WEBVTT - How Music Works - The Physics 0:00:04.400 --> 0:00:07.760 Welcome to text Stuff, a production from my Heart Radio. 0:00:12.160 --> 0:00:14.960 Hey there, and welcome to tech Stuff. I'm your host, 0:00:15.120 --> 0:00:18.560 Jonathan Strickland. I'm an executive producer with I Heart Radio, 0:00:18.680 --> 0:00:22.360 and I love all things tech. And here's a really 0:00:22.400 --> 0:00:28.680 cool thing about technology. Technology is the proof that science works. 0:00:29.160 --> 0:00:31.360 So you can think of technology is sort of the 0:00:31.400 --> 0:00:35.800 physical manifestation of our understanding of science. And as we 0:00:35.920 --> 0:00:39.120 learn more about how our universe works, we can build 0:00:39.159 --> 0:00:43.040 stuff that leverages what we've learned. We can even leverage 0:00:43.040 --> 0:00:47.040 how the universe works without having a full understanding of 0:00:47.040 --> 0:00:50.960 the scientific principles. Though in general, the better we understand 0:00:50.960 --> 0:00:54.680 those principles, the better technology we can make. And one 0:00:54.760 --> 0:00:58.360 subset of technology that I think really illustrates this well 0:00:59.040 --> 0:01:02.560 is musical instrument and so in this episode and in 0:01:02.600 --> 0:01:05.920 the next episode, I'll talk about the science behind music 0:01:06.000 --> 0:01:09.720 without getting too deep into musical theory that's its own thing, 0:01:10.400 --> 0:01:14.880 and how musical instruments are an example of physics and action. Now, 0:01:14.959 --> 0:01:18.640 in the past, I've done episodes on stuff like synthesizers 0:01:18.680 --> 0:01:22.200 and electric guitars and pickups and amplifiers, you know, describing 0:01:22.240 --> 0:01:26.880 how electronics gave musicians new ways to make sounds, including 0:01:26.880 --> 0:01:30.280 sounds that have never been created before. But honestly, the 0:01:30.480 --> 0:01:34.360 entire history of musical instruments kind of follows that path. 0:01:34.959 --> 0:01:37.759 It's just that some of those instruments are the kind 0:01:37.800 --> 0:01:40.600 that you plug in or that you connect to amplifiers 0:01:40.680 --> 0:01:44.280 or whatever, and some aren't. But they all relate back 0:01:44.319 --> 0:01:47.920 to science in some way or another. Music marries the 0:01:48.000 --> 0:01:51.520 scientific with the creative, and it's one of the manifestations 0:01:51.520 --> 0:01:54.920 of ingenuity that I really love. Case in point, the 0:01:55.000 --> 0:01:58.280 inspiration for today's episode came out of something I was 0:01:58.520 --> 0:02:02.840 genuinely curious about out myself. See, I'm not a musician 0:02:03.040 --> 0:02:06.280 by any stretch of the imagination. Though I do own 0:02:06.440 --> 0:02:10.280 a few musical instruments, I was never in band or 0:02:10.400 --> 0:02:13.760 orchestra or anything like that. So I was sitting there thinking, 0:02:14.520 --> 0:02:17.600 how the heck does a trumpet work? And I researched it, 0:02:17.639 --> 0:02:19.280 and then I thought, you know, I should do a 0:02:19.320 --> 0:02:22.560 tech stuff episode on this. But then I kept going 0:02:22.560 --> 0:02:25.120 down the rabbit hole and decided to do something a 0:02:25.200 --> 0:02:28.400 little more ambitious than how a trumpet works. So in 0:02:28.440 --> 0:02:32.239 today's episode, I'm going to talk more generally about music 0:02:32.280 --> 0:02:36.040 instruments and how they work. By explaining the physics behind 0:02:36.320 --> 0:02:38.920 the art of music, because when you get down to it, 0:02:39.160 --> 0:02:42.040 a musical instrument is really just taking what we understand 0:02:42.040 --> 0:02:45.760 about physics, building a real world object based on that understanding, 0:02:45.880 --> 0:02:48.160 and then putting it to use to make something beautiful 0:02:48.520 --> 0:02:53.600 or interesting, or, in my case, terrible. To understand all this, 0:02:53.880 --> 0:02:57.240 it's best to start with a scientific breakdown of the 0:02:57.280 --> 0:03:02.520 phenomenon of sound. And there's an old philosophical question that says, 0:03:02.880 --> 0:03:05.960 if a tree falls in the forest