Traveling Waves: Crash Course Physics #17

Summary

This script explores the physics of traveling waves using a simple rope as a demonstration tool. It delves into wave characteristics like amplitude, wavelength, frequency, and speed, and distinguishes between pulse, continuous, transverse, and longitudinal waves. The educational narrative covers energy transfer, wave reflection, and interference phenomena, highlighting their real-world applications such as noise-canceling headphones. The episode is part of Crash Course Physics, aiming to demystify wave dynamics and their significance in our daily lives.

Takeaways

• 🧵 The rope serves as an example to demonstrate the physics of traveling waves, showing how movement can travel as a wave through a medium.
• 🌊 Waves are formed by disturbances that cause information to move outward from the source in every direction, taking a wave shape.
• 📏 Waves consist of peaks (crests) and troughs, with amplitude being the distance from the peak to the middle, and wavelength being the distance between crests.
• 🔢 The speed of a wave is determined by multiplying the wavelength by the frequency, and it depends solely on the medium through which it travels.
• 🔊 Sound waves are an example of how wave speed is independent of the sound's loudness, only on the medium it travels through.
• 💥 There are four main types of waves: pulse waves, continuous waves, transverse waves, and longitudinal waves, each with unique properties.
• 🔄 Transverse waves oscillate perpendicular to the direction of wave travel, while longitudinal waves oscillate in the same direction as the wave travels.
• ⚡ Waves transport energy, with the energy of a wave being proportional to the square of its amplitude.
• 📉 The intensity of a wave decreases as it spreads out, with the intensity reducing by the square of the distance from the source.
• 🔁 Reflection of waves can occur differently depending on whether the end of the medium is free to move or fixed, leading to wave inversion.
• 🌀 Interference, both constructive and destructive, occurs when waves overlap, either building on each other or canceling out, and has practical applications like noise-canceling technology.

Q & A

What special power does the ordinary piece of rope have in the script?

The ordinary piece of rope has the special power to demonstrate the physics of traveling waves due to its ability to transmit the movement of the hand as a wave along its length.

How does a disturbance in the physical world create a wave?

A disturbance in the physical world creates a wave by causing information about the disturbance to move outward from the source in every direction, gradually taking the shape of a wave as it travels.

What are the three main characteristics of a wave?

The three main characteristics of a wave are amplitude, wavelength, and frequency. Amplitude is the distance from the peaks to the middle of the wave, wavelength is the distance between crests, and frequency is the number of cycles that pass through a point every second.

How is the speed of a wave determined?

The speed of a wave is determined by the medium through which it is traveling. It is independent of the wave's properties, such as its amplitude or frequency.

What are the four main kinds of waves mentioned in the script?

The four main kinds of waves mentioned in the script are pulse waves, continuous waves, transverse waves, and longitudinal waves.

How does a pulse wave differ from a continuous wave?

A pulse wave occurs when the end of the rope is moved back and forth just once, creating a single crest that travels through the rope. A continuous wave is created by continuously moving the rope back and forth, acting as an oscillator and creating a series of crests and troughs.

What is the relationship between a wave's amplitude and its energy?

A wave's energy is proportional to the square of its amplitude. This means that if the amplitude is doubled, the energy becomes four times greater, and if the amplitude is tripled, the energy becomes nine times greater.

Why do waves get weaker as they spread out?

Waves get weaker as they spread out because they are distributed over a larger area. The intensity of a wave decreases with the square of the distance from its source due to the increasing surface area over which the wave's energy is spread.

What happens when a pulse wave reaches the end of a rope that is fixed?

When a pulse wave reaches the end of a rope that is fixed, it is reflected back along the rope as a trough, inverting the wave because the fixed end prevents the rope from sliding upward.

What is constructive interference and how does it occur?

Constructive interference occurs when two or more waves with the same amplitude and phase overlap, resulting in a wave with a higher amplitude than the original waves. This happens because the waves build on each other.

What is destructive interference and how does it differ from constructive interference?

Destructive interference occurs when two waves with the same amplitude but opposite phases (one crest and one trough) overlap, resulting in a flat line where it appears as if the waves have disappeared. This is different from constructive interference, where waves with the same phase add together to increase amplitude.

