What is Doppler Effect?
The Doppler effect, also called the Doppler shift, happens when the source of waves moves relative to the observer. For example, the Doppler Effect can be seen when an ambulance crosses your path while its siren is going off.
Working Principle of the Doppler Effect
The Doppler Effect happens with both light and sound. For example, when a sound source moves toward you, the frequency of the sound waves goes up, which makes the sound louder. On the other hand, if it moves away from you, the sound waves slow down and the pitch drops. So, this is the working principle of the Doppler effect.
The formula of the Doppler Effect
The general formula which is used to calculate the Doppler effect is
where :c is the speed of waves in the medium
vr is the receiver’s rate of speed in relation to the medium, If the receiver is moving toward the source, the signal is positive; otherwise, it is negative.
vc is the speed of the source in relation to the medium; +c is for sources moving away from the receiver, -c is for sources moving in the receiver’s direction.
The primary Doppler effect equation exists. But various circumstances can alter this equation. Depending on the observer’s or the sound source’s velocity, it is altered or adjusted. The various Doppler effect formulas will be seen in a number of situations or cases.
Examples of the Doppler Effect
Let us discuss this example in cases which are as follows:
Case 1: As shown in the picture below, two people, observer 1 and observer 2, are standing on the road.
Who hears the sound of the engine revving louder?
Observer 2 hears more of the sound of the engine revving than observer 1. When observer 1 stands behind the car, he or she hears a low-pitched sound because there are fewer waves per second. But observer 2, who is in front of the car, hears more of these ripples per second. Because of this, the waves have a higher frequency, which means the sound has a higher pitch.
Case 2: Let us categorize this case 2 into further two situations.
Situation 1: How do the waves form when someone jumps into a pond all of a sudden?
Situation 2: How do the waves in a pond form when someone walk through it?
The picture below shows how the patterns of waves are different in each case.
Who discovered the Doppler Effect?
Christian Doppler was an Austrian physicist who was born on November 29, 1803, in Salzburg and died on March 17, 1853, in Venice discovered the Doppler effect phenomenon.
He was the first person to explain how the motion of the source and the detector affects the frequency of light and sound waves that can be seen or heard. The name “Doppler effect” was given to this effect.
When does Doppler Effect occur?
When the speed of the source is slower than the speed of the waves, the Doppler effect is seen. But a different thing happens when the source moves at the same speed as or faster than the wave itself. The main reason we see the Doppler effect is that as the source of the wave moves toward the observer, each new wave crest it makes comes from a place closer to the observer.
Derivation of the Formula
Let us discuss the different cases of this phenomenon
Case 1
In this instance, the observer is veering off of a still source. It suggests that
The constant k should be less than 1.
The relative velocity of sound with respect to the moving observer is V – Vo.
Therefore,
Comparing this with k < 1
We will get
Case 2
Given that the observer is currently moving in the direction of the stationary source, it follows that
Fa > Fo
Make k a constant that is bigger than 1.
V + Vo is the formula for the sound’s relative velocity in relation to a moving observer.
Therefore,
When compared to (k > 1)
We get,
Case 3
In this instance, the source is moving away from the observer who is still. It suggests that,
fa < fo
A constant that is less than 1 should be used as k.
V + Vs is the formula for the sound’s relative velocity in relation to a moving source.
Therefore,
Putting this next to k 1,
We get,
Case 4
In this case, the source is moving toward the observer who is standing still. It shows that
fa > f
Let k be a constant number that is bigger than 1.
The speed of sound in relation to the moving source is given by V – Vs.
Therefore,
Putting this together with (k > 1)
We get,
Case 5
In this case, both the source and the observer are moving towards each other, which means that fa > fo.
Or, fa = kfo if (k > 1)
Let k be a constant that is greater than 1
The speed of sound in relation to the moving source is given by V – Vs.
V + Vo is the speed of sound relative to an observer who is moving.
From the above, we can say that
Putting this together with k > 1,
We get,
Case 6
In this case, both the source and the observer are moving away from each other.
Fa = KFo, where K is less than 1.
Let k be a constant that isn’t equal to 1
The speed of sound in relation to a moving source is equal to V + Vs.
V – Vo is the speed of sound relative to an observer who is moving.
From what’s been said, we can say,
Putting this next to k 1,
We get,
Case 7
In this case, both the source and the observer are moving in the direction of the speed of sound (v).
When both are moving in the same direction, the source will move toward the observer if the observer suddenly stops.
When both the source and the observer are moving in the same direction, and the source suddenly stops, the observer will move away from the source.