and nobody is 0:03:06.000 --> 0:03:09.200 around to hear it, does it make a sound? Now, 0:03:09.280 --> 0:03:12.680 one point of this question could be to say, if 0:03:12.720 --> 0:03:16.240 there's no way to observe something happening, can we really 0:03:16.280 --> 0:03:20.720 be sure that it actually happened, particularly something as ephemeral 0:03:20.760 --> 0:03:23.440 as sound, So if no one was there to observe it, 0:03:23.520 --> 0:03:28.200 can we say for sure that something observable happened. But 0:03:28.280 --> 0:03:30.600 another way that we could look at the same question 0:03:30.800 --> 0:03:33.919 is to say, is sound really a thing if there 0:03:34.040 --> 0:03:36.480 is no one there to perceive it? Because sound is 0:03:36.520 --> 0:03:41.440 really describing how our brains process incoming fluctuations of air pressure. 0:03:42.000 --> 0:03:45.520 In this case, we're not necessarily asking if the vibrations 0:03:45.560 --> 0:03:49.000 from the tree happened or not. It's more that if 0:03:49.000 --> 0:03:52.880 there is no one to experience that as sound, would 0:03:52.920 --> 0:03:56.280 we really say that a sound happened? Is the experience 0:03:56.360 --> 0:04:00.280 necessary to call it sound? Now I don't have an 0:04:00.280 --> 0:04:02.440 answer to that question, but I do want to talk 0:04:02.480 --> 0:04:06.240 more about what's going on with sounds. So at the 0:04:06.320 --> 0:04:10.720 very heart of it, sound comes from vibrations. Generally, when 0:04:10.720 --> 0:04:13.640 we talk about sound, we typically mean it comes from 0:04:14.080 --> 0:04:18.080 vibrations of air molecules, which gets to that fluctuation and 0:04:18.160 --> 0:04:21.240 air pressure that I was talking about. It's fluctuations and 0:04:21.279 --> 0:04:25.840 air pressure that ultimately are sound most of the time 0:04:25.880 --> 0:04:28.440 when we're talking about it. Sound can actually travel through 0:04:28.680 --> 0:04:32.360 really any physical medium. It's just that it travels more 0:04:32.360 --> 0:04:35.280 easily through some rather than others. And the way we 0:04:35.720 --> 0:04:38.880 usually encounter it is through the air. So let's say 0:04:38.920 --> 0:04:42.280 for a moment that you have the incredible superpower to 0:04:42.520 --> 0:04:45.640 zoom and enhance your vision, and you can also see 0:04:45.800 --> 0:04:49.279 air molecules, so you're actually looking at the air molecules 0:04:49.320 --> 0:04:52.520 all around you. Now, imagine that you see someone clap 0:04:52.600 --> 0:04:55.800 their hands, and as they clap their hands, they're causing 0:04:55.839 --> 0:04:59.440 a bunch of air molecules to bounce around into each other, 0:04:59.680 --> 0:05:02.560 and that creates a chain reaction that passes from the 0:05:02.600 --> 0:05:07.000 point of origin, that being the clapping hands outward like 0:05:07.040 --> 0:05:09.840 a ripple and a pond, almost but in all directions. 0:05:10.160 --> 0:05:13.080 Now you're paying really close attention, and you notice that 0:05:13.160 --> 0:05:16.919 as the collisions move outward, the reaction as a whole 0:05:17.200 --> 0:05:20.159 begins to appear to lose energy. So the further you 0:05:20.240 --> 0:05:23.040 out from the point of origin, the less you'll see 0:05:23.040 --> 0:05:26.279 those air molecules move, and eventually you'll be far enough 0:05:26.279 --> 0:05:29.400 out where the movement is imperceptible. And this is why 0:05:29.440 --> 0:05:32.640 sounds are louder when you're closer to the point of origin, 0:05:32.880 --> 0:05:36.120 which I admit is about as basic an idea as 0:05:36.160 --> 0:05:39.680 I can communicate. But the reason those sounds are softer 0:05:39.800 --> 0:05:43.280 when you're further away, assuming you don't have some interesting 0:05:43.320 --> 0:05:48.320 curvature of the acoustic area around you, the reason that 0:05:48.440 --> 0:05:51.320 they're softer is that the energy of that initial vibration 0:05:51.520 --> 0:05:54.760 gets diluted as the reaction passes outward. And you can 0:05:54.800 --> 0:05:57.760 think of it as the origin of the sound affects 0:05:57.800 --> 0:06:00.400 a relatively small number of air molecules