Okay, so let's talk about computing. Learn how to compute fundamental period, amplitude, and fundamental frequency. Okay, there we go. Alright, so we'll start this by taking a look at the equation. for a sine wave.
And of course, you know, you have to know this for the exam. You have to memorize it. Totally kidding. You don't have to do that. Wouldn't that be terrible?
You don't even really have to know it for the class. But I do just want to show it to you because there's a couple things in here that are important, I think, to understanding how we go from a sine wave, from a wave to a sine wave. And, um... that all the components that we're going to talk about, amplitude, frequency, and phase, are all in this equation, and that's how we end up with a sine wave.
So the first thing that I'll have you look at is the A. This is the amplitude, and basically it's out here in front of everything else. So it's A times sine wave and all this other stuff, because what we're doing with it is we're just multiplying all of this other junk by the amplitude.
That makes sense though, right? Because the amplitude is just how loud the wave is, how tall the wave is, how stretched out it is from top to bottom. And so you can have, you figure out everything, like the speed of how fast the wave is moving and where it's going to start. And then you can just adjust the height really easily. That's why the A is out front.
Just multiply it by the amplitude, essentially. Now frequency and phase, these are a little bit different. So you've got f right here, frequency, it's in the middle of all this good stuff right here.
It's actually being like operated on by the rest of these, by the rest of this math, and that's because the frequency is one of like the most fundamental pieces of a sine wave calculation. That's because... That's how quickly the wave is moving. That's how you know the period of just one cycle of the wave. So we have to know the cycle.
It's really important to the rest of the sine wave. Phase, which is phi, which is this Greek letter right here that kind of looks like a zero with a line through it. That's phase.
And you're just adding that to everything else. Phase is going to... go from 0 to 360 or 0 to 2 pi if you remember radians. And so you can just add it on, or you can even forget about it if you're starting at 0. So if you're starting at 0, it's plus 0, and then you basically just drop it from the calculation.
But it's there in case you're not starting from 0. So then we've got... here to pi if you remember from like high school math radians instead of degrees um that's what we're looking at with this little like wagon wheel thing that's happening down below me um is radians showing you how radians map on to like the movement of the the distance around a circle we start at zero and then at 180 degrees we're at pi 360, we're at 2 pi. That's in there just because this equation needs radians to arrive at the proper calculation instead of degrees.
So that's why 2 pi is in there. So essentially what we're doing with a sine wave is we're tracing one particular spot on a circle as it moves. So if you imagine...
the wave that we talked about last time or two times ago uh it's basically a circular motion right so the individual particles air particle something a buoy in water or a boat or whatever it's going to move kind of like in a circular fashion if you just pick one spot on air mode and it's going to move like this it's going to move and come back moving and um we're kind of tracing that out but we're having to put it in time so like i can do this and just in space but time's playing out for you so you see this happening over and over but if we're putting it into a graph we don't have really a representation of time so what we do is we do it like this so we make that circle but we stretch the circle out so we kind of trace it in time where it is now the only problem with this graphic is it doesn't start at zero It actually starts out of phase, so it should start right here, where the center of the wheel is, right there, if it was a good sine wave starting at zero and totally in phase. So it should start here and then move up and then come down and back up and end here in the same place, but it doesn't, but you get the idea. First thing we're going to do is we're going to look at the amplitude.
How do we find the amplitude? So here are some graphs of sound. The word graph just didn't want to come out of my brain for some reason.
Here are some graphs of sound, and we're looking at amplitude. And there's really supposed to be two ways to... book talks about two ways and some other instructors talk about two ways that you can measure amplitude but the second way is basically just the same as the first but making more work for yourself basically what we want to do is we want to go from the zero zero where the where an in-phase wave starts right here zero amplitude is what we're measuring over here so zero and you want to see where the peak is or the nadir The thing about that is amplitude is always positive. So even though we have negative values over here, that's really there just to describe compression and rarefaction. So we've got compression and then we've got rarefaction down here.
