Shock waves
Summary
TLDRThis video script delves into shock waves, using a Ripple tank simulation to illustrate how wavelength compresses ahead and elongates behind a moving source. It explores scenarios where the source moves at the speed of the wave, creating zero wavelength and high amplitude, leading to a sonic boom when surpassing the speed of sound. The script explains shock waves, their generation by objects moving faster than sound, and the concept of Mach number, which quantifies the speed of an object relative to the speed of sound.
Takeaways
- π When a wave source moves, the wavelengths in front of it compress, and those behind it elongate.
- π If the source moves at the same speed as the wavefront, the wavelength at the source becomes zero.
- π A 3D view of this scenario shows a region of high amplitude, indicative of high pressure.
- π₯ When the source moves faster than the speed of sound, it creates a shock wave, also known as a sonic boom.
- π³ The phenomenon is similar to a boat moving faster than the waves it creates, leaving a wake behind.
- π The shock wave's angle can be calculated using the formula speed of sound over speed of source, which is the Mach number.
- π The half-angle of the shock wave cone is given by the inverse of the Mach number.
- π Sonic booms are the sounds produced when a source moves faster than sound, creating a pressure wave.
- π Shock waves can be extremely destructive, capable of damaging buildings or even killing people.
- π’ The Mach number is a key parameter in understanding the behavior of shock waves and the speed of the source relative to the speed of sound.
Q & A
What happens to the wavelength in front of a moving source in a Ripple tank simulation?
-In a Ripple tank simulation, when the source moves, the wavelength in front of it becomes compressed, while the wavelength behind gets longer.
What occurs when a source moves at the same speed as the wavefront?
-If the source moves at the same speed as the wavefront, the wavelength becomes zero, resulting in a region of high amplitude.
What is the term for the region of high amplitude when a source moves at the speed of the wave?
-The region of high amplitude when a source moves at the speed of the wave is referred to as a shock wave.
What phenomenon occurs when a source moves faster than the speed of sound?
-When a source moves faster than the speed of sound, it generates a sonic boom, which is characterized by a conical or triangular shape of increased pressure.
How does the shock wave generated by a bullet differ from the one created by an explosion?
-The shock wave created by a bullet is conical and is generated by the bullet traveling faster than sound, while the spherical shock wave is created by the gases of the explosion also traveling faster than sound.
What is the visual effect of a sonic boom as seen in the sky?
-A sonic boom can be seen as a cone shape created by the condensation of water vapor in the sky, following the pressure wave.
What is the destructive potential of a shock wave?
-A shock wave can be so destructive that it can kill people, destroy buildings, or planes due to the immense pressure it generates.
What is the Mach number and how is it calculated?
-The Mach number is the ratio of the speed of the source to the speed of sound. It indicates how many times faster the source is moving compared to the speed of sound.
How can you determine the speed of a bullet by observing the shock wave it creates?
-By observing the angle of the shock wave cone and knowing the speed of sound, you can calculate the Mach number and thus determine the speed of the bullet.
What is the significance of the half-angle of the shock wave cone?
-The half-angle of the shock wave cone is significant because it is directly related to the Mach number. The sine of the half-angle is equal to one over the Mach number.
Outlines
π Understanding Shock Waves
The script discusses shock waves using a Ripple tank simulation to demonstrate the behavior of waves as the source moves. When the source moves, the wavelength in front of it compresses, while behind it, the wavelength elongates. If the source moves at the same speed as the wavefront, the wavelength becomes zero, resulting in a region of high amplitude. This phenomenon is likened to breaking the sound barrier, where the source moves faster than the wave, creating a wake-like pattern. The script also touches on the concept of a sonic boom, which occurs when the source exceeds the speed of sound, generating a conical shock wave and a significant pressure increase.
π₯ Sonic Booms and Shock Waves
This paragraph delves deeper into sonic booms, which are the sounds produced when an object moves faster than sound, creating shock waves. The script describes how a sonic boom is generated, using a plane as an example to illustrate how the shock wave appears as a cone shape due to water vapor condensation. It explains that the sound comes after the plane because the source moves faster than the sound waves it creates. The concept of overlapping sound waves forming a shock wave is introduced, and the destructive power of shock waves is highlighted, noting that they can be lethal and cause significant damage.