and at least 0:06:00.400 --> 0:06:03.599 surrounding that point of origin, and it causes those air 0:06:03.600 --> 0:06:07.680 molecules to fluctuate. Those fluctuating air molecules cause a larger 0:06:07.760 --> 0:06:12.120 number of surrounding air molecules to fluctuate. But because you're 0:06:12.120 --> 0:06:16.160 talking about transferring energy from a smaller number of molecules 0:06:16.200 --> 0:06:19.480 to a larger number of molecules, the amount of energy 0:06:19.560 --> 0:06:23.520 transmitted to that second group of air molecules means that 0:06:23.600 --> 0:06:26.920 each individual molecule is getting less than the first group. 0:06:27.440 --> 0:06:30.120 You know, energy cannot be created or destroyed, so we're 0:06:30.120 --> 0:06:33.200 not getting rid of energy here, it's just we're spreading 0:06:33.200 --> 0:06:37.480 it out across a larger area, so each individual component 0:06:38.000 --> 0:06:41.360 is getting slightly less energy than the previous group. Now, 0:06:41.400 --> 0:06:43.760 of course, in the real world it's not quite so 0:06:43.960 --> 0:06:47.400 neat and simple as saying a circle of air molecules 0:06:47.600 --> 0:06:50.880 than affects and slightly larger circle that affects a slightly 0:06:51.000 --> 0:06:54.120 larger circle, and so on. But you get the idea. 0:06:54.320 --> 0:06:58.000 When we talk about vibrations, we mentioned stuff like frequency, 0:06:58.320 --> 0:07:00.760 and that word is all about the number of times 0:07:00.800 --> 0:07:04.400 a repeating event occurs within a given unit of time. 0:07:04.839 --> 0:07:07.880 So with sound, we usually refer to frequency in terms 0:07:07.920 --> 0:07:12.040 of units called hurts, h, E, R, t z. This 0:07:12.120 --> 0:07:15.680 tells us how many times this particular repeated event, and 0:07:15.840 --> 0:07:20.840 oscillation happens within the span of a second. Twenty hurts, 0:07:20.960 --> 0:07:23.520 which is generally said to be the lower end of 0:07:23.560 --> 0:07:27.360 the typical range for human hearing, would be a wave 0:07:27.400 --> 0:07:32.480 that's oscillating twenty times per second. Any vibration slower than 0:07:32.520 --> 0:07:34.560 that would be at such a low frequency that the 0:07:34.600 --> 0:07:37.880 average person would be unable to hear it. A twenty 0:07:38.000 --> 0:07:41.280 killer hurts sound, which is at the tippy top end 0:07:41.400 --> 0:07:45.240 of typical human hearing, would mean that the oscillating wave 0:07:45.480 --> 0:07:49.200 is oscillating at a speed of twenty thousand times per second. 0:07:49.800 --> 0:07:52.440 So that means if you had a string that vibrated 0:07:52.480 --> 0:07:55.120 at twenty hurts, you can set up a high speed 0:07:55.160 --> 0:07:58.760 camera on that string, and when you pluck the string 0:07:59.280 --> 0:08:01.800 and you're use that high speed camera to shoot video 0:08:01.840 --> 0:08:04.640 of it, you would see that for every second in 0:08:04.720 --> 0:08:07.600 real time that passes, you could count the string making 0:08:07.640 --> 0:08:11.560 twenty full cycles, which means going up and down past 0:08:11.640 --> 0:08:14.280 the camera that's one full cycle. Not just passing it once, 0:08:14.280 --> 0:08:18.600 it has to pass it twice. That would be twenty hurts. Now, 0:08:18.760 --> 0:08:22.440 we also tend to talk about sound waves, and this 0:08:22.480 --> 0:08:24.960 gets a little complicated because we can mean different things 0:08:25.040 --> 0:08:27.160 by sound waves. We could be talking about the actual 0:08:27.320 --> 0:08:32.000 physical wave of air fluctuations that propagates outwards from the 0:08:32.080 --> 0:08:34.440 origin of sound, or we could be talking about a 0:08:34.559 --> 0:08:40.319 visualization of the qualities of a sound. And this gets 0:08:40.320 --> 0:08:42.920 into a territory where it's tricky to explain this without 0:08:43.040 --> 0:08:45.320 visual aids, but we're gonna try. So we're gonna talk 0:08:45.360 --> 0:08:48.520 about the visualization without visual aids. So I want you 0:08:48.559 --> 0:08:51.480 to imagine that you have a piece of paper, and 0:08:51.760 --> 0:08:54.040 across the middle of this