Doppler effect

Summary

This educational video explores the Doppler Effect, demonstrating how sound frequency changes when a source moves relative to an observer. Using a simulation app, the presenter illustrates the effect by adjusting sound frequency and observer position. Key concepts like wavelength, frequency, and relative velocity are explained, with examples of sound source and listener movement. The video concludes with a formula for calculating the Doppler Effect and a practical example involving a moving police car siren.

Takeaways

• 🎵 The Doppler Effect is discussed with a focus on how sound frequency changes when the source or the observer is in motion.
• 📊 A simulation app is used to demonstrate the Doppler Effect, showing how frequency and wavelength change when the source of sound moves towards or away from an observer.
• 🏃‍♂️ When the source of sound moves towards an observer, the frequency increases because the wavelength decreases.
• 🔁 Conversely, when the source moves away, the frequency decreases as the wavelength increases.
• 👂 The observer's perception of sound frequency also changes if they are moving towards or away from the source.
• 🚗 An example using a car and a ball illustrates the concept of relative velocity, which is analogous to the Doppler Effect with sound.
• 🌊 The wavelength of sound in front of a moving source is calculated as the speed of sound times the period minus the speed of the source times the period.
• 🔄 Behind the source, the wavelength is the speed of sound times the period plus the speed of the source times the period.
• 📐 The perceived frequency by a listener is given by the speed of sound divided by the perceived wavelength, which depends on the listener's and source's relative motion.
• 🚓 A practical example is given with a police car siren, showing how to calculate the frequency heard by a stationary observer as the car approaches.
• ➡️ The direction of motion between the source and the observer determines whether the perceived frequency is higher or lower, using a rule of drawing an arrow from the listener to the source to decide the sign in the Doppler Effect formula.

Q & A

What is the Doppler Effect?

The Doppler Effect is a phenomenon that causes a change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It results in a higher frequency when the source and observer are moving closer to each other and a lower frequency when they are moving apart.

How does the Doppler Effect relate to sound waves?

In the context of sound waves, the Doppler Effect causes the pitch of a sound to appear higher when the source is moving towards the observer and lower when the source is moving away. This is due to the change in wavelength and frequency as perceived by the observer.

What is the role of the observer's movement in the Doppler Effect?

The observer's movement also affects the perceived frequency of a sound source. If the observer is moving towards the source, the perceived frequency increases, and if moving away, the perceived frequency decreases.

What is the formula used to calculate the frequency perceived by a listener when the source is moving?

The formula to calculate the perceived frequency when the source is moving is given by the speed of sound divided by the wavelength in front of the source, which is (V - VS) / (VS * T), where V is the speed of sound, VS is the speed of the source, and T is the period of the wave.

How does the Doppler Effect differ when the listener is moving instead of the source?

When the listener is moving, the perceived frequency changes based on the relative speed of sound, which is the speed of sound plus or minus the speed of the listener. The wavelength perceived by the listener changes, affecting the frequency.

What is the general expression for the Doppler Effect when both the listener and the source are moving?

The general expression for the Doppler Effect when both the listener and the source are moving is f_L = f_S * (V / (V ± VL)), where f_L is the frequency perceived by the listener, f_S is the frequency emitted by the source, V is the speed of sound, VL is the speed of the listener, and the plus or minus sign depends on the relative direction of movement.

What is the significance of drawing an arrow from the listener to the source when calculating the Doppler Effect?

Drawing an arrow from the listener to the source helps determine the direction of movement relative to each other. This reference direction is used to decide whether to use a plus or minus sign in the Doppler Effect calculations.

How does the Doppler Effect relate to the concept of relative velocity?

The Doppler Effect is closely related to the concept of relative velocity. It demonstrates how the perceived frequency or speed of a wave source changes based on the relative motion between the source and the observer.

What is an example of the Doppler Effect in the script involving a police car siren?

In the script, an example is given where a police car (source) is moving at 10 m/s and emits a siren frequency of 3000 Hz. If the listener is stationary, the perceived frequency is calculated using the Doppler Effect formula, resulting in a higher frequency due to the approaching source.

How does the perceived frequency change if the listener is moving towards the source?

If the listener is moving towards the source, the perceived frequency increases. This is because the relative speed of sound is higher, leading to shorter wavelengths and higher frequencies being perceived by the listener.

