The Science of Everything Podcast - Episode 24: Vibrations and Waves

Episode Date: November 29, 2011

An overview of the basic principles of wave phenomena, including a definition of waves, a discussion of wave mediums, wavelength, frequency and amplitude. I also discuss a variety of interesting wave behaviours including interference, polarization, resonance, reflection, absorption, refraction, diffraction and standing waves. This episode will form the foundation for later discussion of sound and light.

You're listening to The Science of Everything Podcast, episode 24. Vibrations and Waves. I'm your host, James Fodor. In this episode, we're going to look at, well, vibrations and waves. Specifically, I'll give an overview of the basic properties of wave phenomena, including a definition of waves, a discussion of the mediums through which waves travel, and a look at wavelength, frequency, and amplitude.

I'll also discuss some of the more interesting behaviors that waves can be involved in, including interference, polarization, resonance, reflection, absorption, refraction, defraction and also standing waves. This episode will sort of be the basis for future episodes that I plan to do on sound and light, which requires some basic understanding of wave phenomena. So if some of this is a bit theoretical, bear with me because you'll need this background for later episodes. Plus, it can also be quite helpful to understand these wave terms more generally because they come up quite often in sort of more scientific or even pseudoscientific discourse.

All right, so let's jump in. What is a wave? In physics, a wave refers to a disturbance, that travels through time and space, or through space time, which is accompanied by a transfer of energy. Wave is not the same thing as a vibration. Vibrations basically a single disturbance in some medium, which is propagated through it.

A wave is more like an ongoing or continuous disturbance, or at least it's a broader phenomenon. So, for example, if you were to shake a string once up and down, say you had a string connected onto some hook embedded in a wall, and you would shake that once, that would be a vibration. But if you were to keep shaking it, or the vibrations, multiple vibrations, traveled up and down the string, that would be a wave. So it's a little bit sort of arbitrary,

the exact distinction between a vibration and wave. And when you look at the actual physical world, pretty much everything's a more or less a wave because you don't generally get single vibrations so much. Like, for example, if you throw a rock into a pond, you get waves. You can't just get sort of one vibration ripple going out. It's going to be a wave. But anyway, that's the basic idea. A wave is sort of a broad, a larger thing than just a single vibration. Or, in other words, a wave is made up of numerous repeated vibrations. Now, I've said that wave is a disturbance, so what do I mean by that? Well, exactly what a disturbance is depends on the medium in which a wave is travelling. Now the medium, or the transmission medium, is the material

substance through which waves are propagated. Mediums can include air, or water, or wood, really any material substance that can, through which vibrations that form the wave can propagate. The way a wave works is that one, we'll call it a molecule, but it could be an atom or even even large than that, but for the moment we'll call it a molecule. One molecule sort of vibrates, maybe up and down, backwards and forwards, whatever, and then it, that molecule, that vibration in turn causes a vibration in another molecule, perhaps to the left or to the right of the first molecule, which then causes the second molecule to vibrate in a similar way, which then causes a third molecule to vibrate and so on. So in that sense, the energy, the vibration energy, or the energy

of motion is passed along from one molecule and one atom or one whatever to the next one, and thereby the energy travels through the medium. But the key thing about a wave is that no matter is actually transferred in the process of transferring, of moving the wave. So for example, if you have a water wave, go back to our example, throwing a rock in a pond. When you see those ripples move outwards from the centre where the rock fell in, water is not actually moving. Water molecules or massive water are not actually moving from the place where the rock fell outwards towards the edge of the pond, unless you're doing something else.

But just the wave itself will not move water from the center outwards. All that's happening is energy is moving from the center outwards in the form of those waves, which in turn essentially formed of vibrations of water molecules vibrating up and down, or in this case it's up and down essentially, and then passing that energy on to the next water molecule, to the next water molecule, to the next water molecule, and so on. And so the energy is transferred, but no matter is actually transferred. And as I said, the medium is the material substance that transmits the vibrations across space.

