Wave properties

0:00- [Instructor] You probably know that when you disturb water, you see circular ripples going outwards, waves of water. But the big question is, what exactly is a wave and what are its characteristic features? That's what we're gonna figure out in this video. So, let's begin.

0:14So, let's investigate this. When you disturb water, say by pouring a drop onto it, what really happens? Well, the molecule of water that's right over there, let's model it by using just a circle over here, that gets disturbed. It starts vibrating. So, maybe it goes down and then goes up.

0:28So, it starts vibrating. But here's the thing. That molecule of water is connected to the molecules of the water that are surrounding it. There's a force of attraction between them. And as a result, that molecules of water also makes these molecules of water vibrate.

0:42So, they too go down and then go back up. But they are connected to the molecules of water that are surrounding them. There is a force of attraction between them as well. And so, they will make these molecules of water also vibrate. They too go down and up and so on and so forth.

0:59And as a result, look, the disturbance propagates outwards and that's what we see as circular ripples going outwards. So, what exactly is a wave? Well, we saw that the disturbance got transferred, it propagated, it moved from one point to another. In other words, energy got transferred from one point to another, but the water molecules did not move from one point to another.

1:25They were pretty much in their own place vibrating. So, waves transfer energy, but not matter. It's very similar to the human wave that you see in a stadium. Look at that, you see a disturbance propagating to the left, isn't it? But notice the humans over there, people, they're just vibrating up and down.

1:45They're not moving. Humans are not moving from one place to another. But the disturbance is, that's what a wave is. Okay, so, now to investigate further, let's consider a type of wave that has repeating patterns. For example, in this PhET simulation, if I were to switch on this tap, a drop keeps falling every second.

2:01And now we have a wave that keeps repeating itself. Okay, this is very nice and this is much easier to analyze. We call such a wave that has a repeating pattern, we call it a periodic wave, because it's repeating itself periodically. So, let's think about the different features of the wave.

2:19The first one is called the frequency. The frequency of a wave is basically the number of waves that are passing through any given point in some given time. For example, in this particular case, every second one drop is falling down and therefore, if I were to look at any particular point, you'll find one wave passing through that point every second, what is the frequency of the wave.

2:46So, we can say the frequency of this wave is one wave per second, and a wave per second is also called hertz. So, we can say the frequency of the wave over here is one hertz. Now, let's see what it would, what things would look like if I were to increase the rate at which the water drops.

3:04So, if I were to now make the two drops of waterfall every second, let's see what's gonna happen. Ooh, ooh. Now, you can see there'll be two waves passing through a point every second. And therefore, we would say this has a frequency, this wave has a frequency of two hertz.

3:22And we can just compare the two. Here's a side by side comparison. You can see one hertz versus two hertz, one wave per second passing through any point, two waves per second passing through any point. But look at the speed of the wave. The speed of the wave is the same.

3:40In both the cases, the wave is traveling the same amount of distance in a given time. So, do not confuse frequency with speed. In both these cases, the speed of the wave is exactly the same. It's a distance that the wave travels per second, you can say, so, that is different from the frequency.

3:56Okay, what else do we have? Well, to understand another feature, let's look at the whole thing from the side. Now, before the wave starts, look at the level of the water. This is the equilibrium position, okay? Now, let's look at what happens when we start our tap.

4:08Okay, what you notice is that now the water level, there is this bottom level and there's this top level like, lemme just pause the video. All right, we find these peaks, which are the highest points about the equilibrium line. We call them the crests. And we find these valleys, which are the lowest point below the equilibrium line.

4:24We call them the troughs. And now, the distance between any two consecutive crests are consecutive troughs, that is what we call the wavelength. So, we can think of the wavelength as a measure of how big the wave is, and you can call that as a distance between any two consecutive troughs or consecutive crests.

4:45And since it's a length, the length is measured in units of length, like meters or maybe centimeters. And now here's the interesting thing, what do you think is gonna happen to the wavelength as you change the frequency? Well, let's look at the simulation side-by-side.

4:59So, on the top we're gonna have 1 hertz, one drop per second. On the bottom we have 2 hertz, two drops per second. Can you compare the wavelength? What do you notice? You can see the wavelength over here is bigger compared to over here. Here look at the distance between the crest-to-crest is much bigger than what you see over here.

5:16So, if you have higher frequency, you get smaller wavelength. Why is that? Well, that's because the speed of the wave in both the case was exactly the same. And so, if you're cramming more waves, then the distance between the waves is going to reduce. Amazing, isn't it?

5:32Finally, the last feature we wanna talk about is how far the water has moved from the equilibrium position? In other words, how high these peaks are, or how low these valleys are. That maximum change from the equilibrium position. We call that the amplitude. So, in this particular snapshot, this is how much the amplitude is.

5:54Now, let's see what happens if we change the amplitude. What does the picture look like? Again, let's do a side-by-side comparison. All right, take a look at these two cases and comment on the frequency and the amplitudes. What do you find? Well, the frequency is exactly the same.

6:09You have one drop falling per second in both the cases. So, you have one hertz of frequency. But look at the amplitude. Here, the peaks are much higher and the valleys are much lower compared to the peaks and valley over here. So, clearly this represents a high amplitude wave and this represents a low amplitude wave.

6:28All right, let's put it all together and do one final comparison. I want you to have a look at this simulation and compare their speeds, amplitudes frequencies, and wavelengths. This will also help us recap everything. Here it goes. Okay, let's start with the wave speed.

6:42Can you compare the speed of the waves? Well, remember, the speed of the wave is basically how fast the wave is traveling, how much distance the wave is traveling per second, for example. And you can see in both the cases is exactly the same. The waves are traveling at exactly the same speed.

6:55So, the speed is the same in both cases. Okay, what about the amplitude? Well, remember amplitude represents how far away, how high the peaks are, how low the valleys are, how much is the change from the equilibrium position. You can clearly see the changes more over here compared to over here.

7:10So, you have high amplitude here, lower amplitude over here. Okay, what about their frequencies? Well, remember frequency represents the number of waves passing per second, let's say at a given point. You can see there are less number of waves passing here per second.

7:24More number of waves passing here per second. Can you see that? So, the frequency is low here, high over here. In fact, the frequency is one hertz over here, two hertz over here. Two waves are passing per second over here. One wave is passing per second over here.

7:38Okay, finally, what about the wavelength? Okay, wavelength represents the distance between two consecutive crests and troughs. You can see that distance is larger over here compared to over here. So, we have higher wavelength here, lower wavelength over here.