Doppler effect
Summary
TLDRThis 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
🎵 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.
🚗 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.
📐 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.
Mindmap
Keywords
💡Doppler Effect
💡Frequency
💡Wavelength
💡Source of Sound
💡Observer
💡Relative Velocity
💡Galilean Relativity
💡Pitch
💡App Simulation
💡Sound Wave
💡Speed of Sound
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
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