Intro to Waves - Video Tutorials & Practice Problems
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1
concept
Intro to Waves and Wave Speed
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Hey guys. So for the next couple of videos in this chapter, we're gonna be talking about waves. So in this video, I'm gonna give you a brief introduction on the types of waves that we'll be talking about and also 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 you're interested in your textbook is that it's a disturbance in space. So 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 gonna create some ripples on the surface and that's a disturbance. And if also you speak or you know, you create some sound, that's actually a disturbance that travels through space. All those three are examples. Now, a wave requires a medium to travel through and a medium is really just a material or a substance that um that wave travels through. So for example, the string that I mentioned before, that is the medium that that disturbance propagates through with the rock in the water, the water is actually the medium and in the case of sound, sound actually travels through air. Air is the medium by which that wave travels through. Now, there's two different types of waves that we'll be talking about. So I wanna go ahead and discuss those similarities and differences. One's called the transverse and longitudinal. The way I always like to remember, this is a transverse wave is as if you took a slinky and you sort of attach one into the wall wall here and you just whipped it up and down. So what happens is you're just whipping this thing up and down, you're creating these wavy patterns uh 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're basically just gonna push in and out like that. So 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, what happens is that the wave, the overall pattern travels to the right as you go like this, the whole pattern moves off to the right like this. But the particles that are on the medium on the string actually move, move up and down, they don't move to the right. So basically what happens is that 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, they move vertically like this 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 slinky actually 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. All right, that's basically the biggest difference between those. Now, there's a couple of important uh definitions and variables you'll need to know in both of these equations. So let's check it out. So remember the wavelength we've actually talked about that before. The wavelength is just a horizontal distance from crest to crest to train verse waves have these peaks and valleys, these crests and troughs and the horizontal distance between each peaks, each of the peaks is a delta X that's a distance. And we call that a wavelength. Now, it also takes some time for the wave to actually go between those uh hills and valleys. And the time that it takes is called the period. That's t that's big T now just remember that big T and frequency are related by inverses of each other. So the uh frequency is one over the period. All right. So a wavelength for a longitudinal wave, it's a little bit different because it's a distance from compression to compression. Now, longitudinal waves don't have crests and troughs because it's not moving up and down. Instead what they have are these regions where they get really, really with the slinky gets really, really tightly packed together, that's compression and then where the slinky sort of loosens up and expands again. So what happens is as you push back and forth, the whole entire wave is doing this. And so these are the places where the slinky sort of bunches up together like this. And 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, right where like darker shades are like sort of like more densely packed particles of slinky, then a wavelength is just gonna be one full sort of period or one cycle from compression to compression. So this is your wavelength here. Now 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. So this right here is the amplitude, whereas in a longitudinal wave amplitude actually doesn't really matter. So let's go ahead and attach some numbers to this, right. So we've got each of the waves here and we actually got some numbers we want to determine the amplitude and the wavelength. So actually, I'm gonna erase this. So we want to determine the amplitude and then the wavelength here. So the amplitude is actually the easiest one because remember it's just the height above the x axis of this wave. So what happens here is this wave just goes up and down like this and it oscillates between these two points right here, right? So this one and this one. So basically this distance here is your amplitude and this just equals 2 m. It's just the height from 0 to 2. So a equals two. What about the wavelength or 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 like sort of uh you know, one exactly one wave uh away from each other. So this is gonna be my wavelength and really this is this, this is just the horizontal distance. So I'm going from 1 to 2. So that means that my wavelength here is actually just one. 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 lambda is one for part B I just wanted to determine the wavelength here. Remember we're just gonna look for regions of, of compression or rarer faction and it's just gonna be a cycle from point to the successive point of the next cycle. So we have a, a rare faction right here. This is where the slinky gets loosened up a little bit and another one right here. So therefore, our lambda, our, our, our wavelength here is just the difference between these is just just 1.5 m. All right. So very straightforward. 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, right, with some sort of wave speed and all types of waves have the same relationship between speed and uh between their frequency and their wavelength. So remember that any velocity is just gonna be delta X over delta T 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 LAMBDA over T now, for some reason, most textbooks will actually decide to flip this and they'll basically use the relationship that again, uh the f equals one over period. And what do is they'll rewrite this as LAMBDA times frequency. All right. So that's the equation that most textbooks are gonna show you. That's really all there is to it, you just need to know to those three variables and you'll be able to solve. So for instance, in our example, here we have sound which is the longitude and the wave it travels with a speed of 343 m per second. So there's 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 we want to figure out what is our lambda. So we're just gonna use this equation here. V equals lambda F. And now we want to figure out what this lambda is. So we just rearrange lambda is gonna be V divided by F which is gonna be 343 divided by 260. And you're gonna get 1.32 so 1.32 m and that's it. No, that's the wavelength. So that's it for this one guys. Let me know if you have any questions.
2
Problem
Problem
A wave has a wavelength of 10mm and moves at a speed of 50mm/s. What is the frequency of this wave?
A
f = 50 Hz/s
B
f = 5 Hz
C
f = 500 s
3
example
Example 1
Video duration:
3m
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Hey guys, hopefully you're able to work on this problem on your own. So we're given that some wave is on some stretch horizontal rope. And we're told on this problem that the vertical and horizontal distances from crest to trough are some of these values here. So, in my opinion, the best thing you can do is actually draw this out and sort of see for yourself what these distances correspond to. So I've got this sort of wave like this, I'm gonna draw the little sort of sketch this out doesn't have to be perfect. But basically, what I'm told here is that the vertical distance from crest, remember that's the top of the wave to the trough, which is sort of like the bottom of the most minimum part of the wave is equal to 15 centimeters. So let's figure this out, right. So I've got this distance over here is equal to 15 centimeters. And then I'm told that the horizontal distance from crest to trough is 20 centimeters. So is that gonna be from here to here or is that gonna be from crest to trough? That's actually just gonna be this distance because this is the crest and this is the trough. So this horizontal distance here represents 20 centimeters, right? It's obviously not scale. Um but that's just the distance, right. So basically, we have to figure out what's the amplitude and the wavelength here. So I've got the amplitude and the amplitude is what remember the definition for the amplitude is it's the height of the wave off of the axis or the midline. It's not the entire height of the wave. It's just basically how high the wave gets off of this middle axis here. So this is actually this distance right here represents the ample two. So that's actually just gonna be one half of the total distance from crest to trough. So it's gonna be one half of 15 centimeters. This is just 7.5 centimeters or if you want to convert this to si units, you can ship the decimal place back and this will be 0.075 m. So since the problem didn't specify, we can just write it either way. All right. So now we have to figure out the wavelength for this wave. This is the wavelength I remember that's LAMBDA. Now remember the definition for LAMBDA is that it is the distance between the same sort of two identical points uh for the different waves. So for example, crest to crest or trough to trough or let's say this point over here to the next point where it's going up again, either one of these horizontal distances all represent the wavelength. So how do we figure that out? So I'm just gonna label this here. This is gonna be my lambda. Well, the only thing I'm told, the only information I'm told about horizontal distances is that this distance here is equal to 20 centimeters. So what is this 20? Is this an entire wavelength here? If you think about it? It's not because you have to go all the way from the crest down to the trough and then go all the way back up again for you to complete one cycle, one up down, up. So really this distance here actually only represents one half of the wavelength. So this lambda here is actually two times 20 centimeters and this is equal to 40 centimeters. And again, we can just rewrite this as 0.04. Actually, no, this is gonna be 0.4 m. And so those are the correct answers. So this distance here represents the wavelength and this represents the amplitude. Hopefully, that makes sense. Let me know if you have any questions.