Hey guys. So in the last couple of videos we saw that waves can interfere with each other to produce special types of patterns. In this video. I want to show you a special type of interference with sound waves which is called beats. So just like the other videos, the most tricky part of this is actually visualizing what's going on with these interference patterns. So I'm gonna show you this step by step and I'm gonna show you what exactly a beat is. So let's check this out. We're gonna come back to this in just a second here. What I want you to do is imagine that you have two sound waves that you're playing sort of it like with two speakers at the same time. So I'm gonna call this one sound wave A and sound wave B. Now, even though these are sound waves, we're still gonna model them kind of like transverse waves because it's gonna help us figure out or sort of visualize what's going on here. So if you were to go ahead and calculate the frequency of this wave, remember the frequency is cycles per second, you're gonna find out that this frequency is eight hertz. You can pause video and check for yourself. Basically, I have eight sort of crest to crest patterns along this wave. If you do the same thing for wave B, if you go and pause video and count up the number of cycles that I have, you're gonna get 10 Hertz for these two waves here. So what happens if you were to play both of these sound waves with these frequencies at the same exact time, they're gonna interfere with each other. So what I'm gonna do in this third diagram is I'm actually gonna overlap these two things on top of each other, these two waves and we end up sort of with some interesting sort of patterns here. You'll notice at the beginning of the wave, these waves are totally out of sync. But then there's other parts where the waves actually are gonna basically line up to each other perfectly and there's other parts where they get out of sync, other parts where they get in sync again and then so on and so forth. So these sort of alternating patterns are basically interference patterns. So remember that constructive interference happens when the waves are sort of overlapping on top of each other. So these are the points that I have highlighted in yellow here. So here are the points where you have constructive interference, destructive interference is when the waves are canceling each other out. So, destructive interference are basically the highlights in tal. So we have one here and then you have one here and then you have one all the way over here. So, what we're gonna do now is we're actually gonna draw out what this net wave would look like. What would the superposition of these two sound waves look like? Well, to do this, the best way to do this is we have these two spots right here where the waves are gonna interfere with each other. They're gonna add up together almost perfectly to produce a bigger wave like this. So we're gonna have these two spots right here. And then in the teal spots, we basically have zero displacement because these things are gonna totally cancel each other out. So what happens in the middle? Well, basically what happens is that from here to here, the wave is slowly getting in sync and the amplitudes are gonna slowly start building on top of each other. So really what this wave is gonna look like is it's gonna kind of look like this where the wave size is getting bigger and bigger as you go to the right once you hit this point though, as you move to the right, the waves are getting out of sync. So basically, the reverse is going to happen and this wave is gonna get smaller and smaller until eventually goes to zero. And then basically this whole pattern is gonna repeat again. So you're gonna have sort of a wave like this. Oops when I do this, like that's, and then here it's gonna sort of get smaller and smaller and eventually go to zero. So we can see here that the difference between these sort of two patterns here and this net wave is that these two patterns always have the same amplitude. The amplitude is always the same along the same part of the wave. But in this part right here, this net wave has a varying amplitude, it goes from zero up to a maximum value. And that's what a beat is a beat is really just an oscillation in amplitude that happens for sound waves. And this happens when you have two sound waves with similar frequencies that interfere with each other. So the idea here is that the only reason we weren't able to get this pattern is because we have two sound waves that had similar frequencies eight and 10. If you had something like 15 and then 50 you wouldn't get something like this sort of wave pattern. All right. So there's a couple of things that you need to know about these beats. The first is the amplitude, the amplitude is really just gonna be twice of the amplitudes that of the waves that make it up. So the idea here is that if this amplitude is one and this amplitude is also one, then that means that the net wave is gonna have an amplitude of two these things are just gonna add up to each other right now. The the most important variable you need to know is the beat frequency. The beat frequency is the number of oscillations or the number of amplitudes that you hear in one second. So basically, it's the number of patterns that you get in one second. Remember this whole thing happens in just one second. How many beats do we have, we have one beat here and then we have one beat here. So the equation to calculate this beat frequency is gonna be the absolute value of the difference of the two frequencies of the waves that sort of make this us make this beat up. So the idea here is that when we had eight and 10, our, our uh beat frequency is just gonna be the absolute value of eight minus 10 and we get two Hertz. Now, basically this two Hertz should make some sense because we have two oscillations from zero to amplitude and then down to zero again. So it goes from zero to max and then down to zero again and then up to max again and then down to zero again. So this happens twice in one second. Therefore, we have two Hertz. All right. The last thing we wanna talk about here is what the resulting sound would actually sound like. So if you actually have these two waves that were creating this beat, what would it sound like? Well, the resulting sound you hear is gonna have a pitch, it's gonna have a frequency of F sound. And this F sound here is really just gonna be an average of the two frequencies that make it up. But this F sound is not the same thing as the beat frequency. The uh the sound frequency is gonna be the average. So basically what we have here here is eight plus 10 divided by two. So we're gonna have a sound frequency of nine Hertz. But the amplitude, the loudness is gonna vary at this beat frequency here. So the loudness is related to the beat frequency, but the pitch is related to the sound and basically this is just an average whereas this is a difference. So what this would actually sound like here is it would sound like, wow, wow, twice in one second. That's basically what a beat would sound like. All right. So let's go ahead and take a look at our example here. So we have two musicians that try to play the same notes. Uh One has a wavelength of 65 which has a wavelength of 65 centimeters at the same time. So lambda equals 0.65. However, one of the instruments is actually out of tune. And so it plays a note with a wavelength of 65.4 slightly longer. So what I'm gonna do is I'm gonna call this one, Lambda A and then Lambda B is gonna be 0.654. I'm just converting this to meters here, right? So I'm just moving the decimal place over. Now, we wanna calculate the frequency of the beats that the musicians are going to hear. We're gonna assume that the speed of sound is 343. So this is gonna be RV here. This is gonna be RV. All right. So how do we figure this out? Well, remember the equation we have for the beat frequency is we're gonna have to subtract, we're gonna have to subtract these two frequencies and then take the absolute value. So let's go ahead and do that. So we're gonna have F beats is gonna be the, these uh absolute value of fa minus FB. The problem is we actually don't have what these frequencies are, but we do know what their corresponding wavelengths are going to be. So how do we get from wavelength to frequency? Well, remember we can just use the equation uh the equation V equals lambda frequency here. So we have is sound waves. So we have the speed of sound, which is 343. So we have what we have here is that we would solve for the frequency. This is just gonna be V over Lambda A. So it's gonna be 343 divided by 0.65. And what you're gonna get is you're gonna get 527 points seven and this is gonna be in Hertz. All right. So the same thing for FB, if you go ahead and find out what FB is, we're just gonna get V over Lambda B and this is gonna be 343 divided by 0.654. But you're gonna get is 524.5 Hertz. So we have these two notes that are being played these two sound waves and they're very, very slightly off, right. The difference between them is very, very small. So they're gonna create this beat frequency here. And so what happens is this beat frequency is just going to be the absolute value of 527.7 minus 524.5. And you end up with a beat frequency of 3.2 Hertz. So basically, you would hear uh an oscillation from zero to a maximum amplitude and you would hear that sort of pattern 3.2 times in one second. All right guys. So that's it for this one. Let me, let me know if you have any questions.