piece of paper, you draw 0:08:54.080 --> 0:08:57.480 a straight horizontal line from left to right goes all 0:08:57.480 --> 0:09:00.520 the way across the paper. And this law line in 0:09:00.559 --> 0:09:03.959 this particular representation is going to represent time. This is 0:09:04.000 --> 0:09:07.520 the X axis. So the left side of your paper, 0:09:08.080 --> 0:09:11.520 where you're starting point is, represents zero seconds. The far 0:09:11.720 --> 0:09:15.480 right sign represents some arbitrary point of time. We'll get 0:09:15.520 --> 0:09:17.600 to that in a second, because it all depends on 0:09:17.679 --> 0:09:21.000 the specific kind of wave you're drawing. So now let's 0:09:21.000 --> 0:09:26.000 just imagine drawing a nice sign wave, and we start 0:09:26.040 --> 0:09:30.079 on the leftmost side at the center point, so zero 0:09:30.160 --> 0:09:33.560 at the center horizontal line, and draw a nice gentle 0:09:33.760 --> 0:09:37.560 crest up and then we come back down cross that 0:09:37.720 --> 0:09:42.559 center line and then draw an equally gentle trough that 0:09:42.720 --> 0:09:46.280 is of equivalent size to the crest on the opposite side. 0:09:46.760 --> 0:09:50.360 And then once the line comes back up and crosses 0:09:50.360 --> 0:09:54.440 the horizontal line again, we've got one wavelength of a 0:09:54.480 --> 0:09:57.560 sound wave that this would be in what we would 0:09:57.600 --> 0:10:00.880 call the time domain. The reason we call it the 0:10:00.920 --> 0:10:04.160 time domain is that we are visualizing a sound wave 0:10:04.600 --> 0:10:08.880 with regard to the passing of time. That X axis 0:10:08.920 --> 0:10:12.600 again is showing the time is passing. So the wavelength 0:10:12.640 --> 0:10:16.480 describes the distance or the amount of time that passes 0:10:16.520 --> 0:10:21.360 between two corresponding points on a sign wave. So let's 0:10:21.360 --> 0:10:23.280 say we draw a series of these like we get 0:10:23.320 --> 0:10:28.240 twenty sheets of paper, and we draw equal sign waves 0:10:28.280 --> 0:10:30.120 on each of those twenty sheets of paper, and we 0:10:30.160 --> 0:10:31.800 put them all side by side, so we get a 0:10:31.880 --> 0:10:36.199 nice continuous wave all the way down these twenty sheets wide. 0:10:36.960 --> 0:10:41.960 And we say that each sheet represents one twentieth of 0:10:42.000 --> 0:10:44.319 a second, so that when we have twenty of them 0:10:44.360 --> 0:10:47.880 side by side, that represents one seconds worth of time. 0:10:48.320 --> 0:10:51.840 You would say I have twenty wave lengths that span 0:10:52.000 --> 0:10:57.400 one second. That means that this represents twenty hurts. This 0:10:57.480 --> 0:11:00.240 is a sound wave with a frequency of twenty Hurts 0:11:00.280 --> 0:11:04.520 because it takes twenty of these will pass a given 0:11:04.600 --> 0:11:08.840 point in space within the span of one second. So 0:11:08.880 --> 0:11:12.360 then we need to talk about the period of a wave, 0:11:12.679 --> 0:11:16.200 and this is the inverse of Frequency is the amount 0:11:16.200 --> 0:11:20.000 of time it takes for one wavelength to complete one cycle. 0:11:20.720 --> 0:11:23.920 So frequency is the number of cycles per second. The 0:11:24.000 --> 0:11:27.280 period of a wave is the number of seconds per cycle. 0:11:27.600 --> 0:11:32.000 So for a twenty Hurts frequency, the period of the 0:11:32.040 --> 0:11:35.800 wave would be one seconds per cycle. That's why we 0:11:35.800 --> 0:11:39.400 would need twenty sheets of paper with just one nice 0:11:39.480 --> 0:11:44.400 curvy wave on each piece to represent a twenty Hurts wave. 0:11:44.520 --> 0:11:46.640 Now you could just do this on one sheet of paper, 0:11:46.880 --> 0:11:49.360 you know, you just change the scale. So you change 0:11:49.360 --> 0:11:53.720 the scale so that every single wavelength represents of a second. 0:11:54.280 --> 0:11:56.640 You draw twenty of those on one sheet of paper. 