Often when describing waves, you'll talk about them as either on a string or in water, because they're familiar examples that we can relate to, but waves is more of an abstract idea. When I talk about a medium, this applies, for example, even to light waves or to other type of electromagnetic radiation waves. So sometimes the medium or exactly what we mean by vibration or exactly what is doing the vibrating is not so obvious, but we still apply the basic framework to it. So for example, Mexican wave where, you know, one person stands up in a crowd and waves, and then the person next to them stands up and so on and that moves through the stadium.

That is a wave, and the energy that we're talking about is essentially the energy of motion of the people moving up and down. but no people actually move across the stadium. It's only the wave or the energy in some sense that moves. And in that case, the medium would be the people or the spectators in the stadium, and the vibrations really consist of the individual things that are vibrating, are really just people standing up and down. So that's a more abstract example of what a wave is. Other examples of waves include, as I've already said, water waves on the ocean, sound waves in the air, radio waves, microwaves used in microovins, light waves emitted by the sun or lights. Waves are very, very common in nature. I've already mentioned,

electromagneticism, of which light is an important subset and sound, two very important waves, and very common in nature. So that's why it's very important to get this sort of basic understanding of them and how we can describe them and so on, how we can understand their behavior. Okay, before we leave the basics, I just want to talk about the two different types of waves. Remember, there's different media in which wave can travel. We've covered, that's the water waves, the sound waves, and so on. But all of those can be classified into two broad categories of waves, the transverse waves and the longitudinal waves. A transverse wave is basically where the direction of travel of the wave itself, or the direction in which the energy

is moving, is perpendicular to the direction of vibration of the individual molecules. And lightwave would be an example of this, or light waves would be an example of this. Also, water waves would be another one. Basically, the light waves, or probably water, waves is an easy one to visualize. At least ocean waves on the surface of the water, the water molecules go up and down, but the wave itself is traveling along the surface of the water. So the direction of motion are perpendicular to each other. That's also a wave on a string would be an example of that. Remember that string connected to the wall by a hook. The string, the part of the string that are waving go up and down,

but the wave itself travels back and forth along the string. So that's another example of transverse wave. Longitudinal wave is where the direction of vibration of the individual components and the direction of the energy both are in the same direction, or at least in the same plane. So sound waves as an example of that. The air molecules move backwards and forward in the same direction. That sound is traveling towards us or away from us.

they don't sort of go up and down and the sound travels forwards and backwards. It's in the same direction, or the same axes in a sense. So these two different types of waves, transversal and longitudinal, can have some and different behaviours in some circumstances. So that's the basics of what are waves and wave media and how they travel. Now let's talk about how waves can be described in a bit more detail. As I said, waves are a broad phenomena, and they can differ depending on whether they're transversal longest,

and also depending on what medium they travel through. But even giving those things constant, so let's say let's just pick transverse waves. in water or just long-dustra waves in air. Holding those two things constant, there are still many different ways in which waves can vary. Probably the foremost important properties I'm going to talk about are amplitude, period, wavelength, and frequency. And these are quite close related to each other, particularly the last three. But just before I get on to those, I'll talk about the concept of sinusoidal waves. Hopefully, those of you

listening have at least some background in mathematics, even just like early high school, would be sufficient. If you remember those sine or cos waves, some of you may be quite proficient in mathematics, I don't really know. But anyway, you remember sign or cosways, or cos graph, sign or cause function, trigonometry. They're basically that graph that kind of goes up and down and repeats on forever. It's a smooth curve that continues to go up down onwards. And basically, sine and cosign or sign and cos, they have the, they have the same shape that one's just shifted horizontally relative to the other. But hopefully you can picture what I'm talking about. If not look up cos graph on Google images or whatever and just see that shape,

That shape is what we use in physics, well in actually most of science really, to describe the behavior of waves, because it turns out that even though theoretically waves can have any shape, they're just vibration, so you could have a saw-tooth wave, for example, where effectively you just go diagonally up and then a sharp break diagonally down, diagonal up, dangle up, dagily down, just like the tooth of a sore, a straight tooth of a sore, theoretically that could be a wave shape, and ways like that can occur. But most of the waves that we actually find in nature, and that we want to describe a sinusoidal in shape. So they essentially look like that sign and cause graph that we talked about, or at least could be described in those terms.