By Combining (a) and (b) we get
Case 8
In this case, both the source and the observer are moving in the same direction, but the direction of the speed of sound is the opposite (v).
When both are moving in the same direction, the source will move away from the observer if the observer suddenly stops.
When both the source and the observer are moving in the same direction, and the source suddenly stops, the observer will move towards the source.
Characteristics of the Doppler Effect
Some of the characteristics of this effect are as follows:
The phenomenon of the Doppler effect in the water
Let’s start our look at the Doppler effect by thinking about a source that makes waves in the water that move at a certain speed. This source makes a series of wave fronts, and each one moves outward in a sphere with the source at its center. The wavelength, or the distance between wave crests, will be the same all the way around the sphere. If you stand in front of the source of the waves, you’ll see that they all come in at the same time. So will someone who is standing behind the source of the wave.
Now, let’s think about a situation in which the source is not still, but instead is moving to the right as it makes waves. Since the source is moving, it starts to catch up to the wave crests on one side while moving away from the crests on the other side. If you stand in front of the source, you can see how the crests are clumped together. If you stand behind the source, you can see how far apart the waves are. Remember that the frequency is equal to the number of waves that pass a certain point per second, so, someone in front of the source will see a higher frequency than someone in the back.
The phenomenon of the Doppler effect in the sound
Since sound waves can only be heard and not seen, an observer will hear the waves that are closer together as higher-pitched sounds and the waves that are farther apart as lower-pitched sounds. For example, think about a car driving down a highway between two people. The roar of the engine and the friction between the tires and the road surface make a sound called “vroom” that both onlookers and the driver can hear.
The driver will always hear this noise. But if you stand in front of the car, you’ll hear a higher-pitched sound. Why? Because the sound waves get smaller as the vehicle gets closer to the person in front of it. This makes the wave go faster and raises the pitch of the vroom. As the car moves away, the sound waves spread out, making the noise from behind the car sound lower in pitch. This makes the wave less often, so the pitch of the vroom goes down.
The phenomenon of the Doppler effect in the Light
Light waves are seen as colors, so an observer will see the waves that are closer together as bluer and the waves that are farther apart as redder. Take the example of an astronomer looking through a telescope at a galaxy. If the galaxy is hurtling toward Earth, its light waves will bunch up as they get closer to the telescope. This makes the wave’s frequency go up, which makes the blue colors in its spectral output stand out more. If the galaxy is moving away from Earth quickly, the light waves it makes will spread out as the galaxy moves away from the telescope. This makes the wave’s frequency go down, which makes its spectral output move toward red.
How do redshift and blueshift relate to the doppler effect?
The Doppler effect of light is when the observer sees a change in the frequency of the light because the source of the light is moving and the observer is not.
The equations for the Doppler shift are very different for sound waves, though, depending on whether the source, the observer, or the air is moving. Light doesn’t need anything to travel through, and the Doppler shift for light traveling in a vacuum depends only on how fast the observer and source are moving relative to each other.
- When the source of light moves away from the observer, the frequency that the observer receives will be less than the frequency that the source sends out. This makes the visible light spectrum move toward the red end. It is called the “redshift” by astronomers.
- When the source of light moves toward the observer, the frequency that the observer receives will be higher than the frequency that the source sends out. This makes the visible light spectrum move toward the high-frequency end. It’s called the “blueshift” by astronomers.
Applications of the Doppler Effect
People often think that the Doppler effect only works with sound waves. It works with all kinds of waves, even light waves. Here are a few ways that the Doppler effect can be used:
Sirens
As an ambulance speeds toward you with its sirens going, you hear a high-pitched sound. This is because the moving ambulance is squashing together the sound waves in front of it. This means that your ear gets more vibrations per second. A siren on an ambulance makes a sound with a frequency of 1500 Hz. The speed of sound is 340 m/s.
Radars
Doppler radar sends out waves of energy and listens for any signals that come back. The effect is like the “Doppler shift” that can be seen with sound waves. With the “Doppler shift,” the pitch of a sound made by an object moving toward you is higher because the sound waves are being squeezed together, which changes the phase. Radar data can be used to figure out how storms are built and help predict how bad storms will be.
Astronomy
The pitch change is bigger when something is moving faster. The Doppler effect can happen with both light and sound. For example, astronomers often measure how much their light is “stretched” into the lower frequency, red part of the spectrum to figure out how fast stars and galaxies are moving away from us. If a star gets closer or farther away from us, the light waves in its continuous spectrum look shorter or longer, and the dark lines look the same way. A star wobbles as a planet goes around it. This makes something called a Doppler shift happen to the star’s spectrum.