0:11:56.800 --> 0:11:59.559 Will be much smaller than our original example, but that 0:11:59.559 --> 0:12:01.640 would still will be a twenty Hurts wave. It's all 0:12:01.760 --> 0:12:06.480 dependent on the scale of your representation. Wavelength and frequency 0:12:06.520 --> 0:12:10.320 are related, and we see that in an equation where 0:12:10.360 --> 0:12:16.680 we say velocity equals wavelength times frequency. So velocity describes 0:12:16.720 --> 0:12:19.560 the speed and direction. But we can ignore that for 0:12:19.640 --> 0:12:23.040 now of a wave as it passes a stationary point. 0:12:23.400 --> 0:12:26.240 So if we know two of those three factors, we 0:12:26.280 --> 0:12:28.480 can figure out the third. But just a little math, right, 0:12:28.640 --> 0:12:31.280 If we know the velocity and we know the wavelength, well, 0:12:31.520 --> 0:12:33.760 we can divide the velocity by the wavelength and then 0:12:33.760 --> 0:12:36.360 we have the frequency. Or if we know the frequency 0:12:36.400 --> 0:12:39.040 but not the wavelength, we can divide the velocity by 0:12:39.080 --> 0:12:41.640 the frequency. We get the wavelength. If we know the 0:12:41.679 --> 0:12:43.800 frequency and the wavelength, we multiply them together, we get 0:12:43.800 --> 0:12:50.679 the velocity. Pretty easy stuff. Now, speed of sound is 0:12:51.200 --> 0:12:53.200 not that difficult for us to to get our minds 0:12:53.240 --> 0:12:55.800 wrapped around, because we know what the speed of sound 0:12:55.960 --> 0:13:00.120 is generally speaking, so the speed of sound depends partly 0:13:00.320 --> 0:13:03.600 upon the medium through which the sound is traveling. Sound 0:13:03.679 --> 0:13:06.400 moves at different speeds through water than it does through 0:13:06.400 --> 0:13:09.240 the air, for example. But even in the air, stuff 0:13:09.400 --> 0:13:12.160 can affect the speed of sound, like the air's humidity 0:13:12.240 --> 0:13:15.880 and its temperature. Essentially, we're talking about density. The density 0:13:15.920 --> 0:13:18.559 of those air molecules will affect how quickly sound can 0:13:18.559 --> 0:13:21.560 travel through it. So when we talk about the speed 0:13:21.559 --> 0:13:24.640 of sound, we have to get more specific. So we 0:13:24.760 --> 0:13:27.880 tend to describe the speed of sound as being three 0:13:27.960 --> 0:13:31.520 hundred forty three meters per second in dry air at 0:13:31.559 --> 0:13:35.120 twenty degrees celsius. Now, for my fellow Americans out there 0:13:35.120 --> 0:13:37.480 who ain't got time to truck with no sensible metrics 0:13:37.480 --> 0:13:40.840 system or celsius or anything, this would mean sound travels 0:13:40.840 --> 0:13:44.160 at about one thousand, one twenty five ft per second 0:13:44.320 --> 0:13:48.240 when the air is sixty eight degrees fahrenheit. Sound at 0:13:48.280 --> 0:13:52.720 all frequencies will travel at the same speed through any 0:13:52.840 --> 0:13:56.319 given medium. So that means that a low pitch sound 0:13:56.600 --> 0:13:59.400 and a high pitch sound will both cover the same 0:13:59.440 --> 0:14:02.280 amount of space in the same amount of time through 0:14:02.360 --> 0:14:06.600 the same medium. But low sounds have low frequencies and 0:14:06.640 --> 0:14:10.839 thus longer wavelengths than high sounds, which are higher frequencies 0:14:11.000 --> 0:14:13.840 with shorter wavelengths. It will take the same amount of 0:14:13.840 --> 0:14:16.160 time for a high pitch note on a trumpet to 0:14:16.280 --> 0:14:18.880 get to you as a low blast note on a 0:14:18.920 --> 0:14:22.360 tuba that's played at the same distance, but the high 0:14:22.400 --> 0:14:24.640 pitched note will have a higher frequency and a shorter 0:14:24.720 --> 0:14:27.760 wavelength than the tubus note. Now I've used this analogy 0:14:27.800 --> 0:14:30.520 several times before, but imagine that you've got a two 0:14:30.680 --> 0:14:34.160 lane highway and you've got a line of buses that 0:14:34.200 --> 0:14:36.680 are in the right lane, and the buses are one 0:14:36.760 --> 0:14:39.600 right after the other. And in the left lane you've 0:14:39.600 --> 0:14:43.280 got a line of compact cars. And for every bus, 0:14:43.440 --> 0:14:46.640 you can fit three cars in that same length of space. 