Outlines

00:00

🎵 Understanding the Doppler Effect

The paragraph introduces the Doppler Effect through a video demonstration. It explains how the frequency of sound changes as the source of sound moves towards or away from an observer. The presenter uses an app to simulate the Doppler Effect, showing how decreasing the frequency results in longer wavelengths and vice versa. The simulation illustrates that when the source moves towards the listener, the frequency increases due to shorter wavelengths, and when the source moves away, the frequency decreases due to longer wavelengths. The paragraph also touches on the concept of relative velocity, comparing the Doppler Effect to the perceived speed of a ball thrown from a moving car.

05:01

🚗 Doppler Effect with Moving Source and Listener

This paragraph delves deeper into the Doppler Effect, focusing on scenarios where both the source of sound and the listener are in motion. The presenter uses diagrams to explain how the wavelength of sound changes based on the relative motion of the source and listener. It's explained that the perceived frequency is determined by the speed of sound divided by the wavelength perceived by the listener. The paragraph also discusses how the Doppler Effect can be calculated using the relative velocity between the source and listener, and how this is analogous to the concept of relative velocity in Galilean relativity.

10:04

📐 Calculating the Doppler Effect

The final paragraph provides a practical approach to calculating the Doppler Effect. It combines the scenarios of a moving source and a moving listener into a general equation. The presenter corrects a mistake in the equation, emphasizing the importance of understanding whether the listener or the source is moving. An example is given involving a police car siren, showing how to calculate the perceived frequency when the source (the car) is moving and the listener is stationary. The paragraph concludes with another example where both the listener and the source are moving, illustrating how to determine the perceived frequency in such a case.

Keywords

💡Doppler Effect

The Doppler Effect is a phenomenon that occurs when the frequency of a wave changes for an observer who is moving relative to the source of the wave. In the video, this concept is central as it is used to explain how the pitch of a sound changes when the listener or the source of the sound is moving. The script uses the example of a moving car's siren to demonstrate how the frequency of the siren appears to increase to a stationary observer as the car approaches and decrease as it moves away.

💡Frequency

Frequency refers to the number of occurrences of a repeating event per unit of time, typically measured in Hertz (Hz). In the context of the video, frequency is discussed in relation to the pitch of sound. As the script explains, when a sound source moves towards an observer, the frequency of the sound increases, resulting in a higher pitch. Conversely, when the source moves away, the frequency decreases, leading to a lower pitch.

💡Wavelength

Wavelength is the physical length of one wave cycle, typically measured from peak to peak or valley to valley. The video script uses the concept of wavelength to explain the Doppler Effect, showing that as a sound source moves towards an observer, the wavelength shortens, leading to an increase in frequency. When the source moves away, the wavelength lengthens, resulting in a decrease in frequency.

💡Source of Sound

The source of sound is the origin of a sound wave. In the video, the script discusses how the Doppler Effect is observed when the source of sound moves relative to an observer. It uses an app simulation to demonstrate that when the source moves towards the observer, the frequency of the sound increases, and when it moves away, the frequency decreases.

💡Observer

An observer, in the context of the Doppler Effect, is the person or device that perceives the change in frequency of a sound wave. The video script explains that the Doppler Effect can occur not only when the source of sound moves but also when the observer moves. The observer's movement relative to the sound source affects the perceived frequency of the sound.

💡Relative Velocity

Relative velocity is the velocity of an object as observed from a particular frame of reference. The script uses the concept of relative velocity to explain how the perceived speed of an object, like a ball thrown from a moving car, changes depending on whether the observer is moving towards or away from the object. This concept is analogous to the Doppler Effect, where the perceived frequency of a sound changes based on the relative motion between the source and the observer.

💡Galilean Relativity

Galilean Relativity is a principle that states the laws of motion are the same in all inertial frames of reference. The video script briefly mentions Galilean Relativity to contextualize the concept of relative velocity, explaining that the perceived velocity of an object is dependent on the motion of both the object and the observer, which is a fundamental concept in understanding the Doppler Effect.

💡Pitch

Pitch is the perceptual property of a sound that allows its frequency to be identified as 'high' or 'low'. In the video, pitch is directly related to the frequency of a sound wave. The script explains that as the frequency of a sound wave increases, the pitch perceived by the listener also increases, which is a direct result of the Doppler Effect when the source is moving towards the listener.

💡App Simulation

An app simulation is a digital model used to demonstrate or experiment with real-world phenomena. In the video script, the presenter uses an app simulation to visually illustrate the Doppler Effect. The simulation allows the presenter to adjust the frequency of a sound source and the movement of an observer, showing how these changes affect the perceived frequency and thus the pitch of the sound.