Is it negative? It's not really negative. Maybe it's negative pressure. But when we're talking about amplitude, it's never negative, even though there are negative numbers.
So amplitude... is an absolute value. So what you do is you go from the zero and you measure to the peak or the nadir. And in this case, it is one.
The amplitude is one, because you go just from zero to one. Now, the other thing is you can go peak to nadir, not peak to peak. It shouldn't say peak to peak.
It should say peak to nadir. You can measure that, and that's two. But of course, that's two times the amplitude.
You have 2a. You have to divide by two and you end up with one. Another typo.
I should have put one. So this should say peak to nadir and 2a. But look, that's like double the work.
You're having to add this to this and then you have to divide by two. You can clearly see a zero is always marked in all of your graphs of sound. So just go from peak to zero, nadir to zero. That's your amplitude.
What about on the right? Well that looks like roughly 2.5 is what I would say. So it goes from zero to negative 2.5 but it's always positive value.
Take the absolute value so it's 2.5 or here 0 to 2.5. So I'd say 2.5 and again peak to nadir is 2 times the amplitude so it'd be 5. You divide by 2 and you get 2.5. But just go from the 0 and then go to the peak. Okay, well that was easy. Amplitude is super easy.
Period is also super easy. But calculating the period is also just highly bonded to calculating the frequency. So that's what we're going to talk about next is finding the frequency.
The way that we do that is with this formula right here. Frequency equals one over time. T is actually period, so time is the period of the wave.
So frequency equals one over period. If you're wondering, so if you're thinking back to like high school math and they're like, you always have to write out your units or physics, they have you do this as well, right? So you're calculating how fast something is going and you... It's what? 60 meters in three seconds, and so it's 20 meters per second, and that's what they want you to put it in, or it's miles per hour, because it went a certain number of miles in a certain number of hours, and there's miles per hour, right?
That works here too, actually. So frequency, remember, is hertz, measured in hertz, and hertz is cycles per second. We talked about that last time, the last lecture, I think, and so when we look at this, formula one over time one over period one is really standing there for one cycle and t is the period of one cycle the time it takes to do one cycle in seconds and so if you think about it like this you're doing the frequency equals the site one cycle divided by t seconds so then you have cycles per second frequency of cycles per second hertz in cycles per second. So it works out. Okay, so let's do some math with this.
What's the frequency of a sine wave with a period of 0.1? Well, what do we know? We know that t in this case equals 0.1. So we can substitute t in our formula, f equals 1 over t, for 0.1. And when we do that, we get f equals 1 over 0.1.
And if you put it into your handy calculator... phone or excel or whatever you've got point one is 10. you can't see that and maybe it's backwards whatever it's in the powerpoint i guess you could just just just trust me on these you can put them into your calculator and check them too Next one. So what is the frequency of a sine wave with a period of 0.001 seconds? We'll do the same thing.
We're going to take what we know. We know t, the time or the period here is 0.001. And we're going to put it into our formula of f equals 1 over t.
So then it's f equals 1 over 0.001. And do that math and that ends up as 1,000 hertz. So that would be like...
Sorry if that broke your ear. That's sort of close to a thousand. I don't know.
Maybe. What is... So let's do one. Let's move on and we'll do one that's a little bit more difficult because it's not just zeros and ones. So the frequency of a sine wave with a period of 0.025 seconds.
t equals 0.025. Put it in our... Formula F equals 1 over T.
What do we get? F equals 1 over 0.025. Put that in your calculator and you get 40 hertz.
That's how you calculate the frequency from the period. But what if you're not always given the period? What if you're given a graph? You have to do this differently. So this is how you do that.
What you want to do is you want to look for your major grid lines. So here's 0.01 seconds and here's 0.02. Now, you know, I can't tell you why I thought it was easier to do 0.02 to do six cycles rather than 0.01.
