, the observer, or the air, which is moving. Light requires no medium, and the Doppler shift for light traveling in vacuum depends only on the relative speed of the observer and source.
The Relativistic Doppler Effect
Suppose an observer in S sees light from a source in moving away at velocity v ((Figure)). The wavelength of the light could be measured within —for example, by using a mirror to set up standing waves and measuring the distance between nodes. These distances are proper lengths with as their rest frame, and change by a factor when measured in the observer’s frame S, where the ruler measuring the wavelength in is seen as moving.
If the source were stationary in S, the observer would see a length of the wave pattern in time But because of the motion of relative to S, considered solely within S, the observer sees the wave pattern, and therefore the wavelength, stretched out by a factor of
as illustrated in (b) of (Figure). The overall increase from both effects gives
where is the wavelength of the light seen by the source in and is the wavelength that the observer detects within S.
Red Shifts and Blue Shifts
The observed wavelength of electromagnetic radiation is longer (called a “red shift”) than that emitted by the source when the source moves away from the observer. Similarly, the wavelength is shorter (called a “blue shift”) when the source moves toward the observer. The amount of change is determined by
where is the wavelength in the frame of reference of the source, and v is the relative velocity of the two frames S and The velocity v is positive for motion away from an observer and negative for motion toward an observer. In terms of source frequency and observed frequency, this equation can be written as
Notice that the signs are different from those of the wavelength equation.
Calculating a Doppler Shift Suppose a galaxy is moving away from Earth at a speed 0.825c. It emits radio waves with a wavelength of
0.525 m. What wavelength would we detect on Earth?
Strategy Because the galaxy is moving at a relativistic speed, we must determine the Doppler shift of the radio waves using the relativistic Doppler shift instead of the classical Doppler shift.
Solution
- Identify the knowns:
- Identify the unknown:
- Express the answer as an equation:
- Do the calculation:
Significance Because the galaxy is moving away from Earth, we expect the wavelengths of radiation it emits to be redshifted. The wavelength we calculated is 1.70 m, which is redshifted from the original wavelength of 0.525 m. You will see in Particle Physics and Cosmology that detecting redshifted radiation led to present-day understanding of the origin and evolution of the universe.
Check Your Understanding Suppose a space probe moves away from Earth at a speed 0.350c. It sends a radio-wave message back to Earth at a frequency of 1.50 GHz. At what frequency is the message received on Earth?
We can substitute the data directly into the equation for relativistic Doppler frequency:
The relativistic Doppler effect has applications ranging from Doppler radar storm monitoring to providing information on the motion and distance of stars. We describe some of these applications in the exercises.
Summary
- An observer of electromagnetic radiation sees relativistic Doppler effects if the source of the radiation is moving relative to the observer. The wavelength of the radiation is longer (called a red shift) than that emitted by the source when the source moves away from the observer and shorter (called a blue shift) when the source moves toward the observer. The shifted wavelength is described by the equation:
where is the observed wavelength, is the source wavelength, and v is the relative velocity of the source to the observer.
Conceptual Questions
Explain the meaning of the terms “red shift” and “blue shift” as they relate to the relativistic Doppler effect.
What happens to the relativistic Doppler effect when relative velocity is zero? Is this the expected result?
There is no measured change in wavelength or frequency in this case. The relativistic Doppler effect depends only on the relative velocity of the source and the observer, not any speed relative to a medium for the light waves.
Is the relativistic Doppler effect consistent with the classical Doppler effect in the respect that is larger for motion away?
All galaxies farther away than about exhibit a red shift in their emitted light that is proportional to distance, with those farther and farther away having progressively greater red shifts. What does this imply, assuming that the only source of red shift is relative motion?
It shows that the stars are getting more distant from Earth, that the universe is expanding, and doing so at an accelerating rate, with greater velocity for more distant stars.]
Problems
A highway patrol officer uses a device that measures the speed of vehicles by bouncing radar off them and measuring the Doppler shift. The outgoing radar has a frequency of 100 GHz and the returning echo has a frequency 15.0 kHz higher. What is the velocity of the vehicle? Note that there are two Doppler shifts in echoes. Be certain not to round off until the end of the problem, because the effect is small.
What is Doppler effect?
“The apparent change in the frequency due to relative motion between source and observer is known as Doppler effect.”
When a listener is in motion toward a stationary source of sound ,the pitch (frequency) of the sound heard is higher than when the listener is at rest.If the listener is in motion away from the stationary source,a lower pitch is heard.We obtain similar results when the source is in motion toward or away from a stationary listener.The pitch of the whistle of a locomotive or the siren of a fire engine is higher when the source is approaching the hearer than when it has passed and receding.