If not a single sign or cos graph, then we can actually include multiple sine of cos waves and sort of superimpose them on one another and create more complicated waves. And I'll talk about that in more detail. But I just want you to understand the basic point that the amplitude period and stuff that I'm going to talk about now apply most specifically to sinusoidal waves, sign and cos wave, basically. But that in turn can be used to describe pretty much all the waves that actually exist.

So from now on, sort of when you think of wave, think specifically of that sinus sort of shape. And just remember that that sinus sort of shape, first of all, is very common in it itself. And second of all, can be combined or sort of altered in a way that it can be applied more generally even to cases where it doesn't apply. So it's a very useful basic models to understand.

Okay, so taking that basic sign-cos graph shape, the sinus sort of wave, I'll now talk about its four key properties, amplitude, period, wavelength, and frequency. Amplitude just refers to the distance between the mean value of whatever is oscillating. So in this case, the mean value of the graph, in the default case it's zero, the distance between there and the maximum or minimum positions that the wave gets to, or in this case the graph gets to. So basically, you know, the sign curve just goes up and then turns and comes down and then up and then down, and it continually moves up and down with a mean of zero. The distance between zero and either the top, the maximum, or the minimum value that the graph gets to, that is the amplitude. Now be careful here. It's the distance between the middle or the median and the top or the bottom. Those will be the same because it's symmetrical. Not the distance from the top to the bottom,

The full distance from the top to the bottom is twice the amplitude. And generally speaking, the amplitude kind of represents the power or the energy that's in the wave, although that doesn't work perfectly because it depends on exactly whether we're talking about a sound wave or whatever. But that's kind of the basic idea. So the higher the amplitude, the more sort of power there's in the wave in some generic sense. Don't take that power word too literally, just as a broad idea. Next period. The period is the time interval between each oscillating variable,

or each particle or whatever we were going to call them, return to any particular state following a full wave cycle. So imagine a water molecule on the surface of the ocean or a pond wherever. The vibration comes along, so it starts going up, and then it reaches its maximum, that's the top of the amplitude, and then it starts going down again. It returns to the median point where it started, but now it's going down, so it continues below the medium point,

reaches the minimum point, and then comes back up again. And now it's where it was originally traveling in the same direction. Let's traveling up, say it started traveling up, just for the sake of a... argument. So basically it went up and came down, then went down and came up again. That's a full, a full cycle of the wave. The time that it took for that oscillating variable, in this case the particle, or it could be an air molecule or whatever, the time it took for that to happen is the period. The short of the period, the quicker each molecule or each variable, whatever's

moving, returns to its initial position. So to take our maximum wave example in the stadium, the period could represent the time period between one person standing up, sitting down and standing up again. Obviously, the short of the period, essentially the more rapidly the wave is travelling, although there are other variables as well. Next is the wavelength. The wavelength refers to the distance over which the wave repeats, or the distance travelled by the wave in a single period. So, remember, I said that period, wavelength, and frequency are kind of closely related to each other, and speed as well. So a period is, remember, the time, the time interval between a particle being in the given position and then the particle being in the same position

going in the same direction the next time after one wave cycle. That's a particle. That's a particle being in the That's the period. The wavelength is the sort of the horizontal distance or the distance travelled by the wave during that time. So, for example, return to our water molecule analogy, the water molecule goes up, comes down and then returns to its initial position, goes up a bit again. That takes a certain amount of time. During that amount of time, the wave has traveled a certain horizontal distance in this case. That distance is one wavelength. It's really much easier to see this if you just look at a graph, just type in like a sign graph or something like that or sign wavelength period, something like that.

