Shock waves

Summary

This 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

• 🌊 When a wave source moves, the wavelengths in front of it compress, and those behind it elongate.
• 🚀 If the source moves at the same speed as the wavefront, the wavelength at the source becomes zero.
• 🔍 A 3D view of this scenario shows a region of high amplitude, indicative of high pressure.
• 💥 When the source moves faster than the speed of sound, it creates a shock wave, also known as a sonic boom.
• 🛳 The phenomenon is similar to a boat moving faster than the waves it creates, leaving a wake behind.
• 📉 The shock wave's angle can be calculated using the formula speed of sound over speed of source, which is the Mach number.
• 📐 The half-angle of the shock wave cone is given by the inverse of the Mach number.
• 🔊 Sonic booms are the sounds produced when a source moves faster than sound, creating a pressure wave.
• 🏗 Shock waves can be extremely destructive, capable of damaging buildings or even killing people.
• 🔢 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

00:00

🌊 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.

05:00

💥 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.

10:01

📐 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.

Keywords

💡Shock Waves

Shock waves are intense pressure waves that occur when an object moves through a medium faster than the speed of sound in that medium. In the video, shock waves are discussed in the context of their formation when a source moves faster than the wavefront, leading to a high-pressure region. The script mentions shock waves being created by both bullets and explosions, which travel faster than sound, resulting in a destructive pressure wave.

💡Wavelength

Wavelength is the physical length of one wave cycle, measured from any point in the wave to the same point in the next cycle. The video script describes how the wavelength changes when the source moves: it compresses in front of the source and elongates behind it. This concept is crucial in understanding how shock waves form and how they affect the amplitude of the waves.

💡Amplitude

Amplitude refers to the maximum extent of a wave's displacement from its rest position. In the context of the video, amplitude is used to describe the height of the wave, which increases dramatically when the source moves at the speed of the wavefront, resulting in a shock wave with a high-pressure region.

💡Sound Barrier

The sound barrier is a term used to describe the point at which an object moves at or faster than the speed of sound, leading to the formation of shock waves. The video script uses this term to illustrate the transition from normal wave propagation to the formation of a shock wave, which is characterized by a significant increase in amplitude and pressure.

💡Sonic Boom

A sonic boom is a loud sound created by the shock waves produced when an object travels through the air faster than the speed of sound. The video script mentions sonic booms as a result of objects like planes and rockets moving faster than sound, creating a 'wall of sound' or pressure that can be heard as a loud boom.

💡Pressure Wave

A pressure wave is a type of wave that transmits energy through a medium due to pressure differences. In the video, pressure waves are discussed in relation to shock waves, where the high-pressure region created by an object moving faster than sound is referred to as a pressure wave.

💡Ripple Tank Simulation

A ripple tank simulation is a visual tool used to demonstrate the behavior of waves, particularly how they interact with moving sources. The script describes using such a simulation to show how wavelengths compress and elongate as the source moves, which is a fundamental concept in understanding shock wave formation.

💡Mach Number

The Mach number is the ratio of the speed of an object to the speed of sound in the medium through which it is traveling. The video script explains how the Mach number is used to calculate the angle of the shock wave cone, which is crucial for understanding the relationship between an object's speed and the shock wave it generates.

💡Wavefront

A wavefront is the surface of a wave that is moving through a medium at a particular point in time. The video script discusses how the wavefront's behavior changes based on the speed of the source, which is key to understanding the formation of shock waves and the changes in wavelength.

💡Concentric Sound Waves

Concentric sound waves are waves that emanate from a central point and expand outward in a circular pattern. The video script uses this concept to describe how shock waves can form concentric patterns as the source moves and generates sound waves at different positions, leading to the overlapping and merging of these waves.

💡Destructive Power

Destructive power refers to the ability of a force or phenomenon to cause damage or destruction. In the context of the video, the destructive power of shock waves is highlighted, explaining how the immense pressure generated by shock waves can cause significant damage to structures or even be lethal.

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

90° 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 90° 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. 47° here so roughly in total

is 40° 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