In a paper written in 1842,Christian Johann Doppler (1803 – 1853,Austrian) called attention to the fact that motion of the body and the observer.This Doppler effect ,as it is called,applies to waves in general.Doppler himself mentions the application of his principle to sound waves.An experimental test was carried out in Holland in 1845 by Buys Ballot,”using a locomotive drawing an open car with several trumpeters.”
An important of phenomenon observed in waves in the Doppler effect. This effect shows that if there is some relative motion between the source of waves and the observer, An apparent change in frequency of the waves is observed.
This effect was observed by Johann Doppler while he was observing the frequency of light emitted from distant stars. In some cases, the frequency of light emitted from a star was found to be slightly different from that emitted from a similar source on the Earth. He found that the change in frequency of light depends on the motion of star relative to the Earth.
This effect can be observed with sound waves also. When an observer is standing on a railway plat form,the pitch of the whistle of an approaching locomotive is heard to be higher. But when the same locomotive moves away,the pitch of the whistle becomes lower.
The change in the frequency due to Doppler effect can be calculated easily if the relative motion between the source and the observer is along a straight line joining them. Suppose v is the velocity of the sound in the medium and the source emits a sound of frequency f and wavelength λ. If both the source and the observer are stationary, then:
Doppler Effect Example Sound
V = νλ ……..(1)
λ = V/ν ………(2)
ν =V/λ …………(3)
There are four possible cases to discuss the Doppler’s effect.
4 cases of doppler effect
Case 1:When observer moves towards the stationary source of sound:
If the observer moves towards the source with a velocity v0. The relative velocity of the waves and the observer is
v +v0
Now the number of waves received in one second or changed frequency νA is given by:
Thus the pitch of the sound increases.
Case 2:When observer moves away from the stationary source of sound:
If the observer moves towards the source with a velocity V0. The relative velocity of the waves and the observer is:
V – V0.
Now the number of waves received in one second or changed frequency νB is given by:
Thus the pitch of the sound decreases.
Case 3:When source of sound moves towards the stationary observer:
Suppose the source of sound waves towards the stationary observer with velocity V0 .Now in one second ,the waves are compressed by an amount known as Doppler shift represented by Δλ,so:
VS =ν Δλ
Δλ = VS/ν …………..(6)
Doppler Effect Examples Video
The compression of waves is due to the fact that same number of waves are contained in a shorter space depending upon the velocity of the source.The wavelength for observer is then:
Thus the pitch of the sound increases.
Case 4:When source of sound moves away from stationary observer:
Suppose the source of sound moves with velocity Vs away from the stationary observer.Now the modified frequency of the sound waves heard by observer will be:
Thus the pitch of the sound decreases.
Doppler effect Applications
- Doppler effect is also applicable to electromagnetic waves. One of its important applications in the radar system, which uses radio waves to determine the elevation and speed of an aeroplane. Radar is a device, which transmits and receives radio waves. If an aeroplane approaches towards the radar, then the wavelength of the wave reflected from aeroplane would be shorter and if it moves away. Similarly speed of satellites moving around the Earth can also be determined by the same principle.
- Sonar is an acronym derived from “sound navigation and ranging”. The general name for sonic or ultrasonic underwater echo-ranging and echo-sounding system. Sonar is the name of a technique for detecting the presence of objects underwater by acoustical echo.
In sonar “Doppler detection” relies upon the relative speed of the target and the detector to provide an indicator of the target speed. It employs the Doppler effect, in which an apparent change in frequency occurs when the source and the observer are in relative motion to one another. Its known military applications include the detection and location of submarines,control of antisubmarine weapons,mine hunting and depth measurement of sea.
- Astronomers use the Doppler effect to calculate the speeds of distant the stars and galaxies. By comparing the line spectrum of light from the star with light a laboratory source, the Doppler shift of the star’s light can be measured. Then the speed of the star can be calculated.
Doppler Effect Problem Examples
Stars moving towards the Earth show a blue shift. This is because the wavelength of light emitted by the star are shorter than is the star had been at rest. So, the spectrum is shifted towards shorter wavelength, i.e., top the blue end of the spectrum.
Stars moving away from the Earth show a red shift. The emitted waves have a longer wavelength than if the star had been at rest. So the spectrum is shifted towards longer wavelength i.e., towards the red end of the spectrum .Astronomers have also discovered that all the distant galaxies are moving away from us and by measuring their red shift, they have estimated their speeds.
- Another important applications of the Doppler shift using electromagnetic waves is the radar speed trap. Microwaves are emitted from a transmitter in short bursts. Each burst is reflected off any car in the path of microwaves in between sending out bursts. The transmitter is open to detect reflected microwaves. If the reflection is caused by a moving obstacle, the reflected microwaves are Doppler shifted. By measuring the Doppler shift, the speed at which the car moves is calculated by computer programme.
Doppler Effect Examples Physics
See also video of Doppler effect and its applications:
For related Topics visit our page: Sound and oscillations