π Mathematics of Shock Waves
The final paragraph focuses on the mathematical relationship between the speed of sound and the speed of the source to determine the angle of the shock wave cone. It introduces the Mach number, which is the ratio of the source's speed to the speed of sound. The script explains how the half-angle of the shock wave cone is related to the Mach number, using the formula speed of sound over speed of source. It also mentions how the angle of the shock wave can be used to estimate the speed of an object, such as a bullet, by observing the angle of the cone it creates.
Mindmap
Keywords
π‘Shock Waves
π‘Wavelength
π‘Amplitude
π‘Sound Barrier
π‘Sonic Boom
π‘Pressure Wave
π‘Ripple Tank Simulation
π‘Mach Number
π‘Wavefront
π‘Concentric Sound Waves
π‘Destructive Power
Highlights
Explains the concept of shock waves using a ripple tank simulation.
Describes how wavelength changes when the source moves at different speeds relative to the wavefront.
Illustrates the compression of wavelength in front and elongation behind when the source moves.
Discusses the scenario where the source moves at the same speed as the wavefront, resulting in zero wavelength.
Mentions the difficulty of simulating the source moving at the speed of the wave with a mouse.
Demonstrates a 3D view of the region where wavelength becomes zero, showing increased amplitude.
Introduces the term 'sound barrier' for the region of high amplitude and pressure.
Explains the phenomenon of a sonic boom when the source moves faster than sound.
Compares the wake of a boat to the shock wave generated by a source moving faster than sound.
Describes the difference between a shock wave created by a bullet and one created by an explosion.
Shows a photo of a sonic boom generated by a plane, illustrating the cone shape of condensed water vapor.
Discusses how the sonic boom is heard after the plane has passed due to the shock wave.
Explains the destructive power of shock waves and their ability to kill or destroy structures.
Introduces the concept of Mach number and its relation to the speed of sound and the source.
Calculates the angle of the shock wave cone based on the Mach number.
Concludes by emphasizing the importance of understanding shock waves for practical applications.
Transcripts
good
day um in this video we will talk about
shock
waves so um to discuss the shock waves
let's take a look at the simulation the
Ripple tank simulation in which we saw
how when we start moving the
source the wavelength in front of it
becomes
compressed while the wavelength behind
the wavelength gets
longer what if what if the source was
was to
move at this what if the source moves at
the same speed as the pulse as the
information look you this is very hard
to do this is not going to work with
this mouse let me see if I can try
again on the other side if I move well
it's working it's working more or less
more or less you see if I move exactly
if I move the source exactly at the same
rate as the wavefront meaning as the
information itself then the wavelength
becomes
zero the wavelength becomes
zero and uh and then what happens
is want to try I want to try I want to
try want to try you see stop if I stop
look look at this region where the
wavelength became zero if I do a 3D view
of it what you will see is that in this
region you see the amplitude is long is
is
larger here we can see all the effects
the com the the compression of the
wavelength the elongation of the
wavelength but for some for some
instance I managed to move the source at
the speed of the wave and you see how
the amplitude here became a little
higher good that's good well what we
call this this this um region of high
amplitude this is a pre you can talk
about the pressure wave if you want this
is a region of high
pressure this is a region of high
pressure that we called the sound
barrier now if
um if I go back what happens if the
source drop S faster than sound let's
say this is a sound wave this could be a
water wave or this could be sound
doesn't matter but if the source travels
faster than sound look what
happens you see you see the conb move
this away you see that the what happens
here look at that it looks like a
wake look look looks like a wake uh of a
boat in water
let me show you you see here in this
photo the boat as it moves the boat
actually moves faster than the
superficial waves it generates on the
surface of the water even docks can
travel faster than the propagation of of
water on the the prop not not the water
the prop the propagation of a of a wave
a disturbance on the surface of the
water as you can see in these photos and
also based from experience
so yeah same thing here right same thing
here they
waves when you move faster when the
source moves faster than the wave itself
it generates this wake uh shape if if
you talk about sound then um then these
are spheres and as the source moves it
generates a cone right that cone well
the at the surface at the interface at
the
boundary I want to try to do
this where
the uh it didn't work well I have a I
have a there is a simulation
here I'm looking I'm
looking here it is I found it I'm going
to move this moving
faster I want to stop it let's see the
3D view you see it's just the same we we
can think of this as the boat and then