There's not a good reason you could do either one. Now, your answer is going to come out the same way. But what I don't want you to do...
is to eyeball this and say, well, here's one cycle, and that's like roughly a third of this time, 0.01. So I'm just going to guess that it's 0.003. Don't do that. Go to the major grid line. Find where it actually repeats, where you've got a cycle ending and a major coinciding with a major grid line.
So we've got one. Two, three, and right there. Oh, I know why. I know why I didn't like that.
Because you don't have a full cycle right there. Oh, this isn't the one that I was thinking it is. In a couple slides, you'll see that I have one.
where I've done something stupid. But I could just look at the numbers that are on here. Anyway. So you've got one cycle, two cycles, two and a half maybe?
Looks like it's about right there, but let's find where we actually end. So there's three cycles, four cycles, five cycles. That coincides with a major group, 0.02. So we have five cycles in 0.02 seconds.
Well, shoot, because actually what we need is the period of just one cycle. So dang, we have to figure out... what the period of one cycle is.
And so what we're going to do to find that out is we're going to divide the amount of time that it took to make five cycles by the number of cycles. So we're going to take 0.02 divided by 5, and that gives us 0.004. Okay, now if you followed why we divided 0.02 by 5, don't listen to what I'm going to say now. If you're a little bit confused about why we divided.
0.02 by five, then do keep listening. So imagine that you're at the store, you need a pen, one pen is 350. It's a really expensive price of a pen, but whatever. One pen is 350. Or you can buy a three pack of pens for $9.
And you want to get the cheapest pen that you can buy. So, yes, it's true. I like orange and black pens only.
Makes everything I write look like it's for Halloween, which is awesome. It's how I roll, man. Anyway, here's a three pack of pens. It's $9.
How much is it per pen? What I'm going to do is I'm going to... take the amount of money, nine, and I'm going to divide it by the number of actual items that I can count, right? So by three.
I'm going to take the whole, the total number of money, amount of money, I'm going to divide it by one, two, three different items. Nine dollars divided by three. I end up with each of these costs three dollars.
And so I know that these are cheaper than the single pen that costs $3.50. So I want to buy the three pack because I'm saving. 50 cents per pen. That's what we're doing here, too.
We have an amount, which amount of time in this case, which is 0.02, and we're dividing it by the actual number of discrete things that we can actually count, which is the number of cycles. So we've got, again, one cycle, two cycles, three, four, five cycles. And we're going to take the amount of time, in this case, and divide it by five. And we end up with 0.004 seconds per cycle. One cycle takes 0.004 seconds to make a complete cycle.
Okay, so now we have the period. It's 0.004. And we're going to go back. Sorry, hang on.
I got to put my pens back where they were because I'm going to go to look for them. Later, I'll be like, where's my pen? Anyway, so... Our period, in this case, is 0.004.
We want to find the frequency. And so we put it into our formula of frequency equals 1 over time, and we sub out time for 0.004. We get frequency equals 1 over 0.004.
Do the math and your frequency is 250 hertz. So now we have the period 0.004 and the frequency 250. Next, what about simple tones, complex tones? Well simple tone is just one sine wave. So like it's a simple tone it's just one sine wave. That's all there is to know.
A complex tone is many sine waves. And so this line up here is a complex tone. This is all of these sine waves here basically mixed together.
And that's how we create a complex tone. You add sine waves. You just literally add the amplitudes. So if you took many, many, many tiny, tiny slices of all of these...
waves right here and you looked at where their amplitude was and you added them together and then you like put a dot for where what your amplitude adds up to and then connected all those dots that's how you get this wave right here this complex wave that's exactly what audacity does too when i have like multiple sine waves and it adds them together it has a sampling frequency And the sampling frequency is basically just like where it's measuring the amplitude of all these different sine waves. And then when I mix something together, like three different sine waves into a wave file, what it does is it just goes through and it adds together all of these amplitudes, like just billions or more numbers of amplitudes that it's adding together to create one sound. And that's kind of how it happens in the world also. I mean, instead of just like individual slices, it's, you know, individual atoms moving.
