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Current time:0:00Total duration:7:24

Video transcript

so let's say you had a string here and you give that string a little Yoink up and down you'd see a little wave pulse travel down that string but here's a question if someone else on the other end of this string also sent a wave pulse down the line toward the first wave what would happen when they overlap so let's try to figure this out let's say you had a wave coming in this way and yes this is square kind of weird it'd be hard you have to be pretty talented to do this on a string but this doesn't have to be a string let's say it could be a sound wave an electromagnetic wave any wave at all the fact that it's a square just going to make it easier for us to analyze so you got this wave coming in this way and then another wave coming in this way so it'd be clear this is the same string there aren't like two strings here there's one string two waves coming at each other so to be real I mean honestly there's only one string so this should be string coming here and then there's a pulse up this way so this string shouldn't be here this string moved up to that point it got disturbed and it comes back down to zero and then there shouldn't be two strings here you don't have two strings in the same spot so this would be the string up there and then it comes back down but in these examples I don't have to erase these all the time and make the video really long so let's just any time there's a string underneath a pulse we're just going to pretend like there's no string in there so what would happen what would happen when these pulses overlap well let's just find out if I take one and I move this here and then another wave is gonna move over the top of that one I'm gonna get wave interference this is the term wave interference for when two or more waves overlap in the same region so what's going to happen well the string can't be in two places at once there can only be one string and one shape of that string and the way you find out what the total wave is going to look like is simply by adding up the contributions of the two waves that are overlapping so in other words if I want to know the height of the total wave I'm going to call that height Y T T for total that's just going to equal the height of the first wave I'll call that y1 plus the height of the second wave and I'll call that y2 so if you're familiar with the wave equations you can just plug in those two wave equations here add them up and you get a total wave equation but a lot of times you don't have to resort to the full-blown mathematics of the wave equation you can kind of just look at the picture and figure out what the total wave would look like so let's do that let's put a little backdrop here so we can add these up so we'll call this one unit hi and there's gonna be two units hi and it's gonna be three units hi it could be meters or centimeters but it doesn't matter we'll just say 1 unit 2 unit 3 unit and now to figure out what the total wave is going to look like I just add up the contributions from each individual wave so both waves are 0 over here so that's easy 0 plus 0 is 0 then it gets to here the blue wave will call that wave 1 has a value of 1 unit hi the pink wave will call that wave 2 has a value of 2 units hi they're going in different directions doesn't matter right now they're overlapping so one unit hi plus 2 units hi is going to be equal to 3 unit I my total wave would look something like this so if I were to ask what would the wave actually look like the string if this were a string would actually look like this it would just be one big three unit high wave all those two waves are overlapping so that one was kind of easy how does this get harder let's say we asked the question what are these two waves look like when they're only partially overlapping so maybe when they get to this point where they're only halfway overlapped what's that total wave going to look like we're still going to use this rule we're going to add up both contributions to get the total so over here we have 0 + 0 + 0 0 until you get to here now the blue wave wave 1 has a value of 1 unit high the height of this wave is 1 unit the height of the pink wave wave 2 is 0 units 1 plus 0 is 1 so my total wave would look like this in that region and now in this region the blue wave is one unit high the pink wave is 2 units high 1 plus 2 is 3 so it would look like this in this region now over here since the blue wave dropped down we have to figure out a new value so the blue wave has a value of 0 the pink wave has a value of 2 2 plus 0 is 2 and so my total wave is going to look like this so the total string when those are overlapping halfway would look something like this which if it was a string would be really hard to do because it's hard to get an exactly square wave but electronic signals can have square waves and this is what they would look like if they were overlapping now I want to warn you about one thing this idea of wave interference is a cool idea but you got to be careful the term interference is a little misleading yes while these waves are overlapping they create a different wave they get distorted because the total wave will be the sum of the two waves but these waves pass right through each other which is great because when our send out a text message or a call to someone else everyone else's phone is also sending out a message in that same air those electromagnetic waves are traveling right through each other if they bounced off of each other right if these waves like balanced or got corrupted and the information got changed so that the shape isn't the same after as it was before it'd be really hard to make phone calls and send text messages but the wave interference is only happening while they're overlapping the waves make it through unaffected so the interference is only happening while they're overlapping otherwise they pass right through each other unaffected which is good so let's look at one more example that's a little more challenging so I'm gonna get rid of these and let's say you had these two wave pulses the same square pulse then you got this weird triangular pulse coming in and they're going to overlap so this wave pulse makes it to hear this triangular pulse makes it to hear oh and you get the state of Nevada so the string is not going to take the shape of Nevada the string can't be in two places at once so what's our total wave going to look like we're going to use the same rules that we did before for wave interference we're going to add up the values of each wave at a particular point to get the value of the total wave at that point so what do we get we've got zero plus zero over here so that's easy and now at this moment the value of the blue wave is 1 the value of the pink wave is zero so zero plus one is one and in here it's a little weird like you've got this pink wave changing but over here it's easy because the blue wave has a value of one the pink wave let's assume this drops down one as well so this is negative one unit blue wave is one pink wave is negative one that's going to be 0 1 plus negative 1 is 0 and after there it's going to be 0 but what is it in between well the simplest answer is actually the correct answer here it just drops down like this why does it do that well let's consider a point in the middle this point in the middle this blue wave has a value of 1 the pink wave has a value of negative 1/2 so 1 plus negative 1/2 is positive 1/2 or consider a point over here the value of the wave right here for the blue wave is 1 the value of the pink wave is like negative 3/4 so the value of the total wave would be positive 1/4 that's why this drops down linearly if this is linear this pink wave just keeps taking a bigger and bigger bite out of this blue wave and the total wave would look like that so if we get rid of these this would be what the total wave looks like when these two waves overlap so I should say that this technique of just adding up the values of each wave at that point it's called the superposition principle it's a very lofty intimidating name for something that's actually pretty simple to find the total wave if you just add up the values of the individual waves so recapping wave interference is the term we use to refer to the situation where two or more waves are overlapping in the same region and to find the value of the total wave while they're overlapping you can use the superposition principle which just says to add up the values of the individual waves at a given point to find the value of the total wave at that point
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