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Wave interference

Waves add and subtract their amplitudes when they overlap, a phenomenon known as wave interference. Learn how overlapping waves can lead to constructive interference, forming amplified waves, or destructive interference, resulting in cancelled waves. Uncover the significance of phase shifts and path length differences in shaping wave behavior. Created by David SantoPietro.

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Video transcript

- [Voiceover] If two waves overlap in the same medium, we say that there's wave interference. So this box here could represent a speaker and this could be the sound wave it generates or it could represent a laser and this would be the light wave it generates or it could be some sort of ripple tank generator and this is the water wave it generates. Regardless, if you had a second source of a wave and these were to overlap, you'd cause wave interference and what that would look like would be something like this. So let's say these are speakers. I like thinking about it in terms of speakers, I think it's easy to think about and I put this speaker right next to the first speaker, side-by-side. So they'd be creating sound waves in this region and I wouldn't really have two sound waves necessarily. You can think of it as just having one total sound wave and how would we find the size of that total sound wave? Well if I put an axis in here. The axis will make it easier to think about this. I'm going to put an axis through here like this What I can do is I can just ask myself this, I'm going to say, what was the value of the first wave, so I'm going to take that value. What was the value of second wave and I'm just going to add them up. To get the value of the total wave, I'd take that value of the first wave plus the value of the second wave and well I'd just get double in this case. I can come over to here okay. The value here plus the value there, I get double that point. It's not going to be as high because they weren't as high.. Then over here I got zero and zero is just zero. and you start to see what's happening. I can come down here very low or very negative and I get double that down here and if I were to trace this out, what I would get is one big total sound wave that would look like this. So these have been amplified. So that's one possibility. When two waves overlap, you can get this case where the peaks match the peaks and the valleys match the valleys and you get constructive interference. So notice how each valley matches the valley, each peak matches the peak and this is called, Constructive Interference because these constructively combine to form one bigger wave. So this is Constructive Interference. So what would you hear? If your ear was over here somewhere waiting to hear this sound. What you'd actually hear is a loud note. This would be much louder than it was. It would be twice as loud in fact. Which makes sense. You've got a second speaker in here. It's twice as loud. That makes sense. What's a little bit harder to understand is you can also have something called, Destructive Interference. What would that look like? Well, imagine you had two speakers but they looked like this so that the peak of the first one lined up not with the peak of the second one but with the valley of the second one and the valley of the first one lined up with the peak of the second one. These are out of phase we say. Before, when they looked like this. These waves we say are in phase, because they look identical. The peaks match up with the peaks. The valleys with the valleys. These are out of phase. How far out of phase are they? We say that these are 180 degrees out of phase. So these are 180 degrees out of phase. The phase refers to what point on the wave cycle is the wave at and these two are starting completely separately which is 180 degrees. You might think that means 360 but think about it. If you turn around 360 degrees, you're actually back where you started. If we tried to make these 360 degrees out of phase, they'd look identical again because I've moved on so far through a cycle that's it's back to where it started in the first place. So I want to move it 180 degrees out of phase. That's exactly the opposite So that you get peak lining up with valley or if you like radions, this is called pi out of phase because pi and 180 are the same angle. Alright so what happens here if I take these two speakers? I'm going to take this second speaker and I line it up right next to the first speaker. I get something that looks more like this. Look at how weird this looks. These are completely out of phase and what's going to happen is if I add my little axis to help me think about this. I'm going to add an axis straight through here. Now I play the same game. What total wave do I end up with? Well, I take this value. I'm going to add up the values just the same. I take the value of the first wave plus the value of the second wave. I add those up, one's a positive and one's a negative I get zero and then over here zero plus zero is zero and then the valley of the first wave is lining up with the peak of the second wave and if I add these two points up, I get zero again and you probably see what's going to happen. I'm just going to get a flat line. I'm going to get a flat line and I'm going to get no wave at all. These two waves cancel and so we call this not Constructive Interference but Destructive Interference because these have destructively combined to form no wave at all and this is a little strange. How can two waves form no wave? Well, this is how you do it. And what would our ear here if we had our ear over in this area again, and we were listening. If I just had one speaker, I'd hear a noise. If I just had the second speaker, I'd hear a noise. If I have both the first and second speaker together, I don't hear anything. It's silent, which is hard to believe but this works. In fact, this is how noise canceling headphones work if you take a signal from the outside and you send in the exact same signal but flipped. Pi out of phase or 180 degrees out of phase. It cancels it and so you can fight noise with more noise but exactly out of phase and you get silence in here, or at least you can get close to it. Now you might be wondering how do we get a speaker to go 180 degrees out of phase? Well it's not too hard. If you look at the back of these speakers. Let me make a clean view. If you look at the back of these speakers, there will be a positive terminal and a negative terminal or at lease inside there will be and if you can swap the positive terminal for the negative terminal and the negative terminal for the positive terminal, then when one speaker's trying to push air forward, there's a diaphragm on this speaker moving forward and backwards. When one speaker is trying to push air forward the other speaker will be trying to pull air backwards and the net result is that the air just doesn't move because it's got equal and opposite forces on it and since the air just sits