💡Sound Wave

A sound wave is a type of longitudinal wave that propagates through a medium, such as air, by the vibration of particles. The video script discusses sound waves in the context of the Doppler Effect, explaining how the wavelength and frequency of these waves change as the source of the sound moves relative to an observer, which in turn affects the pitch of the sound that the observer hears.

💡Speed of Sound

The speed of sound is the distance that a sound wave travels per unit of time, typically measured in meters per second (m/s). In the video, the script uses the speed of sound (343 m/s in air at room temperature) as a constant value to calculate the perceived frequency of sound as observed by a moving listener or when the source of sound is moving.

Highlights

Introduction to the Doppler Effect

Demonstration of the Doppler Effect through a music video

Explanation of how frequency changes when the source of sound moves towards the listener

Illustration of wavelength changes as the source moves

Discussion on the decrease in frequency when the source moves away

Introduction of the simulation app to demonstrate the Doppler Effect

Explanation of how the observer's movement affects the perceived frequency

Example of relative velocity with a car and a ball

Application of Galilean relativity to the Doppler Effect

Detailed explanation of wavelength changes when the source moves

Calculation of the perceived frequency when the source is moving

Impact of the listener's movement on the perceived frequency

Combining equations for the general Doppler Effect

Explanation of how to handle the plus-minus in the Doppler Effect equation

Practical example of calculating the Doppler Effect with a moving police car

Rule for determining the positive direction in Doppler Effect calculations

Calculation of perceived frequency when both the listener and source are moving

Conclusion and预告 of more problems involving the Doppler Effect in class

Transcripts

good day on this

video we will discuss the Doppler

effect let me show you another

video all right this is how the song

really goes okay

[Music]

[Music]

okay

go oh

[Music]