You'll find a labelled graph that has all these things on it, and it makes it much easier to see than me trying to explain it. Next, frequency. Frequency is the inverse of the wavelength. So that is we, basically, we take one and divide it by the wavelength, and that gives us the frequency, which is, frequency is one of wavelength and vice versa. So frequency and wavelength are directly, they're proportional to each other, directly proportional to each other.

So the high the wavelength, the lower the frequency and vice versa. So translate it into sort of words, if the wavelength is the distance traveled by the wave in one period, the frequency is the number of oscillations per unit of time. The inverse of that, or the flip side you might say, is that the frequency is the number of oscillations per unit of time that occur, or the number of wave cycles that occur per unit of time. So they're directly related to each other wavelength of frequency.

And finally, the speed. Speed is just defined as distance over time, as hopefully you should know. So generically, speed is distance over time. That's just the definition, or the distance traveled over the time taken to travel that distance. That's just the definition of speed. or velocity. In the case of wave though, the distance traveled in one time period is the wavelength, and that time period is going to be the period. So basically, velocity is going to equal distance over time, which in the case of a wave is wavelength over period. So imagine V equals lambda

over T, lambda being the normal symbol for wavelength, or if it makes it easy for you, V equals w over T, T representing time, which is sort of the period. However, given that frequency is the inverse of period, that is frequency is one over period, 1 over t, we can rewrite that equation, V equals lambda over T, as v equals lambda times F, because F is just 1 over T. The frequency is 1 over the period, just as we define it before. So that's just another way of saying that the velocity of a wave is equal to the wavelength times the frequency, or basically the distance traveled by the wave in a given period multiplied by the number of periods per unit of time.

If you want to work out the velocity of the wave, you work out how far the wave travels in each wave cycle, over each period, and then you work out how many periods there are in a unit of time, say in a second or minute, whatever. So distance for each cycle, number of cycles per unit of time, that gives you the speed of the velocity of the wave. That may be a little bit confusing, you may want to sort of look at those equations. That's a pretty simple equation, but look at it written down. But the speed of a wave, by the way, depends upon the medium through which it is traveling and how rapidly or how easily the objects in the medium can vibrate in relation to each other and so on. But anyway, so just to recap, because these concepts are very important.

distance from the medium wave value to the maximum or minimum points. The distance between the maximum and the minimum is twice the amplitude. Period is the time interval between a single particle returning, going through one full wave cycle and returning to its initial state. Wave length is the distance traveled by the wave during a single period. Frequency is the number of oscillations at the wave, or number of wave cycles per unit of time, and the speed of the wave is equal to the wavelength divided by the period,

or, which is the same thing, the wavelength times the frequency. Okay, so hopefully that wasn't too confusing. But those four or five fundamental concepts are very important to understanding what comes later. Okay, I just want to have a brief word on pendulums now. Often, if you read a textbook or other treatments of waves, they'll sort of belabor pendulums, because they're kind of interesting, but I don't want to focus on them too much here. Basically, a pendulum is just a weight suspended from a pivot so that it can swing freely. So, for example, if you can imagine a grandfather clock, you know, they have those, well,

pendulums hanging down from them that rock from side to side, that's a pendulum. or basically if you just have a yo-yo and fix the length of the string so that it doesn't keep on rolling and sort of rock a swing it backwards and forwards, that's a pendulum. Pendulums are an example of wave motion, especially if you represent, for example, the distance of the weight from either its horizontal position or its vertical position either way. It doesn't really matter. You can graph that and you'll get essentially a sinus sort of function. The interesting thing about pendulums is that the size of the swing of the pendulum doesn't actually matter. So in this case, when I say the size of the swing, that's referring to the amplitude.