And so if you've got two sounds that are making an area of compression at the same time, they work together to create more compression. Or if you've got two that are creating rarefaction, they work together to create more rarefaction. All right, so let's talk about adding two sine waves that have the same frequency and phase, but different ampli. So same frequency and phase.
These are both 100 hertz tones is what it looks like to me because the period... No, they're not 100 hertz tones. They're 200 hertz tones.
Because the period looks like 0.005, just in my head I think 0.001 divided by 0.005 is 200? But let's see, am I right? One, two hundred, yay. Okay, so it's a 200 hertz tone and there's two of them.
They both start at a phase of zero. And they've got different amplitudes. So what the hell is going to happen? Well, like I said, they're just going to add together.
They're going to get louder. I have a quiet 200 hertz tone and a medium 200 hertz tone. And they're going to effectively be heard as one loud 200 hertz tone. This is by your ear. If you have a computer, add these two tones together.
It's going to... like show you the black line over here so that's just how those kinds of sine waves work let's take a look at this in audacity row this is the right one this is this is actually we're going to use this later Okay, so let's go to the other one. There we go. All right, so this is a 400 hertz tone that has an amplitude of 0.3. You can kind of tell right there.
This is a 400 hertz tone that has an amplitude of 0.6. Let's listen to just the 0.3. Keep your eye up here and see where this is going to show my levels. you're going to see how loud this is.
So just above 12, right? Right here where that blue line is. That was an amplitude of 0.3.
Now let's listen to just this one above 6. And now let's let them both play together. Almost totally peaking. It's almost too loud.
Which means I should probably apologize to your ears. And I should also probably stop playing it. But it's kind of funny. Okay, so that's adding two sine waves together. They just literally get added together.
Make one louder sound. Okay, so let's go back to the PowerPoint. What if we have the same frequency and the same amplitude, but different phases? Well, here what we've got are two sine waves that are completely out of phase, 180 degrees out of phase.
When one is starting to move up, the other one is starting to move down, and then when this one goes all the way down and starting to come back up and now it's at the peak, this one has started to move down and now it's at the nadir. They're exact mirror images. Again, you add the amplitudes together, and in this case, they are exact opposites, so you end up with nothing.
Absolutely nothing. You end up with this just... It wouldn't even sound... It would sound like this. There.
That's what it sounds like. It's silence. Right on the zero. Because essentially what's going on here is, if you think about one is an area of compression, the other is... in an area of rarefaction.
And then as the other one becomes compression, the other's in rarefaction. And it's kind of like you can't do it, right? So the compression is being canceled out by the rarefaction. And it ends up making no sound at all. Okay, let's take a look at this in Audacity.
Is this the right one? No. It's always, seems like it's always going to be the wrong one.
There we go. All right, so what we've got here is two 400 hertz tones, both amplitudes of 0.3. And right now they're in the same phase. So this is just going to be a louder sound, just like it was before. So we're going to listen to just the top one.
Okay, that goes slightly past 12. Now we're going to listen to just the bottom one. Also slightly past 12, the same amplitude, so it should be. And then we're going to listen to both of them. Now we're going to listen to both of them. Past 6, just past 6. Starting to get a little too loud.
All right, but now what I'm going to do is I'm going to delete part of this wave. I'm going to make them out of phase. Oh, let's go away and the beginning here. Okay, so let's delete that much of that wave.
Now what does it sound like? Well, it still sounds like... Here, it got in my mouth. Gross.
So it still sounds like a 400 hertz tone. Nothing's really changed about that. But look up here. It was past 6 when we played both of them, and it was just a little bit past 12 when we played 1. And now that they're out of phase, it's halfway between 12 and 6. It's at maybe like, you know, 10, 8, somewhere like that. It'd be 9. It looks closer to 8. Anyway, it's gotten quieter than it was before.