0:14:47.400 --> 0:14:49.640 And the front of the first car is in line 0:14:49.640 --> 0:14:52.320 with the front of the first bus. The rear bumper 0:14:52.320 --> 0:14:54.480 of the last car lines up with the rear bumper 0:14:54.520 --> 0:14:57.840 of the last bus. Both lanes of traffic are traveling 0:14:57.920 --> 0:15:01.920 at the exact same speed. Down highway, both lanes of 0:15:01.960 --> 0:15:06.040 traffic will cross a finish line at the exact same time. However, 0:15:06.520 --> 0:15:09.200 you have more cars in lane two than you have 0:15:09.320 --> 0:15:12.560 buses in lane one. Everyone's going at the same speed. 0:15:12.840 --> 0:15:14.640 That's kind of the way we have to think about 0:15:14.760 --> 0:15:18.600 sound waves and frequencies. If a sound is low enough, 0:15:18.880 --> 0:15:20.760 we may not hear it at all, But if it 0:15:20.840 --> 0:15:22.880 is a strong enough signal, meaning it has a great 0:15:22.880 --> 0:15:26.480 deal of amplitude, we could physically feel it. You remember, 0:15:26.520 --> 0:15:31.000 it's air fluctuations, it's actual air pressure. So typically we 0:15:31.040 --> 0:15:34.320 would perceive amplitude as volume, and in our sketch of 0:15:34.320 --> 0:15:36.320 a wave, it would mean that the peaks and low 0:15:36.360 --> 0:15:39.440 points would be really far out from that center line, 0:15:39.520 --> 0:15:42.080 you know, the taller those peaks are, the greater the 0:15:42.160 --> 0:15:45.600 amplitude or greater the volume. If you've ever been near 0:15:45.680 --> 0:15:49.240 a massive sub whiffer and you felt pressure, like in 0:15:49.280 --> 0:15:53.120 your chest, but you couldn't really hear anything, chances are 0:15:53.120 --> 0:15:56.280 it means the sub whoffer was blasting out vibrations below 0:15:56.320 --> 0:15:59.840 your threshold of hearing. Typically, when we talk about music, 0:16:00.160 --> 0:16:03.480 we talk a lot more about frequencies than we do 0:16:03.560 --> 0:16:07.720 about wavelength and that's because of this relationship between frequency 0:16:07.800 --> 0:16:11.160 and pitch. But wavelengths are also important as they will 0:16:11.200 --> 0:16:14.480 become a key component of stuff like resonance and harmonics 0:16:14.520 --> 0:16:18.400 and boyality. Let me tell you, preparing this section of 0:16:18.440 --> 0:16:20.680 the podcast was a heck of a thing all by itself, 0:16:20.760 --> 0:16:23.960 because this is stuff that's way easier to explain with 0:16:24.040 --> 0:16:26.320 visual aids. But stick with me because I know you 0:16:26.320 --> 0:16:28.600 guys are smart enough to suss it all out, so 0:16:28.640 --> 0:16:30.840 it really just falls on me to describe it clearly. 0:16:31.360 --> 0:16:34.320 So another thing we need to understand before we jump 0:16:34.360 --> 0:16:36.120 into that, and we'll take a break before we get 0:16:36.160 --> 0:16:38.200 to resonance and harmonics. But one other thing I want 0:16:38.240 --> 0:16:41.840 to explain is the phase of a wave. A wave's 0:16:42.000 --> 0:16:46.239 phase refers to how it is offset from some specific 0:16:46.280 --> 0:16:49.440 starting position. And it really becomes important when you're talking 0:16:49.440 --> 0:16:53.480 about multiple waves. Because multiple waves can be offset from 0:16:53.520 --> 0:16:56.080 one another. They can be out of phase with each other, 0:16:56.400 --> 0:16:59.920 and that affects the sounds that we perceive. So, going 0:17:00.000 --> 0:17:03.160 back to our original sketch of a single wave, imagine 0:17:03.160 --> 0:17:06.359 that you draw a new wave using that same series 0:17:06.400 --> 0:17:09.080 of pieces of paper, but you use a different color 0:17:09.359 --> 0:17:11.840 for this new wave, and you offset it a bit. 0:17:12.000 --> 0:17:13.960 So instead of starting at the far left of the 0:17:14.000 --> 0:17:17.479 first sheet, let's say you start one inch in so 0:17:17.520 --> 0:17:20.159 it's offset from that first wave. Otherwise it follows the 0:17:20.160 --> 0:17:23.600 exact same trajectory. Well, these two waves would be out 0:17:23.640 --> 0:17:27.080 of phase with respect of each other. Why is this 0:17:27.160 --> 0:17:30.640 all important? I'll explain in a second, but first let's 0:17:30.640 --> 0:17:41.000 take a quick break. Okay, So before the break, I 0:17:41.080 --> 0:17:44.240 talked about the phase of a sound wave. Imagine you've 0:17:44.240 --> 0:17:47.520 got two of the same frequency of sound, but they're 0:17:47.520 --> 0:17:50.000 out of phase with each other. That would affect how 0:17:50.040 --> 0:17:53.560 we perceived the sound. It could get pretty noisy. Actually. 