Outlines

00:00

🌊 Physics of Traveling Waves

This paragraph introduces the concept of traveling waves using a simple rope as a demonstration tool. It explains how the movement of the hand along the rope creates a wave, illustrating the fundamental properties of waves such as amplitude, wavelength, frequency, and speed. The paragraph also distinguishes between different types of waves, including pulse waves, continuous waves, transverse waves, and longitudinal waves, emphasizing the energy transfer that occurs during wave propagation. The importance of amplitude in determining a wave's energy and intensity is highlighted, with examples of how this principle applies to real-world phenomena like the shockwaves from an earthquake.

05:01

🔊 Wave Reflection and Interference

The second paragraph delves into the phenomena of wave reflection and interference. It describes how a pulse wave behaves differently when it encounters a free end versus a fixed end, resulting in reflection as either a crest or an inverted trough. The concept of constructive and destructive interference is introduced, explaining how waves can either reinforce or cancel each other out when they overlap. The paragraph also touches on practical applications of these principles, such as noise-canceling headphones, which use destructive interference to eliminate unwanted sound waves. The summary concludes with a brief mention of the interconnectedness of frequency, wavelength, and speed in waves, and the educational nature of the Crash Course Physics series.

Keywords

💡Traveling Waves

Traveling waves are disturbances that propagate through a medium, transferring energy without the medium itself moving. In the video, traveling waves are demonstrated using a rope, where the movement from one end travels along the rope's length. This concept is central to understanding how waves behave in various physical scenarios, including the trampoline example where the force of a jump creates a ripple effect across the surface.

💡Amplitude

Amplitude refers to the maximum displacement of a point on a wave from its equilibrium position. It is a measure of the wave's energy and is crucial in determining the intensity of the wave. The video script explains that amplitude is the distance from the peak of a wave to its midpoint and illustrates this with the rope's crests and troughs, showing how changes in amplitude affect the wave's energy.

💡Wavelength

Wavelength is the distance between two consecutive points on a wave that are in the same phase, such as from one crest to the next. It is a fundamental property of waves that, along with frequency, helps determine the wave's speed. The script uses the concept to explain how waves can be measured and how different wavelengths affect the appearance and behavior of waves on the rope.

💡Frequency

Frequency is the number of complete wave cycles that pass a given point in a unit of time, typically measured in Hertz (Hz). The video script describes frequency in the context of how many wave cycles pass through a point every second, emphasizing its role in calculating wave speed and its impact on the perception of sound waves.

💡Wave Speed

Wave speed is the rate at which a wave propagates through a medium and is determined by the medium's properties, not the wave itself. The script clarifies that wave speed is calculated by multiplying the wavelength by the frequency, and it is independent of the wave's characteristics, using the example of sound traveling through air or water at different speeds.

💡Pulse Wave

A pulse wave is a single disturbance that travels through a medium, as opposed to a continuous wave. In the script, the pulse wave is demonstrated by moving the end of the rope once, creating a single crest that travels along the rope. This concept is important for understanding how single events, like a pluck on a string, can generate waves.

💡Continuous Wave

A continuous wave is a wave that is generated when an oscillator, such as a hand moving back and forth on a rope, maintains a constant vibration. The video script explains that this type of wave is created by ongoing disturbances, like the hand's movement, and is key to understanding phenomena like sound and light waves that require sustained energy input.

💡Transverse Waves

Transverse waves are waves where the oscillation of the medium is perpendicular to the direction of wave propagation. The script uses the rope as an example, where the peaks and troughs of the wave are perpendicular to the rope's length, illustrating how these waves transfer energy in a direction perpendicular to the oscillation.

💡Longitudinal Waves

Longitudinal waves involve oscillations in the same direction as the wave's propagation, often involving compression and expansion of the medium. The video script mentions sound waves as an example of longitudinal waves, where the air particles compress and expand as the wave travels, demonstrating how energy can be transferred in the direction of the wave.

💡Energy Transport

Energy transport is the process by which waves carry energy from one point to another without the medium itself moving. The script explains that all waves, regardless of their type, transport energy through the interaction of particles in the medium, which is fundamental to understanding how waves function in various physical phenomena.

💡Interference

Interference is the phenomenon where two or more waves overlap and combine, either constructively (adding together for a higher amplitude) or destructively (canceling each other out). The video script describes both types of interference using the example of pulses sent along the rope, illustrating how waves can interact to create new patterns or even disappear.