look at the wake it lives in water uh
what's important is look at the
amplitude the amplitude of the weight
just like in water is higher so the
pressure effect on on the at the at the
boundary at the interface here is
humongous same thing happens with sound
it's just that instead of a triangular
shape it's a conical shape and what you
get is an increasing pressure so great
that it generates a lot of sound and we
and we call that a sonic boom and it's
generated when the source of sound moves
faster than sound generates this Sonic
Boom look at this photo that um the
sonic boom is the sound you hear when
you have this region called a shock wave
there's two shock waves this one is
circular and this one is the conical
shock wave but this shock wave is
created by the bullet itself traveling
faster than sound this spherical shock
wave is created by the gases of the
explosion that are that travel also
faster than sound so we have two shock
waves and the sound you you experience
when there is a shock wave is called the
sonic
boom and here I'm going to show you show
you this shock wave generated by a plane
here you see the we see the cone shape
created by the condensation of water
water vapor after the the pressure wave
we hear then the shock wave the sonic
boom
itself I don't know if that's going to
pass on the microphone if not I'll show
you to I'll show you next
class but here you see the
cone notice how the sound came after the
plane went in front of
us that's the Sonic
bom there will be this is another Sonic
Boom generated by the
[Music]
rocket those those booms are the rocket
is not is not traveling faster than
sound is the gases on the on the exit
the nozzle of the of the of the of the
roof
so we can see this is the source right
now right it's right now is here it
generates sound okay by the time let's
say after after a certain time T the the
the this this
the the sound generated by The Source
when it was here well it's there but in
that same amount of time because the
source is moving faster than sound maybe
the source is here and I gener generates
generates another generates another
um sound wave right and by the time this
one the plane goes there well let's say
this one is here now but this big one is
here the the original one is here so you
can generate a lot of
concentric sound
waves right that are not not concentric
a lot of sound
waves that were generated when the plane
when the bullet was well at the
respective centers right and so you get
you get this region here that's the
shock wave here it's when when all the
crests of all the individual sound
waves merge and overlap so this if I if
I were to cut here right if I cut here
you will see there is no sound no sound
no sound and then there's huge a huge
wave or a huge wall of sound or
pressure and that pressure because
pressure pressure pressure is force over
area multiply the pressure by whatever
area captures this sound and then you
see the force
so uh your your ears or even your body
will detect this pressure in an
explosion like we saw on the rifle well
that pressure can kill you that's the
whole point of explosives that to
accelerate gases so fast that they
travel faster than sound so they push
and create a Shu wave and the shock wave
can be so destructive that it kills
people destroys building destroys a
plane or whatever that's a whole point
of Destruction destru um that's a whole
point of explosives and their
destructive
power now if I if I consider just
two like let's say this one and this one
and of course we saw there is this
triangle which is the cone
actually right here I'm going to I'm
going to I'm going to put this radius at
90Β° so the angle here Alpha well you see
this distance speed is distance over
time so distance is a speed times time
so this is the speed of sound times time
at the same that's same time T The
Source move all this so This distance is
the speed of the source times time so
because this is 90Β° I can say that sign
of alpha is opposite speed of sound
times time and then over um hypotenuse
which is speed of source times time the
time cancels and that's that's what you
have speed of I'm going to write it
again speed of
sound over speed spe of
source and this speed of sound over
speed of source is what we call the
Magnum well one of the Mac number
because the Mac number is how many times
your source is moving with respect to
sound right so if you have mac 3 if Mac
is
three Mac you write it like this the Mac
number then that means your
source is moving three times at the
speed of sound so let's say in a 3 * 344
m/s so the sign of the angle the half
angle here of this cone is one over the
Mac number so if a plane is going at Mac
3 well the angle is going to generate is
going to be S of the angle is 1 over 3
so the angle is R sign of 1 over 3
so
1947 de and that's the half angle 1947
de here 19. 47Β° here so roughly in total
is 40Β° so you you you look at a photo
like the one I showed you where is it
here you you find the angle of this
bullet and then you or this one or you
can tell how fast the bullet is
going oops and that's pretty much it
that's the that's the only equation you
need to know that this one s of alpha is
one over the Mac number and of course
remember what the math number
is that's all
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