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Current time:0:00Total duration:11:48

Video transcript

what's up everybody I want to talk to you about beat frequency and to do so let me talk to you about this air displacement versus time graph so this is going to give you the displacement of the air molecules for any time at a particular location so say you had some speaker and it was playing a nice simple harmonic tone and so would sound something like this that's 440 Hertz turns out that's an a note people use that a lot when they're tuning instruments and whatnot so that's what the sound would sound like and let's say it's sending the sound out and at a particular point one point in space we measure what the displacement of the air is as a function of time let's just say we're three meters to the right of this speaker just so we have a number to refer to so there's air over here the airs chillin just relaxing and then the sound wave comes by and that causes this air to get displaced it moves back and forth a miniscule amount but some amount and if we graphed that displacement as a function of time we would get this graph so in other words this entire graph is just personalised for that point in space three meters away from the speaker so why am I telling you this well because we know if you overlap two waves if I take another wave unless you say this wave has the exact same period as the first wave right so I'll put these peak to peak so you can see compare the peaks yep takes the same amount of time for both of these to go through a cycle that means they have the same period so if I overlap these in other words if I took another speaker and I played the same note next to it if I played it like this I'd hear constructive interference because these are overlapping peak to peak Valley to Valley perfectly this note would get louder if I was standing here and listening to it and it would stay loud the whole time it would just sound louder the entire time constructive interference and if I moved that speaker forward a little bit or I switched the leads if I found some way to get it out of phase so that it was destructive interference I'd hear a softer note maybe it would be silent if I did this perfectly and it would stay silent or soft the whole time it would stay destructive in other words so if you overlap two waves that have the same frequency ie the same period then it's going to be constructive and stay constructive or be destructive and stay destructive but here's the cray let me get rid of this what if we overlapped two waves that had different periods what would happened then let's just try it out so let me take this wave this wave has a different period look if I compare these two peaks these two peaks don't line up if I'm looking over here the distance between these two Peaks is not the same as the distance between these two peaks it's hard to see it's almost the same but this red wave has a slightly longer period if you can see the time between Peaks is a little longer than the time between Peaks for the blue wave and you might think ah there's only a little difference here can't be that big video right it kind of is it causes a new phenomenon called beat frequency and I'll show you why it happens here so if I overlap these two so now you take two speakers but the second speaker you play it at a slightly different frequency from the first what would you get let's just look at what happens over here they start out in phase perfectly overlapping right peak to peak so this is constructive this wave starts off constructively interfering with the other wave so you hear constructive interference that means if you were standing at this point at that moment in time notice this axis is time not space so at this moment in time right here you would hear constructive interference which means that those waves would sound loud sound really loud at that moment but then you wait this red waves got a longer period so it's taking longer for this red wave to go through a cycle that means there's going to start becoming out of phase right the peaks aren't going to line up anymore when this blue wave has displaced the air maximally to the right this red wave is going to not have done that yeah just going to take a little longer for it to try to do that so these become out of phase now it's less constructive less constructive less constructive over here look at now the peaks match the valleys this is straight-up destructive it's going to be soft and if you did this perfectly it might be silent at that point you wait a little longer and this blue wave has essentially lapped the red wave right you waited so long the blue wave has gone through an extra whole period compared to the red wave and so now the peaks line up again and now it's constructive again because the peaks match the peaks and the valleys match the valleys so at that point is constructive and it's going to be loud again so what you would hear if you were standing at this point three meters away you'd first at this moment in time the note be loud then you'd hear it become soft and then you'd hear to become loud again you'd hear this note wobble and the name we have for this phenomenon is the beat frequency or sometimes it's just called beats and I don't mean you're going to hear like dr dre out of this thing that's not the kind of beats I'm talking about I'm just talking about that wobble from louder to softer to louder actually let me just play it let me show you what this sounds like so if we play the a note again that's the a note let me play that's 440 Hertz right that's a particular frequency let me play just a slightly different frequency I'll play 443 Hertz and you probably like that just sounds like the exact same thing I can't tell the difference between the two but if I play them both you'll definitely be able to tell the difference so I'm going to play them both now here's the 443 Hertz and here's the 440 and you hear a wobble it starts this thing starts to wobble so let me stop this so that's what physicists are talking about when they say beat frequency your beats they're referring to that wobble and sound loudness that you hear when you overlap two waves that have different frequencies this is important it only works when you have waves of different frequency so what if you wanted to know the actual beat frequency what if you wanted to know how many wobbles you get per second so how often is it going from constructive to destructive back to constructive if that takes a