So imagine that we're graphing the pendulum. Imagine we've got this sign graph. And on the vertical axis, on the y-axis, we've got the, we're plotting the distance, let's say the horizontal distance of the pendulum. So the distant, the horizontal distance to the left or to the right of the straight-down vertical line in the middle of the clock, let's say. So that's on the y-axis. When it's up, it's to the right, and when it's negative. So when it's positive, that means the pendulum's to the right to our right of the middle point when the y value was negative that means the pendulum is to the left the further it is to the left the further down it is on the on the y axis the further the pendulum is to the right the higher it is the larger the value on the x on the y axis of this imaginary graph and um x axis will just represent

time so in this case the further you pull the pendulum to one side or the other to set it off the higher the value of the y axis will be so the higher the value will be on the y axis that you start with and then it goes down and we'll go down to a larger Y value, a larger negative Y value, and then so on. So basically, the Y values will be larger, and that translates to a higher period, excuse me, a higher amplitude, because remember, the amplitude is the difference between the maximum and the middle point of the graph, or between the middle point and the minimum point of the graph. So the longer short of it is the amplitude of a pendulum does not affect its period or swing time. And that is why pendulums, for example, as using grandfather clocks, are so useful for timekeeping,

because it doesn't matter. So say you start the pendulum swinging and then let it go, obviously it's going to, the swings are going to get smaller, smaller over time, essentially because there's a bit of friction occurring there within the wood or in the internal mechanism of the clock and so on, and with the air molecules too. So there's a bit of friction there, that's diminishing the energy, pulling the energy, and so gradually it'll stop swinging. However, gradually the pendulum will stop swinging.

However, in the interim, as it continues swinging, so the swing gets short and ashore, smaller and smaller, and although the amplitude gets smaller and smaller, but the period, the time for one swing to occur, doesn't change, And so you can just keep measuring the number of periods that have occurred and then attract time in that way. All clocks essentially work by counting vibrations or by counting periods of some repeated motion. For example, electronic clocks just basically calculate the changes in polarity in electric circuit. We haven't done electronics, but we'll do that in a future podcast.

But basically that's how clocks work. Even if we just use a solar clock, essentially we're just counting the number of periods that have occurred with the sun rising and setting and so on. Okay, so now I want to start talking about some of the more interesting wave phenomenon. And we'll start with interference. Interference is a fairly simple principle. It basically states that if you have two waves in the same place at the same time, so let's say two water waves on top of each other, they interfere with each other. So they don't just, they're not just independent of each other.

If you had two physical objects, say two cars in the same position at the same time, that's either impossible or they'd crash or whatever, however you're going to arrange that exactly. But that's not the case with waves. Basically, they just add up. You just add them up. So, for example, if two waves are on top of each other, so their maximum points line up, so they're basically the positive amplitudes in the same position,

and their negative troughs are in the same position, then they'll just amplify each other, so that the height is even greater of the final combined wave and the trough or the depth is even lower. The middle points will, of course, be the same, because zero plus zero is still zero, but you essentially add the amplitudes and to make the amplitude of the final wave that much bigger.

That would be an example of what we call constructive interference. Basically, two waves sit on top of each other so that they add up and increase the amplitudes of the final wave. A second type of interference is destructive interference where essentially the peak of one wave overlaps with the trough or lower point of another wave. And so if the amplitudes of those initial two waves were the same, so say they were five in both case,

but if a trough of one of the, waves overlaps with a peak of the other wave, then essentially you've got positive 5 plus negative 5, which adds to zero, regardless of whatever the amplitude is, if the amplitude of the two waves is the same, they'll cancel out completely, and so you'll actually get nothing there. So it's possible to combine two waves together, and because of interference, you can get nothing there. You won't see anything. This is actually interesting, so if you can do this on a string, for example, you put one vibration which goes in one direction, so say it's moving along the wave, so pointing upwards, moving along the string pointing upwards

and then you do another one from the other direction but with the vibration or the wave sort of pointing downwards the two will move across each other and when they reach the middle when they reach each other they'll line up and they'll actually completely cancel that and it'll look like the string isn't moving at all for a second or so there and then they'll emerge from the other side

and the two waves will still be there again so it's very interesting how that works and that's essentially part of the sort of representative of the fact that there's no matter moving here it's all about moving of energy we need to maintain conservation of energy but negative 5 plus positive 5 is 0. So we can sort of go from that zero energy