Highlights

A rope demonstrates the physics of traveling waves, showing how movement travels as a wave.

Waves form due to disturbances, moving outward in every direction from the source.

Waves are characterized by peaks, troughs, amplitude, wavelength, and frequency.

Wave speed depends solely on the medium it travels through, not the wave itself.

Four main kinds of waves are explained: pulse, continuous, transverse, and longitudinal waves.

Transverse waves oscillate perpendicular to the direction of wave travel.

Longitudinal waves involve oscillations in the same direction as the wave movement.

Waves transport energy through the transfer of movement from one particle to another.

The energy of a wave is proportional to its amplitude squared.

Intensity of a wave is related to its energy transport and is affected by the wave's amplitude.

Waves weaken as they spread out due to being distributed over a larger area.

Reflection of waves can result in the wave being inverted at a fixed end.

Constructive interference occurs when overlapping waves combine to increase amplitude.

Destructive interference happens when overlapping waves cancel each other out.

Interference effects are utilized in technology, such as noise-canceling headphones.

The relationship between amplitude and energy transport is crucial for understanding phenomena like earthquake shockwaves.

Crash Course Physics explores the interconnectedness of frequency, wavelength, and speed in waves.

Transcripts

Here we have an ordinary piece of rope.

It’s not one of those magician’s ropes that can mysteriously put itself back together once it's been cut it in half.

And it’s not particularly strong or durable.

But you might say that it does have special powers, because it’ll demonstrate for us the physics of traveling waves.

Ropes and strings are really good for this kind of thing,

because when you move them back and forth the movement of your hand travels through the rope as a wave.

By observing what happens to this rope when we try different things with it, we’ll be able to see how waves behave.

Including, how those waves sometimes disappear completely.

How’s that for a magic trick?

[Theme Music]

This is a typical wave.

And waves form whenever there’s a disturbance of some kind.

Often, when something about the physical world changes, the information about that disturbance

gradually moves outward, away from the source, in every direction.

And as the information travels, it makes a wave shape.

Think about all the disturbance you cause, for example, when you jump on a trampoline.

When you hit the trampoline, the downward push that you create moves the material next to it down a little bit, too.

And the same goes for the material next to that, and so on.

And while that information is traveling outward, the spot where your feet first hit the trampoline

is already recovering, moving upward again, because of the tension force in the trampoline.

And that moves the area next to it upward, too.

This up-and-down motion gradually ripples outward, covering more and more of the trampoline.

And the ripples take the shape of a wave.

Waves are made up of peaks, with crests -- the bumps on top -- and troughs -- the bumps on the bottom.

They have an amplitude, which is the distance from the peaks to the middle of the wave.

They also have a wavelength, which is the distance between crests -- a full cycle of the wave --

and a frequency, which is how many of those cycles pass through a given point every second.

Multiply the wavelength by the frequency, and you get the wave’s speed -- how fast it's going.

And the wave’s speed only depends on the medium it’s traveling through.

That’s why the speed of sound -- which is a wave -- doesn’t depend on the sound itself.

It doesn’t matter how loud or quiet it is.

It just depends on whether the sound is traveling through, say, air or water.

Now, there are four main kinds of waves, and we can use our rope to show the difference between some of them:

A pulse wave is what happens when you move the end of the rope back and forth just one time.

One lonely crest travels through the rope -- that’s the pulse.

Then there’s a continuous wave, which is what happens when you keep moving the rope back and forth.

In that case, your hand is acting as an oscillator.

Anything that causes an oscillation or vibration can create a continuous wave.

Now, things that cause simple harmonic oscillation move in such a way that they create sinusoidal waves --

meaning that if you plotted the waves on a graph, they’d look a lot like the graph of sin(x).

But the waves we’ve mainly been talking about so far are transverse waves --

ones in which the oscillation is perpendicular to the direction that the wave is traveling in.

When a wave travels along this rope, for example,the peaks are perpendicular to the rope’s length.

The same thing was mostly true for the waves that you made on the trampoline:

the waves were traveling along its surface horizontally, but the peaks were vertical.

But there are also longitudinal waves, where the oscillations happen in the same direction as the wave is moving.

