Hey, guys. So for the next couple of videos in this chapter, we're going to be talking about waves. In this video, I'm going to give you a brief introduction to the types of waves that we'll be discussing, as well as the equation for wave speed. Let's go ahead and check it out. First of all, what is a wave? Well, the definition that you'll see here in your textbook is that it's a disturbance in space. Imagine that you grabbed a string or a slinky and you whipped it up and down. That's a disturbance. If you dropped a rock in a pond, it's going to create some ripples on the surface and that's a disturbance. And if you speak or create some sound, that's actually a disturbance that travels through space. All those are examples. Now, a wave requires a medium to travel through and a medium is really just a material or a substance that, the wave travels through. For example, the string that I mentioned before, that is the medium that the disturbance propagates through. With the rock in the water, the water is actually the medium and in the case of sound, sound travels through air. Air is the medium by which the wave travels.
There are two different types of waves that we'll be talking about. So I want to go ahead and discuss their similarities and differences. One's called transverse and longitudinal. The way I always like to remember this is a transverse wave is as if you took a slinky and you attached one end to the wall and you just whipped it up and down. You're creating these wavy patterns, similar to what we've seen in simple harmonic motion. A longitudinal wave, on the other hand, is if you grab that slinky, and instead of whipping it up and down, you're actually pushing it back and forth. You put your hand like this, and you basically just push in and out. The main difference between transverse and longitudinal has to do with the displacement of the particles in that medium. When you whip a slinky up and down, the wave, the overall pattern, travels to the right. As you do this, the whole pattern moves off to the right, but the particles on the string actually move up and down. They don't move to the right. So, the displacement of the particles is actually perpendicular to the wave motion. The wave moves to the right, but the particles just move up and down vertically. A longitudinal wave, on the other hand, is different because when you push and pull a slinky, when you move back and forth, the overall wave pattern moves to the right, just like a transverse wave. But the particles inside of the slinky are just moving back and forth. They're moving in the same direction as the wave motion. So, the displacement is actually parallel to the wave motion.
Now there are a couple of important definitions and variables you'll need to know for both of these equations, so let's check it out. Remember the wavelength, we've actually talked about that before. The wavelength is just a horizontal distance from crest to crest. Transverse waves have these peaks and valleys, these crests and troughs, and the horizontal distance between each of the peaks is a Δx, that's a distance, and we call that a wavelength. It also takes some time for the wave to actually go between those hills and valleys and the time that it takes is called the period. That's T. Just remember that big T and frequency are inverses of each other. So, the frequency is 1 over the period.
A wavelength for a longitudinal wave is a little bit different because it's a distance from compression to compression. Longitudinal waves don't have crests and troughs because it's not moving up and down. Instead, what they have are these regions where the slinky gets really tightly packed together. That's compression and then where the slinky loosens up and expands again. As you push back and forth, the whole entire wave does this. And these are the places where the slinky bunches up together like this. The wavelength is just the distance from one region of maximum compression to the other. So for example, if this is like a density map, where darker shades are like more densely packed particles of slinky, then the wavelength is just one full cycle from compression to compression. The amplitude of a wave is basically just half of the vertical distance of the graph. It's basically just the height from the x-axis. Whereas in a longitudinal wave, amplitude doesn't really matter.
Let's go ahead and attach some numbers to this. Right? So we've got each of the waves here. We actually got some numbers. We want to determine the amplitude and the wavelength. The amplitude is actually the easiest one because remember, it's just the height above the x-axis of this wave. This wave goes up and down, and it oscillates between two points. So, this distance here is your amplitude and this equals 2 meters. It's just the height from 0 to 2, so A equals 2. What about the wavelength? Well, the wavelength is a horizontal distance from crest to crest, or it could be trough to trough. It's basically just any two points that are one wave away from each other. So this distance is just the horizontal distance. So I'm going from one point to another. So, that means that my wavelength here is actually just 1. So it's really just an entire cycle from down and then up again until I reach the same point. That's a wavelength. So my λ is 1.
For part B, I just wanted to determine the wavelength here. Remember, we're just going to look for regions of compression or rarefaction and it's just a cycle from one point to the successive point of the next cycle. So we have a region right here where the slinky gets loosened up a little bit, and another one right here. Therefore, our wavelength here is just the difference between these. It's just 1.5 meters.
Now what's common about both of these types of waves here is the speed. We mentioned that both transverse and longitudinal waves move with some sort of pattern, with some sort of wave speed. And all types of waves have the same relationship between speed, between their frequency and their wavelength. So remember that any velocity is just going to be δx over δt, which is distance over time. Now the distance that we travel in a wave is actually just a wavelength, and the time that it takes to travel that wavelength is called the period. So it's λ over T. Now for some reason, most textbooks will decide to flip this and they'll use the relationship that again, that f equals 1 over period, and what they'll do is they'll rewrite this as λ times frequency. So that's the equation that most textbooks are going to show you.
That's really all there is to it. You just need to know those three variables, and you'll be able to solve. So for instance, in our example here, we have sound which is a longitudinal wave. It travels with the speed of 343 meters per second. So this v here is 343 and we want to figure out what's the wavelength if the frequency is 260. So this frequency is 260 and we want to figure out what is our λ. So we're just going to use this equation here, v = λf, and now we want to figure out what this λ is. So we just rearrange. λ is going to be v divided by f, which is going to be 343 divided by 260, and you're going to get 1.32. So 1.32 meters, and that's it. Well, that's the wavelength. So that's it for this one, guys. Let me know if you have any questions.