0:17:53.960 --> 0:17:57.640 If the two frequencies, however, are perfectly opposite each other, 0:17:58.000 --> 0:18:01.479 so that the crests in sound wave a match up 0:18:01.520 --> 0:18:05.360 perfectly with the troughs of sound wave B, and they're 0:18:05.400 --> 0:18:09.040 of the exact same frequency and amplitude, we wouldn't hear 0:18:09.119 --> 0:18:12.160 the sound at all because those two sound waves would 0:18:12.160 --> 0:18:14.560 cancel each other out. You can think of it in 0:18:14.600 --> 0:18:18.000 this way. Think of air molecule number one is pushing 0:18:18.000 --> 0:18:20.920 to the right on air molecule number two, but air 0:18:21.000 --> 0:18:24.600 molecule two is pushing just as hard on the left 0:18:24.680 --> 0:18:27.960 to air molecule number one, which means neither air molecule 0:18:27.960 --> 0:18:31.880 will actually move. This is how noise canceling headphones work. 0:18:31.920 --> 0:18:35.200 By the way, the headphones incorporate a microphone. It picks 0:18:35.280 --> 0:18:38.800 up the ambient sounds in your environment, and then speakers 0:18:38.840 --> 0:18:42.160 in the headphones generate the equal but opposite sound waves 0:18:42.200 --> 0:18:44.360 to cancel out the ones that you would otherwise hear 0:18:44.880 --> 0:18:48.040 as long as the latency that being the lag between 0:18:48.119 --> 0:18:51.719 detecting a sound and generating the opposite sound, As long 0:18:51.760 --> 0:18:53.800 as that latency is low enough, we humans are too 0:18:53.880 --> 0:18:55.880 slow to pick up on the difference, and our perception 0:18:55.960 --> 0:18:58.399 is really limited in that way. But the out of 0:18:58.440 --> 0:19:00.680 face stuff also matters a lot when we talk about 0:19:00.680 --> 0:19:05.160 things like resonance and harmonics as well. So I guess 0:19:05.240 --> 0:19:07.720 there's no time like the present to finally get into 0:19:07.760 --> 0:19:11.000 all that stuff. It is incredibly important with musical instruments, 0:19:11.040 --> 0:19:14.000 So the descriptions I've used so far really refer to 0:19:14.160 --> 0:19:17.240 pure pitches, which is something we can generate with electronics, 0:19:17.320 --> 0:19:20.040 but it's not typically what we get with musical instruments 0:19:20.040 --> 0:19:24.000 outside of things like tuning forks. A pure pitch describes 0:19:24.119 --> 0:19:28.119 a single frequency with no harmonics or overtones, so we 0:19:28.200 --> 0:19:31.320 don't get any other frequencies other than the base one, 0:19:31.400 --> 0:19:35.040 the fundamental frequency. We're getting a pure tone, which we 0:19:35.080 --> 0:19:38.439 could plot as a smooth, consistent sign wave with equal 0:19:38.480 --> 0:19:41.359 crests and troughs, nice and neat, kind of like the 0:19:41.400 --> 0:19:43.680 example I was describing at the top of this episode. 0:19:44.000 --> 0:19:47.159 But in the real world, the sounds we hear typically 0:19:47.200 --> 0:19:51.080 consist of more than one frequency. There are multiple frequencies 0:19:51.119 --> 0:19:54.360 going on here. We can still plot the sound waves, 0:19:54.560 --> 0:19:57.359 but they wouldn't look like those nice, smooth curves we 0:19:57.359 --> 0:20:01.200 were talking about earlier. They would be funk looking potentially, 0:20:01.200 --> 0:20:04.680 with little dips and bumps and the crests and troughs. 