We're getting close to... canceling each other out. So let's trim a little bit more off it.
Let's trim just a little bit more off of this one. Now what do we got? Below 12. So now playing both of these is quieter than playing one of them alone. And now what I'm going to do is I'm going to go in and make it exactly out of phase, 180 degrees out of phase.
Here, by the way, this is that sampling frequency that I talked about. It looks like two sine waves, but the computer can't actually generate, you know, you can't do the math to generate a continuous tone, really. The speakers generate a continuous tone, but when the computer is doing the math for it, it doesn't know what continuous is.
This computer doesn't live in a continuous. And so it has all these little areas where it's computing the amplitude. So you can kind of think about this as like a digital version of like atoms, individual atoms in the air moving, air molecules moving. This is like the digital version of that.
Okay, so now we're exactly 180 degrees out of phase. Let's zoom out a little so we can see it. That becomes a line again at this point. Exactly 180 degrees out of phase. What does it sound like?
Almost nothing. Almost nothing. It's like I didn't quite cut it off perfectly, but it's close. It's really quiet. I mean, it's way quieter than...
Either one of these alone, just to show you. Again, here's one. Above 12. Here's this one. Above 12. And then together, like, slightly above 36. I mean, we're, like, really quiet here. So we're canceling each other out.
Almost. Almost completely. Okay, back to the PowerPoint. So they cancel each other out.
There is... Let me hang on to that for a second. Okay, so what if we add two sine waves that have the same frequency, but they've got different amplitudes and different phases? Well, of course, we're just going to add the amplitudes.
And this is what we end up with, is this right here. A sine wave that's kind of shifted. to somewhere between the two phases and an amplitude that's kind of an average of both of the other amplitudes because they're adding together and it's making it a little bit quieter. Okay, this is basically another way to look at the same thing.
We've got this sine wave at, what would this be, 270 degrees out of phase. And we've got this sine wave that is completely in phase, starts at zero. And you take the sum of the sinusoids, and this is what you end up with. Something that's just a little bit out of phase, kind of between the two.
All right. So noise-canceling headphones are awesome. And they actually use this principle of flipping something 180 degrees out of phase. And canceling it out. So I don't have a subwoofer near me anywhere, but I have this microphone.
I'm also going to have to talk quieter so I don't blow your eardrums out. So basically what's going on in noise-canceling headphones is, which these are not, oh well. You have a microphone right here, this little microphone. Just like I've got... This microphone actually, if you were to take off the cover, you'd actually see that there are three different microphones in here.
And that's because there's a few different settings you can use. So it can actually set up to be kind of like two microphones that are pointed in two different directions. Anyway, so it's got a microphone just like this one, but smaller inside the headphone.
It's also then got a... A speaker, I should put this filter over so I'm not making hissing sounds either. So it's got a speaker right outside on the end of the headphone, so like over here. And what that does is, through the microphone, it's listening to the sound that's coming from the outside. It's then flipping it with a little processor in the headphones, 180 degrees out of phase, and playing it out.
through the speaker right here. And what that does is it cancels out the sound from the outside. It's always a little bit, there's a little bit of lag all the time because it takes a little bit of time to like get the signal, flip it, and then send it back out. So noise canceling headphones aren't perfect. And also, I can set this back down now.
I think it probably is not. Surprising to you that not all noise-canceling headphones are created equal, because cheaper ones are going to have less good connections, not as good microphones, and not as good speakers. So the cheapish, like $50, $70 ones do not have as good of components as the ones that are like upwards of $100. When I was buying these, I just went with studio monitors.
what they do is they block sound from coming in. They also block sound from coming out. So I can listen to more kind of loudish sound here.
