18. Waves & Sound

Intro to Waves

1

concept

## What Is A Wave?

10m

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Hey, guys, in this video, we're gonna start our discussion on waves with just an introduction. What exactly is a wave? All right, let's get to it. Now. What a wave is is it's a moving disturbance, and I've chosen a keyword oscillation. Okay? It's not just any kind of disturbance. It's a disturbance that goes up and down some kind of oscillation, some kind of repetitive movement, and it carries energy. Okay, It's very important to understand that all waves carries some amount of energy and the type of energy that it carries and how to find that energy how to calculate it depends upon the type of wave. But all waves from water waves waves on a string, uh, light sound. They all carry some amount of energy. Okay, One of the most common examples of a wave is just a wave on a string. You could imagine the string fixed to some sort of anchor point. Like a wall. You grab one end of the string, right? You're holding you with your hand and your whipping your hand up and down as you whip your hand up and down, you produce a little pulse that travels down the length of the rope at some speed. Okay, this is a wave. Okay, this is only a single pulse of a wave. But if you're a Whippet, multiple times you would produce a continuous wave along that string and the moving string since the string has mass carries some amount of kinetic energy. Okay, now we're going to focus ourselves entirely on a type of wave called periodic waves. Okay, these airwaves with repeating cycles, okay, and a cycle is to find is a portion of the wave a portion of the motion that begins and ends in the same state. Okay, so if you have a wave, right and a wave is measured by how much displacement has from some zero, Okay, let's say that this wave starts with no displacement, and it's increasing its displacement. It's going in the positive direction. Then this way of completes itself. It's going to return back toe a point worth no displacement. Where when the wave goes on, it's gonna be moving up. Okay, so the same state of motion, same position, same direction of motion. Okay, you could also consider a wave that is already starting with some displacement and then it's gonna go down and up and down again until it reaches that same height. And both of these are going down. Okay. Both of these are examples off cycles, a point that begins a portion that begins and ends at the same state. Okay, the easiest way to measure a cycle is to just go from peak to peak. Okay, that's the simplest way to measure a cycle. Alright. Waves have several important characteristics. I have highlighted a few of them. Okay, You have the period of a wave, which is the amount of time a cycle takes. Okay. How long does it take for a wave to complete one cycle? And this is sort of the characteristic time measurement of a wave. The frequency which is the number of cycles. Okay. Per unit time. Okay, so how frequently do cycles appear? If you have one cycle per second versus two cycles per second, those cycles appear twice as quickly at a frequency of two cycles per second. Then at one cycle per second. Ok, the wave is appearing more quickly per unit time. The wavelength is the distance. The wave travels in a cycle. Okay, So how far does it travel in a cycle. Now? That period in the frequency are two things that you've seen before in oscillate Torrey Motion. Okay, remember, we're talking about oscillations for waves. So we talked about simple harmonic motion, like for a spring, a mass on the spring or a simple pendulum. You also talked about things like frequency and period. But there is an additional aspect of waves that plane harmonic motion doesn't have. It has motion has movement, right? It is a moving disturbance. So because it's moving, it crosses some distance, okay. And the wavelength is how far it travels in a cycle. So the wavelength is the characteristic distance of a wave. And lastly, because the wave is moving, it has some sort of speed, and I don't need to go ahead and define what speed is for you guys. You've You've seen speed over and over and over again. Okay, so here are a couple of graphs that show some of the wave characteristics. We have a graph of displacement given by why versus time in a graph of displacement, given by why versus horizontal distance versus propagation distance. Okay, that's the direction that the wave is traveling in space. Okay, if I identify a cycle as a peak to a peak, so I'm gonna go from peak to peak. Okay, then the distance between two peaks on a time graph is going to be how long a cycle takes, which is, by definition, a period and period. We give with a symbol Capital T. Okay, if I identify a peak to peak on our displacement versus position graph, peak to peak. This is one cycle on the displacement versus position graph. So this is how far it travels in one cycle, which we call the wavelength, which we get by the Greek letter Lambda. Okay. And in both of these instances, we can mark the amplitude, which is just the maximum displacement of that wave. Okay, now there's a fundamental relationship between the wavelength in the period or the wavelength and the frequency of a wave. We can say that the speed of the wave is by definition, how far it travels. Divided by how long that takes, right? So how far does it travel in one cycle? The wavelength. How long does that take the period? Right. This is for a single cycle. for two cycles. It would be too wavelengths and two periods. For three cycles, it would be three wavelengths and three periods. But either way, it's gonna simplify to wave length divided by period. We can rearrange this equation and say this is also equal to the wavelength times the frequency because we know the relationship between the frequency and the period is F equals one over tea. Okay, this equation right here that the speed equals Lambda F is one of the fundamental wave equations that you guys absolutely need to know. Okay, so let's do a quick example. Ah, Wave has a speed of 12 m per second and a wavelength of 5 m. What's the frequency of the wave and what's the period? Okay, well, what equation do we know that relates speed? Wavelength frequency, period. Okay, we have V equals Lambda F. And if we want to find the frequency, all we have to do is divide Lambda over, right? We know the speed. We know the wavelength. We wanna find the frequency lips, wrong color. So the frequency is V over lambda, which is 12 m per second, divided by 5 m. You wanna make sure that the distance unit here is the same. Okay, when in doubt, just use s i units. But if the speed was centimeters per second and the wavelength with centimeters, you could still do this division because those centimeters we're going to cancel. But if one was centimeters per second and the other was meters or millimeters or any other unit, you could not do this division. Okay, just make sure they're inconsistent units. Okay? And 12 divided by five is about to four hurts. Okay, that's the frequency. Now we wanna know the period. Ah, quick way is to use the relationship, right? Given right here of the frequency to the period. So the frequency is one over the period. Which means if I multiply the period up and divide the frequency over, I can say Justus equivalently that the period is one over the frequency. This is 1/2 4 hurts, which is 042 seconds. Alright, guys, that wraps up our introduction into what exactly waves are. Thanks for watching