0:20:04.720 --> 0:20:08.280 And that's because we'd be representing a collection of frequencies 0:20:08.560 --> 0:20:12.000 in a single way. Visualization sort of the visual equivalent 0:20:12.040 --> 0:20:15.040 of how we would perceive the sound through hearing. So 0:20:15.160 --> 0:20:18.080 let's go through with an example. Let's say you're strumming 0:20:18.080 --> 0:20:21.080 a guitar string, and that string will vibrate and not 0:20:21.200 --> 0:20:24.840 just one frequency, but a few different frequencies all at 0:20:24.840 --> 0:20:28.960 the same time. All of these frequencies are resonant frequencies, 0:20:29.160 --> 0:20:32.520 meaning these are the collection of vibration speeds at which 0:20:32.600 --> 0:20:37.919 that string naturally experiences when it is strummed. However, human 0:20:37.920 --> 0:20:40.600 hearing is such that we typically only hear the pitch 0:20:40.760 --> 0:20:44.399 of the lowest resonant frequency in that bunch. This is 0:20:44.400 --> 0:20:47.760 the fundamental frequency. You can think of it as the baseline. 0:20:48.280 --> 0:20:52.960 In musical instruments. The additional resonant frequencies those higher than 0:20:53.000 --> 0:20:57.760 the fundamental frequency, higher in frequency, so more hurts. In 0:20:57.800 --> 0:21:02.479 other words, are typically, but not exclusively, harmonics of the 0:21:02.520 --> 0:21:07.159 fundamental and a harmonic is a whole number multiple of 0:21:07.200 --> 0:21:10.760 the fundamental frequency. So let's focus on that guitar string. 0:21:10.760 --> 0:21:13.120 It's a lot easier if we talk about a specific example. 0:21:14.000 --> 0:21:17.879 So we're gonna say that we're gonna play the A string. 0:21:18.240 --> 0:21:20.720 Why the A string, Well, because it has a fundamental 0:21:20.720 --> 0:21:24.320 frequency of one ten hurts. It makes it very easy 0:21:24.359 --> 0:21:27.760 for us to do multiples. So the fundamental frequency sees 0:21:27.800 --> 0:21:30.760 the string vibrate one hundred ten times per second. That 0:21:30.760 --> 0:21:33.760 means a full sequence of going up and down and 0:21:33.800 --> 0:21:37.760 returning to starting point on times per second. The string 0:21:37.840 --> 0:21:40.320 is anchored at either end of the guitar. If we 0:21:40.359 --> 0:21:42.320 could slow down time, we would see that length of 0:21:42.359 --> 0:21:45.679 string making that up down journey one ten times every second. 0:21:45.840 --> 0:21:49.919 But the string is also vibrating at other frequencies that 0:21:50.000 --> 0:21:53.440 are higher than the fundamental In general, we call these 0:21:53.480 --> 0:21:59.080 overtones together. The overtones with the fundamental frequency are called partials. 0:21:59.520 --> 0:22:02.040 Now I'm going to focus on harmonics first because they 0:22:02.080 --> 0:22:05.040 are the easiest to grasp. So we've got our a 0:22:05.119 --> 0:22:08.560 string with a hundred ten hurts frequency. That's our fundamental 0:22:08.600 --> 0:22:12.400 tone or first harmonic. The next harmonic would be twice 0:22:12.520 --> 0:22:15.960 the frequency as two is the next whole number. It's 0:22:15.960 --> 0:22:19.200 the next integer in the sequence. We start with one, 0:22:19.440 --> 0:22:22.280 but any number of times one is itself. We go 0:22:22.320 --> 0:22:25.600 to the next integer, that's two. So now we multiply 0:22:26.080 --> 0:22:31.600 our frequency hurts by two, we get two hurts. That's 0:22:31.600 --> 0:22:33.879 still an A. It's still the note A, but it's 0:22:33.880 --> 0:22:37.399 an octave higher than the original a note that we played. 0:22:37.920 --> 0:22:41.000 So hypothetically, this also means if you've got a string 0:22:41.400 --> 0:22:45.480 that's tuned to one hurts and you shortened the length 0:22:45.520 --> 0:22:48.200 of that string by half, so you made it half 0:22:48.240 --> 0:22:51.560 as long, you would produce the two D twenty Hurts 0:22:51.600 --> 0:22:54.760 tone when you strummed the half as long string. You 0:22:54.880 --> 0:22:58.240 shortened the wavelength by shortening the string. Thus you increase 0:22:58.280 --> 0:23:03.440 the frequency because remember we remember velocity is wavelength times frequency. 0:23:03.520 --> 0:23:07.000 Velocity is constant, so if we have the wavelength, we 0:23:07.040 --> 0:23:10.000 have to double the frequency. At least that's what would 0:23:10.000 --> 0:23:12.840 happen in an ideal realization of this principle, But in 0:23:12.920 --> 0:23:16.800 reality it gets more complicated because the oscillating wave in 0:23:16.840 --> 0:23:20.680 a guitar string doesn't propagate all the way from one 0:23:20.720 --> 0:23:22.679