If I'm recording a podcast for one of my classes or something, I can hear what's going on in here. But my microphone doesn't pick it up because it blocks the sound from coming out, which not all noise-canceling headphones do. oriented to block sound from coming in they don't really care about the sounds going out and um you can also do music with these you can listen to like other tracks that are going and like play an instrument along with something so it's it's nice for that that's why i got these anyway when i was looking at these there were noise canceling headphones that were like close to a thousand dollars and they're made with gold plated Connectors and wires, the reason why they use gold is it's one of the best conductors, the fastest conductors, really good microphones, large microphones, so they can absorb more noise and really figure out what's going on in pretty large speakers on the outside. The bigger the speaker, the better they are at blocking out low frequency sound, and that's what you want.
you want to block out as much sound as you can. I mean, they're also good at blocking out high frequency sound, but it's not a problem to block out high frequency sound, low frequency sound. It's harder and harder the lower you go. So these like $1,000 noise canceling headphones are really equipped well for that.
There is an even cooler version of this in a museum in Germany where there's just like... a square blocked out on the floor. Nothing. There's no walls around it.
There's nothing. It's just part of the floor. And what you do is you walk into it and they've got speakers set up all around on the ceiling to take in the sound that's coming in. And they're sending sound back out to block it out. Like they take in the sound, they flip it 180. degrees and they send it back out and they block it out and inside the square it is completely silent like you're in a noisy museum and you walk through this threshold and no sound it's like you click mute on a youtube video except if someone is inside the square with you you can absolutely hear them but you can't hear anything that's going on outside it's like dead silence very totally totally totally cool okay let's keep going so what happens when we add sine waves that have a different frequency and a different amplitude in a different phase then we get stuff that looks like this so you can see there's a couple things going on here so there's this 600 hertz tone right here and we can see that still preserved in this the black line here is the added together signal You can see that the 600 Hz tone is still preserved.
It's there. There's still these six these oscillations at 600 Hz. But then the shape of the 200 Hz frequency is preserved too, because the shape overall that the 600 Hz oscillations are moving in is the 200 Hz tone.
And that's true no matter what you add together. So you've got a 200 Hz tone and a 1200 Hz tone. You still retain the shape of both of them.
or a 2400 hertz tone, you still retain the shape of both of those. You add them together, and they meld into a new sound. So we can, here's just looking at adding three of them together. And so basically, you can make a complex tone out of any periodic sound.
In fact, let's go the other way around, like I actually have it written here. You can create any periodic sound from a bunch of different sine waves. A musical instrument, speech.
The sound of animals vocalizations. These can all be recreated because they're periodic, or they're at least quasi-periodic for portions of the sound by sine waves. That's actually how synthesizers work.
Mine is right there, just off camera. But then I've also got a really messy desk, so I'm not going to... I'll show you. But that's basically how synthesizers work. The earliest synthesizers were, like, not great at actually synthesizing sound.
That's where the sound, the name synthesizer comes from, is they're trying to synthesize different instruments. So you'd have, like, an electric guitar, a flute, and all this other stuff, and they would just use combinations of sine waves to try to replicate that. Some of them were good. Some of them were bad. Some of them are extraordinarily bad.
And now you've got electric pianos. I don't even bother calling them synthesizers anymore. And you can totally recreate a ton of different sounds on these electric pianos. Like nowadays, synthesizers are just like sine wave generators, basically. And you're not even really trying to make it sound like a different instrument.
Because that's what the electric piano does. But originally, the instrument was intended to just replicate different sounds. That's how we make speech as well. One of the earliest ways that we were creating synthetic speech, well, the earliest way was with sine waves, but then somewhere in the middle, in the 90s... People started recording voices.
What they would do is they would just grab these little snippets of the voice and they would use those to put together words. So they would grab every phoneme and they would put them together to create words. Of course, there are problems with this because if you take, if I say the word problem, you've got p-r-a-l-e-m. And so then you could put that together to make like rope, but it would not exactly sound right. It would be the rup, something like that.