now let's discuss through this little

app this simulation what's going

on I'm going to

add what we have here is a source of

sound right I'm going to actually

decrease the frequency a little bit and

then um I am going to draw

I'm adding an observer here you see and

then this is the source of sound as you

can see nothing is moving um this the

wavelength of the the sound can be

measured from Peak to Peak or Valley to

Valley now look what happens as the

source starts moving

towards the

listener you can see how how the

frequency

increases because the wavelength

decreases as the Observer moves the two

the two the wavelengths become the

wavelength become shorter and that means

the frequency

increases well as as if I do the

opposite it's hard to do this

consistently but look how look at the

wavelength look at the wavelength in

front is shorter and behind is Big so

what the Observer perceives is a longer

wavelength and that means um that means

low

frequency so this is the first case we

observed you get dupler effect when a

source of sound moves with respect to an

observer the other possibility is that

the source of sound doesn't move but

what moves is The Listener or the

Observer let's look at the perceived

sound down

here as I move you see the frequency

appears to increase it's not because of

the sound the source sound moved it's

because the Observer moved and if I do

the opposite if I move away from the

source you see the

wavelength

decreases look let's let's do the the

extreme case what will be the W

decreases the frequency decreases what

would be the the

frequency if the source stays where it

is without moving and the Observer moves

almost at the same speed as as the crest

itself this is very hard to do but you

you will see you probably can well I

could not I cannot do it with my mouse

it's very hard but if I

try well the the to remain nearly

constant meaning the frequency became

zero if I'm

uh let's just remember something very

quickly if I'm in a car and there is

somebody here and I throw a ball at 10

m/

second right if I'm not

moving and this person is not

moving the person will catch the ball at

10 m/ second now if the car is moving at

5 m/ Second to towards the person the

perceived speed of the bowl when it

reaches will be 15

m/s if I'm moving away the perceived

speed will be 5 m/ Second the same thing

happens if it's the the person moving if

the person moves towards the right at 8

m/s then the ball reaches him at 2 m/s

if the person is moving against the car

right let's say the car is not moving

just the team m per second on the ball

but the person moves against the ball at

10 m/ second then he will perceive the

ball reaching him at 20 m/s this is

called

relative

velocity and is related to Galilean

relativity okay with that in

mind let's see what happens with

sound when when what we saw is

that the source of sound is here right

so and then we said the source can be

moving the receiver can the perceiver

that the

listener listener and Source can be

moving as

well left and right right let's first

see what happens when the source moves

when the source moves the source Starts

Here emits sound right so let's say

after a certain time the whatever sound

was emitted from this position is

here

right this is difficult for me to draw

circles try again okay so it's there but

then at this in this in this time it

took the wave to arrive there because

the source is moving the source ared

here and then here comes the next sound

all right so what is the wavelength the

wavelength

of the

sound is well from here to here this is

the wavelength in front of the source

you see this distance here remember

speed is distance over time so any

distance is speed times time so this

distance is the speed of sound

times let's say one period well here

that looks like an S it's no it's a v

is the speed of sound times the period

let's and then and then from here to

here this is the speed of the source

times the period so you see how the

wavelength in front is this big radius

VT minus this little chunk

VST right or V minus the speed of sound

speed of the

source period or speed of sound speed of

the source over the frequency this is

the wavelength in front and if I want

the wavelength be behind let's say um

the wav be behind the wav room behind

will be will be all this from here to

here this is the distance between one

wavefront and the next one well all you

have to do is put here a negative a plus

because this will be the Big Radius VT

plus this chunk VST so that's the

wavelength that's how the wavelength

changes in front of or behind the

source where this F is the frequency

that the source is emitting okay so s

source is s listener is L so what

frequency does The Listener perceives

remember that velocity is Lambda F so

any frequency is speed speed of sound

over Lambda so the frequency the L the

The Listener receives is the speed of

sound over the wavelength The Listener

receives but that's this

one either front or depends where you

are is is the listener in front of the

source is the listener behind the source

so instead of Lambda listener I'm going

to put all this so v+ minus the speed of

source over the frequency of the source

this is the frequency The Listener that

the listener detects when the source is

moving

now what if the The Listener is moving

if the listener

moves this is still true the frequency

The Listener hears is the speed of sound

over the wavelength The Listener

perceives now if the listener moves you

are in this scenario is the same thing

the the the picture is sending you bolts

at 10 m/s but now the that the obser the

catcher is moving towards the bows so

the speed of the

bow is um is the perceived speed of the

ball the relative velocity is the speed

of the ball plus or minus the speed of

the catcher or in this case this The

Listener well see the same thing happens

here the if the listener moves the

frequency changes because the speed of

sound changed the the relative speed of

sound is different so it's going to be

the speed of sound plus or minus the

speed of the source and then here you

have whatever wavelength which is

constant in this case right in this case

the source is not moving is the listener

moving either towards the source or or

away from the source so the wavelength

The Listener receives is constant and

this is this this is how the frequency

will change if the listener is moving

well I'm going to combine these two

equations I'm going to put in the in the

numerator what happens

um what happens if the the The Listener

moves which is the then the same thing

here and I'm going to put what happens

if the if the source moves which is what

we put on the other

one oh there's a mistake here this is

the listener that's what I put here The

Listener this is the frequency changes

because the because the listener is

moving so here excuse me let's put it

here and then you have and this is the

general expression for doler

effect in um in the case The Listener

moves or the source moves or both move

the plus minus

um how do we deal with a plus minus let

me show

you remember the L means

listener the s means source so how do

you do a

problem um this is a general expression

let's do an quick example let's say you

have a car moving to the right this is

the one generating sound this a is a

it's a police car so there's a siren

there is a siren so the the source is

moving at 10 m/s to the right and here

you have a listener that is not moving

the speed of the listener is zero how do

you use how do we determine the

frequency The Listener will detect if

the car is moving at 10 m/ second let's

say the frequency of the car is 3,000

htz the siron so what you will do V and

V this is the speed of sound so let's

just use 343

3

43 The Listener is not moving so zero

and the source is moving at 10 meters

everything is in meters per second so

now what do you do with a plus minus

here and here well there is a very

simple rule that I can show you what you

do is you draw an arrow from The

Listener towards the

source and this determines your positive

direction so with respect to this

Vector this reference always listener to

Source always listener to source so with

respect to this reference you see VL is

doesn't matter because it's not moving

but vs is negative so you put a negative

and then you get your answer oh sorry

times the frequency of the

source the

3,000 and you get your answer 3,90

me Hertz you see it's higher this is

what we expected you're moving towards

is going to be higher pitch what if do

it again let's do it again but now let's

say The Listener is moving towards the

right at 5

m/s but the source is moving towards the

left at 10 m/ second but now towards the

left so we do this

again 3 4 3 3

43 the frequency is 3,000 and now the

listener is moving at five the source is

moving at 10 once again we draw

reference listener towards the source

this is our positive so with respect to

this positive reference The Listener is

moving

against the reference and the source is

moving with the reference so we put a

plus if you do the calculations you get

2,800

2.5 Hertz so less that you expected less

than the original 3000 right uh we'll do

more problems in involving this in class