there, you've got no sound wave because air has to oscillate to create a sound wave and you get Disruptive Interference. So that's how you can create a speaker pi out of phase. You might be wondering, I don't want to mess with the wires on the back of my speaker in fact, you shouldn't so you don't get shocked but if I've got two speakers in phase like this, I'm stuck, I can't get Destructive Interference but yeah you can. Even if you don't mess with the wires, and don't, don't try this at home, you can still take this speaker, remember before when these where in phase we'd just line them up like that, Constructive Interference but I don't have to put them side-by-side. I can start one speaker a little bit forward and looks what happens. We start to get waves that are out of phase. So my question is how far forward should I move this speaker to get Destructive Interference and we can just watch. So I'm just going to try this and when we get to this point there, now we're out of phase. Now I have Destructive Interference and so how far did I move my speaker forward? If we look at it, here was the front of the speaker originally, right there. Here's the front of the speaker now. If you look at this wave, how much of a wavelength have I moved forward. The amount of wavelength that you had to move forward was 1/2 of a wavelength. So if you take two speakers that are in phase and you move one 1/2 a wavelength forward you get Destructive Interference again. Again, if my ear's over here, I'm not going to hear anything. Even though these two waves started off in phase, move one 1/2 a wavelength forward, they line up so that it's Destructive, I get no noise but if I take this away. We go back to the beginning here. Take my speaker, we start over. If you move it forward a whole wavelength, so I take this here, keep moving it, keep moving it and then Destructive Interference Whoa, here we go, Constructive Interference again. That's a whole wavelength. So if you move it forward a whole wavelength. Look, there's one whole wavelength forward. So the front of the speaker was here now the front of the speaker's here. This is an entire wavelength. I get Constructive Interference. Now I'm going to hear a loud sound again. I'm going to hear twice the noise that there would be if I just had one speaker. So the moral of this story is that even if you have speakers that are in phase, you can get Destructive Interference depending on the difference in the length that these two waves travel. In other words wave two is traveling this far to get to my ear. I'm going to call that x2 and wave one is traveling this far to get to my ear. I'm going to call that x1. If I took the difference between these two, I'd be finding the path length difference. The difference in path lengths that these waves are traveling and that would be this amount. This is the difference right here. I'm going to call it delta x because it's the magnitude of the difference between these two lengths and we saw that if this equals lambda it was constructive and if it equaled a 1/2 a lambda it was destructive but those aren't the only values. We can write down an important result here. If delta x, the path length difference was lambda or it turns out 2 lambda will work or 3 lambda, imagine moving the second speaker one more whole wavelength. Well, you'd be perfectly back in phase again because you'd align back up perfectly or 3 whole wavelengths again, perfectly in phase. Any integer wavelength including zero because zero is just the case where the speaker was right next to speaker one. Where these two speakers were lined up right next to each other, you'll get Constructive Interference. The waves line up perfectly, it's going to be constructive and we saw if, delta x equals a 1/2 wavelength it was destructive but that's not the only case. Any odd 1/2 integer here. So I can't do 2 over 2 because that would be lambda again. I could do 3 lambda over 2 or 5 lambda over 2 or 7 lambda over 2. Any of these will give me Destructive Interference because they'll cause these peaks to match up with valleys. The whole thing would flat line. I'd get no sound. This is an important result. If you've got two speakers that are starting off in phase. In other words they both start off the same way and by that I mean one speaker sends out it's wave going up, the other sends out it's wave going up. There both at the same cycle. If the only difference is the path length difference, this is an important result that let's you determine whether there's constructive or destructive interference but you might ask, hold on, what if... See this was assuming there was no phase difference to start off with. What if you did the old switcheroo on the back of one of these speakers and you swapped the positive end for the negative end so instead of coming out upward, the second one was coming out downward. Then what would happen? Well you might be able to guess. Now, this results just going to flip-flop. In other words, if I look at this case here Look at, now we start off with speakers that are out of phase to begin with. This time, if I start off with zero path length difference, I get destructive destructive instead of constructive. If I move this a whole wavelength forward, there's a whole wavelength, I get destructive again. Two wavelengths forward, destructive again. Three wavelengths forward would be destructive again and so the integer wavelength this time are going to give me destructive. What about the half integers? Let's see, I'll go forward a 1/2 a wavelength. Look at this, perfectly in phase. It's going to be constructive. How about if I go 3 1/2 of a wavelength. Again, perfectly in phase, constructive. So, in this case it turns out if you start off with speakers that were already phase shifted. If one speaker is pi shifted from the other then we got another result here. We've got that... Well actually I'll just go back to my previous result, it's easier. We can just add a little addendum here if if one speaker is pi phase shifted, from the other speaker and remember these don't have to be speakers. They could be any wave source. If one speaker's a pi phase shift from the other speaker then you just flip-flop this. Then you just take this rule and now these give you constructive right here. These would give you constructive and these up here would give you destructive and so the whole thing just gives you the opposite result. Now the whole integer wavelengths give you destructive. The 1/2 integer wavelengths give you constructive and I have to impress upon you the idea that this does not just apply for speakers. This applies for light and some sort of double slit experiment or light in a thin film experiment or sound with speakers or water waves. Any time that's the case, this rule holds in fact, this is the fundamental rule for almost all wave interference aspects. Is that the path length difference along with whether there's a pi phase shift, a relative pi phase shift between the two will determine whether you get constructive or destructive interference.