long time the frequency is going to be small because there aren't going to be many wobbles per second but if this takes a short amount of time if there's not much time between constructive back to constructive then the beat frequency is going to be large there will be many wobbles per second how would you figure out this beat frequency I'll call it FB this would be how many times this goes from constructive back to constructive per second so if it does that 20 times per second this thing would be wobbling 20 times per second and the frequency would be 20 Hertz so how do you find this if you know the frequency of each wave it turns out it's very very easy I'm just going to show you the formula in this video in the next video we'll derive it for those that are interested but in this one I'll just show you what it is show you how to use it so the beat frequency if you want to find it if I know the frequency of the first wave so if wave one has a frequency f1 so say that blue wave has a frequency f1 and wave 2 has a frequency f2 then I can find the beat frequency by just taking the difference I can just take F 1 and then subtract F 2 and it's as simple as that that gives you the beat frequency now you might wonder like wait a minute what if one what if f1 has a smaller frequency than f2 that would give me a negative beat frequency that doesn't make sense we can have a negative frequency so we typically put an absolute value sign around this you should take the higher frequency minus the lower but just in case you don't just stick an absolute value and that gives you the size of this beat frequency which is basically the number of wobbles per second ie the number of times it goes from constructive all the way back to constructive per second that's what this beat frequency means and this formula is how you can find it and I should say to be clear we're playing two different sound waves our ears really just sort of going to hear one total wave so these waves overlap you can do this whole analysis using wave interference you write down the equation of one wave you write down the equation of the other wave you add up the two right we know that the total wave is going to equal the summation of each wave at a particular point in time so at one point in time if we take the value of each wave and they add them up we'd get the total wave what would that look like what would the total wave look like it would look like this if we just add it up you'd get a total wave that looks like this green dashed wave here right over here they add up to twice the wave and then in the middle they cancel to almost nothing and then back over here they add up again and so if you just looked at the total wave it would look something like this so the total wave would start with a large amplitude and then it would die out because they become destructive and then we become a large amplitude again so you see this picture a lot when you're talking about beat frequency because it's showing what the total wave looks like as a function of time when you add up those two individual waves since this is going from constructive to destructive to constructive again and this is why it sounds loud and then soft and then loud again to our ear so what would an example problem look like for beats let's say you were told that there's a flute and let's say this flute is playing a frequency of 440 Hertz like that note we heard earlier and then let's say there's also a clarinet they play it they want to make sure they're in tune they want to make sure their jam sounds good for everyone in the audience but when they both try to play the a note this flute plays 440 this clarinet plays a note and let's say we hear a beat frequency I'll write it in this color we hear a beat frequency of five Hertz so we hear five wobbles per second in fact if you've ever tried to tune an instrument you know that one way to tune it is to try to check two notes that are supposed to be the same you can tell immediately if they're not the same because you'll hear these wobbles and so you keep tuning it until you don't hear the wobble anymore as those notes get closer and closer there will be less wobbles per second and once you hear no wobble at all you know you're at the exact same frequency but these aren't these are off and so the question might ask what are the two possible frequencies of the clarinet well we know that the beat frequency is equal to the absolute value of the difference in the two frequencies so if there's a beat frequency of five Hertz and the flutes playing 440 that means the clarinet is five Hertz off from the flute so the clarinet might be a little too high it might be 445 Hertz playing a little sharp or it might be 435 Hertz might be playing a little flat so it would have to tune to figure out how it can get to the point where there'd be zero beat frequency because when there's zero beat frequencies you know both of these frequencies are the same but what do you do how does it know how does the clarinet player know which one to do you kind of don't sometimes sometimes you just have to test it out let's say the clarinet player assumed all right maybe they were a little too sharp for 45 so they're going to lower their note so they start to tune down what will they listen for they'll listen for less wobbles per second so if you become more in tune instead of whoa-whoa-whoa-whoa-whoa you would hear whoa-ho right and then once you're perfectly in tune will oh and it would be perfect there'd be no wobbles if this person tried it and there were more wobbles per second then this person would know oh I was probably at this lower note because if I'm at 435 and I go to say 430 Hertz that's going to be more out of tune now the beat frequency would be 10 Hertz you'd hear 10 wobbles per second and the person would know immediately whoa that was a bad idea I must not have been too sharp I must have been too flat so now that you know you're a little too flat you start tuning the other way so you can raise this up to 440 Hertz and then you would hear 0 beat frequency 0 wobbles per second a nice tune and you would be playing in harmony so recapping beats or beat frequency occurs when you overlap two waves that have different frequencies this causes the waves to go from being constructive to destructive to constructive over and over which we perceive as a wobble in the loudness of the sound and the way you can find the beat frequency is by taking the difference of the two frequencies of the waves that are overlapping