2

example

## Properties of Waves from Graphs

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Hey, guys, let's do a quick example about waves. What are the properties of the following wave Wave length, period, frequency and speed given in the graphs. Okay, so we have two graphs. We have a sorry, a displacement versus position and a displacement versus time graph. OK, Displacement versus position is gonna tell us things about distances and displacement versus time is gonna tell us things about time now going from peak toe peak, we could define one cycle. The distance that one cycle takes is the wavelength. But we're Onley given half that distance right from a peak to a trough is one half of the wavelength. So we can say one half of the wavelength is two centimeters. Which means that the wavelength is just four centimeters. Right, Double that easy now. The peak to the peak on the time graph will give us the period in that time, as we're shown, is five seconds. So we know that the period is five seconds. Okay, so we know the wavelength and the period. Now we need to find the frequency, the frequency we confined from the period. Really easy. We could just say the frequency is one over the period, which is 1/5 seconds, which is 0.2 hurts. Okay, very easy. Let me give myself just a little bit of space. We know the frequency now, and finally we want to know the speed. The speed equation can either be the wavelength over the period. Or it could be the wavelength times the frequency. It doesn't matter which one you use since you know all three of these pieces of information, but I'll just use for centimeters times 30. seconds, which is 0.8 centimeters per second. And that's the speed. All right. Thanks for watching guys.

3

example

## Distance Between Crests

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Hey, guys, I hope you're able to solve this problem on your own. If not, here's a little bit of help. A wave moves with the speed of 120 m per second. If the frequency of the wave is 300 hertz, what is the distance between wave crests? Okay, distance between wave crests. So if you have a wave that's going up and down and up and down and up and down, what do we call the distance between the crests? Well, each crest is a new cycle, and the distance to those crest is just gonna be the wavelength. Okay, so what we're asking, what the question is asking for is the wavelength, right? The distance traveled during one cycle. So if we know the wave speed and we know the frequency, how do we take that and find the wavelength using our standard wave equation? We'll just say that the frequent Sorry. The speed is a wavelength. Times of frequency. We can then divide the frequency over too big. We can then divide the frequency over and say that the wavelength is the speed divided by the frequency which is 120 m per second, divided by 300 hertz which is 0. m. That is the wavelength and therefore the distance between wave crests. Alright, guys, Thanks for watching.