In the case of a longitudinal wave, the back-and-forth motion is more of a compression-and-expansion.

These are the kinds of waves that you get by compressing and stretching a spring --

and they’re also the kinds by which sound travels, which we’ll talk more about next time.

But all waves -- no matter what kind they are -- have something in common:

They transport energy as they travel.

At a microscopic level, waves occur when the movement of one particle affects the particle next to it.

And to make that next particle start moving, there has to be an energy transfer.

But how can you tell how much energy a wave has?

Well, remember that an object in simple harmonic motion has a total energy of one-half,

times the spring constant, times the amplitude of the motion squared.

Which means for a wave caused by simple harmonic motion,

every particle in the wave will also have that same total energy of (half k A squared).

All of this together tells us that a wave’s energy is proportional to its amplitude, squared.

In other words, if you double the wave’s amplitude, you get four times the energy.

Triple the amplitude, you get nine times the energy.

So why is the relationship between amplitude and energy transport so important?

Well, the intensity of a wave is related to the energy it transports.

More specifically, its intensity is equal to its power, divided by the area it’s spread over and power is energy over time.

So, changing the amplitude of a wave can change its energy -- and therefore its intensity

-- by the square of the change in amplitude.

And this relationship is extremely important for things like figuring out how much damage

can be caused by the shockwaves from an earthquake.

But waves also get weaker as they spread out, because they’re distributed over more area.

A spherical wave, for example -- one that ripples outward in all directions --

will be spread over the surface area of a sphere that gets bigger and bigger, the farther the wave travels.

The surface area of a sphere is equal to (4) times (pi) times (its radius squared).

So, as a spherical wave moves farther from its source, its intensity will decrease by the square of the distance from it.

Two meters away from the source, and the intensity of the wave will be 4 times less than if you were 1 meter away.

Three meters away, and it’ll be 9 times less.

That’s why being just a little bit farther away from the source of an earthquake can sometimes make a huge difference.

Now, let’s go back to the waves we were making with the rope.

Suppose you attach one end of the rope to a ring that’s free to move up and down on a rod.

Then, with your hand, you send a pulse -- in the form of a crest, rippling along it.

When the pulse gets to the end of the rope, the rope slides along the rod.

But then, it slides back to where it was.

That motion -- the sliding back -- reflects the wave back along the rope, again as a crest.

But something totally different happens, if you attach the end of the rope so it’s fixed, and can’t move.

Now, if you send a pulse along the rope, it will still be reflected -- but this time, as a trough.

The wave was inverted.

That’s because, when the pulse reached the fixed end of the rope, it was trying to slide the end of the rope upward.

But it couldn’t, because the end of the rope was fixed.

So, instead, the rope got yanked downward.

And the momentum from that downward movement carried the rope below the fixed end, inverting the wave.

Now sometimes, multiple waves can combine.

For example: Say you send two identical pulses -- both crests -- along a rope, one from each end.

When the two pulses overlap, they’ll combine to make one crest, with a higher amplitude than the original ones.

That’s called constructive interference -- the waves build on each other.

Now, let’s say you do the same thing again.

This time, both waves have the same amplitude, but one’s a crest and the other is a trough.

And when they overlap, the rope will be flat.

It looks like the waves just disappeared!

That’s called destructive interference, when waves cancel each other out.

Constructive and destructive interference happen with all kinds of waves --

pulse or continuous, transverse or longitudinal.

And sometimes, we can use the effects to our advantage.

Noise-canceling headphones, for example, work by analyzing the noise around you and generating

a sound wave that destructively interferes with the sound waves from that noise, canceling it out.

There’s a lot more to talk about when it comes to the physics of sound, but we’ll save that for next time.

Today, you learned about traveling waves, and how their frequency, wavelength, and speed are all connected.

We also talked about different types of waves, including pulse, continuous, transverse, and

longitudinal waves, and how they all transport energy.

Finally, we discussed reflection and interference.

Crash Course Physics is produced in association with PBS Digital Studios.

You can head over to their channel to check out amazing shows like Physics Girl,

Shank's FX, and PBS Space Time.

This episode of Crash Course was filmed in the Doctor Cheryl C. Kinney Crash Course Studio

with the help of these amazing people and our equally amazing graphics team is Thought Cafe