to then having the energy there again. So interference is a very important concept to understand and also understand that interference doesn't have to be all or nothing. It doesn't have to be either the wavelength, the amplitude doubles or they cancels out. It could be a partial canceling out. So if you have a small wave, which partly cancels out a big wave,

then the final wave, the superposition of the two waves has a smaller amplitude than it started with. By the way, interference, only changes the amplitudes of waves. It doesn't affect the period or doesn't affect the wavelength. Those are all the same. It's just the amplitude that it'll change. Okay, so that's interference. Second thing I want to talk about is phase. This is a little bit more complicated, if it wasn't complicated enough already. Phase refers to the fraction of a wave cycle that has elapsed relative to an arbitrary point on the wave. That probably doesn't make any sense.

A more useful way of looking at phase is to consider phase difference between two points on a wave. Basically, phase difference refers to the sort of difference in position, or difference in direction as well, direction of travel, of two points on two waves, or the same wave, having the same frequency and referenced at the same point in time. Now, the key thing that we want to understand here is really whether waves are in phase or out of phase with each other. You actually hear this, well, if you watch science fiction or even just generic shows, they might talk about something being in or out of phase. It's a common, it's particularly common to explain why someone's invisible or can pass through wars or something

like that they're out of phase. This doesn't really mean anything in those contexts. But what the term in phase or out of phase means is essentially how similar the two wave, because you can talk about two points on a single wave or two different waves. But let's just take two separate waves to be a simple case. If the two waves are in phase, it means they have the same frequency and are aligned relative to each other so that they interfere constructively. So imagine we have two waves here, just one, just one, just one wavelength, basically, of the sign graph. Imagine we have that except times two.

The only way for those two waves to be in phase is if they have the same frequency, so there's the same length, basically, and that when you put them in the same place, they are aligned so that they interfere constructively. So peak to peak and trough to trough. If they are slightly offset so that the peaks almost match up, but not quite, or indeed completely offset so that peak lines up with trough and vice versa, then they are not in phase, the outer phase.

And in fact, that's where the concept of phase difference comes in, because the closer they are to being in phase, essentially the lower the phase difference is. If phase difference is exactly zero, then they're precisely in phase. The greater the phase difference is the further away they are from being completely in phase. And remember, you have to be the same frequency,

or same wavelength, obviously those related, as we talked about, and aligned properly. So if you're aligned properly, you might have one peak and trough that overlap each other properly. But if the waves are different, if the two waves you've got a different wavelength or different frequencies, then the next peak will not be in the same position for the two waves

because wavelengths essentially refers to the distance between one peak and the next and if one wave has a larger wavelengths than the other then even if pick one of each wave are in the same position peak two of the two different waves will not be in the same position because one will be closer to the initial peak than the other one and so that the second peaks will not line up and so therefore the two waves are not in phase Similarly, even if you had the same frequency, you still have to be aligned properly so that your peaks line up to your peaks and troughs line up to your troughs.

So being in phase is a fairly strict criterion. Phase difference or the concept being in or out of phase is important, for example, in laser light, because when light is in phase with itself or when multiple photons of light are in phase, then it increases the intensity of the light. We'll talk more about that later. If light is out of phase or if waves are out of phase with each other, the behavior of the wave, the superposition still occurs by the. regardless of where you or interference, it still occurs regardless of whether you're in phase or out of phase. However, the behavior of the interference patterns will be much more complicated if you're out of phase, especially if you have different frequencies because sometimes the peaks will line up, sometimes the troughs will line up, sometimes there'll be some combination,

and that the resultant combination will be very complicated. But in no case that they become invisible or waves, just don't interact with each other or something weird like that. Okay, so that's phase. Now I'm going to talk about polarization. Polarization has some similarities to phase in that it relates to alignment, but it's a bit different. Firstly, polarization only is relevant to transverse waves, so long-distance waves don't have a concept of polarization. Secondly, it refers not to the orientation of, say, peak relative to peak or trough relative to trough, nor does it relate to the frequency of the wave. It essentially relates to the sort of rotational orientation, if you want to think of it like that. Basically, if you think about it as, remember, I said this is a transverse wave, so think about a, think about this sign-cos graph that we've got. It goes up and down.

