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Current time:0:00Total duration:14:29

Video transcript

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 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'm 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 for me to think about this I 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 the 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 just get double in this case I can come over to here okay 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 and then over here I got 0 and 0 is just 0 and you start to see what's happening it 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 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 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'd 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 look 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 a hundred and eighty 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 if you turn around 360 degrees you're actually back to where you started if we tried to make these 360 degrees out of phase they look identical again because I've moved one so far through a cycle that 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 radians this is called pi out of phase because pi and 180 are the same angle all right so what happens here if I I take these two speakers I'm going to take the second speaker and I line it up right next to the first speaker I get something looks more like this 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 not 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 once positive 1/2 negative I get 0 and then over here 0 plus 0 is 0 and then the value of the first waves lining up with the peak of the second wave and if I add these two points up I get 0 again and you probably see what's going to happen I'm just going to get a flat line I 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 combine 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 hear if we had our ear over in this area again we were listening if I just had one speaker I'd hear a noise if I just have 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 cancelling 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 they'll be a positive terminal and a negative terminal released 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 is trying to push air forward there's a diaphragm on the speaker moving forward and backwards when one speaker is trying to push air forward the other speaker will be trying to whole 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 destructive interference so that's how you can create a speaker pie out-of-phase well 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 then 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 were in phase we 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 look at 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 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 wave length have I moved forward the amount of wavelength that you had to move forward was one half of a wavelength so if you take two speakers that are in phase and you move one one-half of a wavelength forward you get destructive interference again again if my ears over here I'm not going to hear anything even though these two waves started off in phase move one half 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 at what destructive interference and now whoa here we go constructive interference again that's a whole wavelength so if you move it forward a whole wavelength there's on whole wavelength forward so the front of the speaker was here now the front of speaker's here this is an entire wavelength I get constructive interference now it's going to 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 constructive or 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 X 2 and wave 1 is traveling this far to get to my ear I'm going to call that X 1 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 1/2 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 to 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 backup perfectly or three 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 1 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 1/2 wavelength it was destructive but that's not the only case any odd half integer here so I can't do 2 over 2 because that would be lambda again I can 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 flatline I'd get 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 its wave whoops one speaker sends out its wave going up the other sends out its way of going up to both of the same cycle if the only difference is the path length difference this is an important result that lets 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 switcheroo on the back of one of these speakers and you swapped the positive end for the negative end so that 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 started off with zero path length difference I get destructive instead of constructive if I move this a whole wave length forward there's a whole wave length I get destructive again two wavelengths forward destructive again three wavelengths four would be destructive again and so the integer wavelengths this time are going to give me destructive what about the half integers let's see I'll go forward a half a wavelength look at this perfectly in phase it's going to be constructive how about if I go three halves 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 if one source 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 from the other speaker and remember these don't have to be speakers they could be any wave source if one speaker is a PI phase shift from the other speaker well 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 energy wavelengths give you destructive the half 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 in some sort of double slit experiment or light in a thin-film experiment or sound with speakers or water waves anytime 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