4

concept

## Types of Waves

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Hey, guys, in this video, we're gonna talk about types of waves. Alright. It turns out that you can divide waves into two broad categories called trans verse waves and longitudinal waves. So we want to know what makes a wave trans verse and what makes a wave longitudinal. So let's get to it. Remember that a wave is a moving oscillation. Okay, It's a moving disturbance in that disturbance is oscillate. Torrey. Okay, that means that a wave has toe have two directions that are important. An oscillation direction. Okay, what way do those oscillations go? Do they go up and down? Do they go forward and backwards? Do they go side to side? And it has to have a motion direction motion we will often refer to as propagation. Okay, so I will use those words interchangeably. Now, as I said, the two broad categories of waves that we can dump everything into our trans verse waves and longitudinal waves. And the difference between the two is the relationship between the oscillation direction and the propagation direction. Okay. And transverse waves. Oscillation is perpendicular to motion or toe oscillation. Okay. For longitudinal waves, the oscillation is parallel to the motion or to the propagation. Trans verse waves are very, very easy to draw. Imagine having a string anchored at a wall and you can hold on to the freedom of the string and you just whip it up and down. You're producing these pulses that are all traveling along the length of the string, so they're traveling horizontally and the vertical position of the string is going up and down, up and down. So there's an oscillation in the vertical position off the string that's along the Y axis. It's vertical, so it's propagating on the X axis horizontally and oscillating along the Y axis vertically. So this is clearly a trans verse wave, the oscillation directions perpendicular to the propagation direction. Now, let's take a very common example of a longitudinal wave. We have a spring anchor to a wall where you could grab the free end of the spring. But instead of whipping it up and down, you push it back and forth. What that's gonna cause is this gonna cause traveling clumps of compression along the spring. So you're gonna get areas where the spring is stacked up really, really, really close to one another. this area of compression, and then you have areas of the spring where it's spaced very, very far apart. It's stretched, okay? And this is technically called rare faction, and you get oscillating compression and rare faction compression and rare faction along the propagation direction. Okay, so this oscillates back and forth along the same direction that the waves are moving. This is why this is a longitudinal wave. Okay, Now both types of waves have to carry energy because all waves carry energy long. I'm sorry. Trans verse waves can carry energy of multiple types. They can carry a whole bunch of different types of energy. And it really depends on the type of wave that it is a wave on a string, which, as I showed above, is it. Trans verse wave carries mainly kinetic energy due to the motion of the string, but it also carries some potential energy because the string actually stretches when you whip it, you have to increase the length to allow for these hills and valleys, so there's some compressed. There's some potential energy due to the stretching of that string. Water waves carry a ton of kinetic energy. Ah, tsunami Can be 100 ft tall. All that water has a lot of mass, and it's moving very, very quickly. Maybe 100 kilometers an hour. Okay, so that carries a ton of kinetic energy Light on its own carries something called electromagnetic energy. But light is not something we're gonna cover here. It's something you're gonna cover much later on in physics. Okay. Now, longitudinal waves mainly carry energy in the form off potential energy due to compression. Okay, The most common type of longitudinal wave is a compression wave in some sort of elastic medium. So if you look at the spring springs air clearly elastic, right, they can stretch their return to the original configuration. They can compress their return to the original configuration. So the energy is carried by the potential energy due to these compressions which are collapsing it into a smaller sorry distance that it should be and rare factions which are stretching it to a larger length than it should be. Both of those give it potential energy. So there's a lot of potential energy in this wave. Sound carries energy on its own two. But sound is actually just a type of compression wave in an elastic medium. Gasses, liquids and solids, which are all media that sound can propagated. All have elastic properties. And, as we'll see later on, sound is just a compression in this a lot. And these elastic media All right, guys. So we have Remember, guys, we're focusing on periodic waves, waves that have repeating cycles and periodic waves. Regardless of whether they're trans verse or longitudinal, obey the same equations. Okay, they have the same characteristics that you could describe. You can talk about amplitude, wave length periods, speed frequency all the same characteristics, and they obey the same speed relationship. Lambda F. Okay, very important to remember that regardless of whether it's a longitudinal wave or a trans verse wave, they obey the same relationship. All right, let's do a quick example. Can longitudinal waves propagate in a fluid? What about trans verse waves? Absolutely. Longitudinal waves can propagate in a fluid because, as you're compressing the fluid, the fluid wants to not be compressed. It wants to return to its original size. Okay, fluids are very, very resistant to compression, so they can propagate compression waves very easily like sound Alright, Now the problem is can they be? Trans verse waves? No trans verse waves do not propagate very, very well in liquids at all. The reason is, is that if you think about the actual molecules inside of the wave, sorry inside of the fluid. When you give it some sort of lift, right, you want those molecules to start going up and start going down right like a wave while it propagates in this direction. But the problem is that centrally to the wave is oscillation. So as this water molecule goes up, it has to come back down. But there's no elasticity. There's nothing to bring it back. Okay, this is different than a wave on a string. When you whip a wave on a string, the wave stretches to allow part of it to go up, and that's stretching stores potential energy that snaps it back down. But there's nothing holding those waterway those water molecules in place, so longitudinal waves propagate very, very well in fluids, right? I chose to talk about the liquid here, but it's saying for a gas, and they propagate very poorly in trans verse waves. Alright, guys, that wraps up our discussion on the types of waves. Thanks for watching. Okay,

5

Problem

ProblemA satellite captures images of a tsunami, and properties of the tsunami can be found from these images, providing important information to people who need to evacuate coastal areas. If satellite images of a tsunami show the distance from one peak to another is 500 km, and the period is 1 hour, how much time do people have to evacuate if the tsunami is found to be 100 km off shore?

A

12 minutes

B

48 minutes

C

3 hours

D

5 hours

Additional resources for Intro to Waves

PRACTICE PROBLEMS AND ACTIVITIES (20)

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