by Patrick Ford

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

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