Medical Imaging
A regular ultrasound also uses sound waves to make pictures of structures inside the body, but it can’t show how blood flows. Doppler ultrasound works by measuring how moving objects, like red blood cells, reflect sound waves. By bouncing high-frequency sound waves (ultrasound) off your red blood cells, a Doppler ultrasound is a noninvasive test that can be used to estimate how much blood is flowing through your blood vessels. Normal ultrasounds use sound waves to make pictures, but they can’t show how blood moves. The Doppler effect is the name for this.
Blood Flow Measurement
Doppler flow is a type of ultrasound that measures how fast blood moves through a blood vessel by using sound waves. On the ultrasound screen, the waves of the blood flow are shown. Doppler flow studies can be used to measure the flow of blood in the umbilical vein and arteries, the fetal brain, the fetal heart, and other organs.
Satellite Communication
It shows that the Doppler effect is mostly about the carrier frequency of the signal and the height of the satellite’s orbit. When the carrier frequency is higher, the height of the satellite’s orbit is lower, and the Doppler effect is worse. Because the earth is curved, the speed changes, and so does the size of the Doppler effect. Dynamic Doppler compensation, in which the frequency of a signal changes gradually as it is sent, is used to make sure that the satellite gets a signal with a constant frequency.
Vibration Measurement
The frequency of light that bounces off of a moving object changes in a way that depends on how fast the object is moving (Doppler effect). Using an interferometer to measure this frequency shift gives a very accurate picture of how the object is vibrating.
Developmental Biology
This “Doppler effect” happens because the end of the tissue that is moving back and forth moves steadily toward the waves that are coming. So, the rhythm of sequential body segmentation is a result of genetic oscillations, the way their wave patterns change, and the shortening of tissues.
Audio
When the sound moves on, the pitch or tone of the sound changes. The Doppler Effect is to blame for that change in pitch. The Doppler effect is a wave phenomenon that happens when either the wave source or the observer is moving.
Velocity Profile Measurement
PSI came up with the ultrasonic velocity profile measuring method for use in fluid mechanics and measuring fluid flow. It uses both pulsed ultrasonic echography and the detection of the Doppler shift frequency in real-time. This method is better than the usual ones in the following ways:
- An efficient flow mapping process
- Applicability to opaque liquids
- A record of the spatiotemporal velocity field
Limitations of the Doppler Effect
- Doppler Effect only works when the speed of both the sound source and the observer is much slower than the speed of sound.
- The source and the observer should both be moving in a straight line.
- If the source of the sound moves toward the listener faster than the speed of the sound, the Doppler effect won’t be seen. The same thing happens if the listener moves faster than the speed of sound toward the source of the sound.
FAQ’s
What is Z in redshift?
z tells you how many years it took for the light from the object to reach us. However, this is not the distance to the object in light years, because as the light traveled, the universe has been expanding, so the object is now much farther away.
What is a redshift of 5?
It might be helpful to take a moment to think about what a redshift of z = 5 means and why it is important. So, z = 5 means that the recession speed is v = 0.946 c (where c is the speed of light in vacuum).
What are the different Doppler modes?
Because transducer elements are used in three modes (B-mode, color flow, and pulsed wave Doppler), the frame rate slows down, the size of the color flow box gets smaller, and the pulse repetition frequency gets lower. This makes aliasing more likely to happen.
What are the different cases of the Doppler effect?
Case I: An observer who is moving away from a source that is still. Case II: An observer who is moving toward a source that is still. Case III: The source is moving away from the observer who is standing still. Case IV: The source is moving toward the observer who is still.
What are two applications of the Doppler effect in medicine?
With the Doppler Effect, doctors can figure out where and how fast blood is moving through arteries and veins. This is used in echocardiograms and medical ultrasonography. It is a good way to figure out what’s wrong with a blood vessel.
Doppler effects can be observed for how many types of waves?
Both types of waves can be seen to have Doppler effects. Both the Doppler effect in sound (waves that move in a straight line) and the Doppler effect in light (waves that move in a circle) are well-known phenomena.
What is Huygens’s principle in ultrasound?
The Huygens principle says that when a sound wave hits the surface of a porous body, it causes the cell wall and the air inside the pores to move relative to each other. This causes friction and viscosity, and some of the sound energy is turned into heat.
What is the conclusion of the Doppler effect?
If we (the observer) are moving in the opposite direction of the sound waves (the source), we will hear a higher frequency. In the same way, if the source of sound waves is moving towards us, the frequency will seem higher to you than it was before.
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