And it's not quite right. There's co-articulation. There's frequency modulation that we do at the beginning and ending of sentences that you really can't do by just taking a bunch of slices of someone's voice. Now what we do is there's machine learning algorithms that figure out what a voice should sound like.
A person's voice should sound like Siri. And then these are played with some sine waves. And sometimes there's recording that can go in there too, but then they're made really smooth. And they change the frequency for intonation by varying the sine waves and the flants and things like that.
So it's really actually... Very cool. But anyway, the basic idea here that I want to get across to you is that a periodic sound, which again can be a voice, a musical instrument, parts of animal vocalizations, certain types of animal vocalizations, these can be built from sine waves.
Sometimes a lot of sine waves, but still sine waves. And that depends on their frequencies or amplitudes and phases of the sine waves that you put together. Okay, so now let's talk about complex tones. With our just sine waves, we were trying to figure out the period and the frequency.
Now that we've got complex tones, we've actually got a period for every frequency that's in the complex tone, and we've got a frequency for every frequency that's in the complex tone. That was a bad sentence, but you get it. What we want to know are the fundamental period and frequency.
There is one that helps describe the signal better than all the others. And which one that is, is the lowest one. So basically, if you look at the signal and there's a reason, it's not just because it's the lowest one, that's the one.
It's actually, it has a reason. So you can see that there's different constituent sine waves here. We've got a peak here. Here, here, sort of here. We've got a trough here, here, here, and sort of here.
But what we want to look for is where does the entire signal repeat again? Not just where the peak starts and where there's a nadir, because we can find multiples of those here. But where does the pattern of peaks and nadirs repeat again and so you can look at this one is really huge right here boop so we're going to start here at the peak of this particular peak and then it's going to come down and move through all these like the landscape here and it's going to come back up and then it repeats again right here so this is the fundamental frequency this is where the entire pattern repeats again Rather, I should say this is the fundamental period for when the entire pattern repeats again.
And from there, we can compute the fundamental frequency. So that's what we're going to work on next. Okay, so we're going to calculate the fundamental period and frequency of this complex tone that is right... Where is my...
It's right here, down there. So what you want to do, the first thing you want to do is look at the tone and figure out where it repeats. again.
And it's right here. I mean, it's this amount, it's this amount, and it's also this one that I've got highlighted for you. So between 0.02 and 0.03, that's one cycle, just one. So 0.02 to 0.03 is a period of 0.01.
We put that into our formula, the same formula as before. Frequency equals 1 over t. In this case, instead of frequency equals 1 over period, we could think of it as fundamental frequency equals 1 over fundamental period. But the math is going to be the same. It's just 1 over this period that we found right here, 0.01.
1 over 0.01, 100 hertz. Fundamental frequency is 100 hertz. Let's do it again.
This is the 1 that I mentioned earlier. So our major grid line... is here at 0.01, and it's also here at 0.02. And you can count that this repeats one, two, three times, and then you're at 0.01. And for some reason, I've decided to go all the way to 0.06.
I don't know. So again, what you don't, what I do not want you to do is don't eyeball, like you can see that it repeats here. You know that...
This is just one unit, and you know that there's three. Don't eyeball it and be like, I don't know, 0.03, 0.04, and just pick one of those. Don't do that.
Go to the major grid line. So we know that there's one, two, three of them in 0.01 seconds. So go back to the pen example.
Three pens, $9. You're going to take the time, 0.01 seconds, divide it by three cycles. 0.01 divided by 3, or if you're a dummy like me, 0.02 divided by 6 equals 0.0033 seconds. That's your fundamental period.
Put it back in our equation that we had before, f equals 1 over period. You're going to put 1 over 0.0033, and that gives you 300 hertz. fundamental frequency here is 300 Hertz.
Hey, that was the end! Alright, I'll see you soon whenever you decide to watch the next video, and we'll talk about distinguishing periodic from aperiodic sounds.