But then imagine we've got a second one. Suppose it has the same frequency. It doesn't actually matter. It can be polarised without having the same frequency or wavelength. But suppose it has the same frequency just for simplicity. But then imagine we've sort of rotated it. Not in the y-axis or in the x-axis,

in the normal ones in the graph, but in the Z-axis, so in the third dimension. So sort of imagine that we pick up, we grab hold of the top of the sign graph and sort of pull it towards us, imagining it was in three dimensions, and we sort of rotate it towards us. And so the peak sort of tips down a bit

and the truffle also sort of move up the other side. Sort of like rotating a wheel around in a sense. Hopefully you can imagine what I'm talking about. Now that new wave that was created by that rotation in the Z-axis, in the axis sort of in and out of the page or in and out of the screen, if you want to think of it like that, that rotation has made the second wave no longer polarized or no longer of the same polarization as the first.

In order to be polarized, the alignment of the direction of vibration of the transverse waves must, be in the same direction. So for example, this sine wave that we've talked about, the x-axis of these graphs still line up perfectly. We haven't actually changed that. We've just rotated around the x-axis. We haven't moved it or changed its orientation. So the x-axis still the same, which means that the direction of travel of the wave itself is identical. That hasn't changed. So if we're talking about light, the light waves are still traveling exactly the same direction. The difference is we've sort of rotated them, rotated the lightwave so that one is sort of at an angle to

the other one, not in terms of the direction they're traveling, but in terms of the direction that the, we'll say, photons are vibrating. So in one case, the photons might be vibrating up and down, but in the second case, the rotated version, maybe they're vibrating on an angle diagonally or something. In those two cases, the waves are not polarized, because the direction of vibration of the molecules or the medium whatever, in the two cases is different. Even though the wave is traveling in the same direction, the vibration's not in the same direction, and so they're not polarized. You can see why this is only one. relevant to transverse waves because long-dracurial waves don't have the direction of trans the direction

in longestrian waves is the same as the direction of travel so uh this concept of sort of rotating one relative to the other doesn't apply an application of polarization is that is basically in polarized sunglasses because what they do in these sort of sunglasses they put lenses in them which keep out light of a certain polarization so light waves basically of a certain orientation but not light waves of a different orientation. And it turns out that reflected sunlight, say, from shiny metallic surfaces or from water, tends to have a different polarization on average than the light that comes to us directly from non-shiny surfaces or just from the sun or from the sky or wherever.

So effectively you can selectively block out the reflected light compared to other, well, light reflected from shiny metallic surfaces and water and stuff like that. You can selectively block that out and allow other light in. That's how sunglasses, polarized sunglasses, for example, can reduce glare. Okay, that's polarization. Now I want to talk about resonance. This is another thing that you might have heard before. In fact, the concept of resonance is mentioned rather a lot in popular discourse I find. Also, people use the word like one thing resonating with another thing or I resonated with

her or whatever. But I don't think too many people really know what that means. Basic idea behind resonance is that things are vibrating together. They're vibrating sort of in step with each other. And so in a sense, they complement each other rather than working cross-purposes. That's the basic idea behind resonance. And that kind of works, that's how people use the word in sort of a popular discourse. It's also kind of how the concept is used in physics as well, but obviously it's much more precise than that. So I'm going to go into more detail now about what resonance actually means.

Every object or system has a natural frequency, which is the frequency at which it tends naturally to vibrate when it's struck or disturbed or knocked in some way. Basically, this natural frequency is determined by the properties of the object like mass and length and stiffness and other things like that and viscosity and whatever else. So when I'm talking about an object or system, I'm talking about an atom, a molecule, a DNA, molecule, a cell, a laptop, whatever. All of these things will have some kind of natural frequency. You can get them to vibrate at different frequencies, but you have to put a lot more energy into them than if you just get them to vibrate normally. And you can easily see this by filling up glasses of water or bottles of water to different levels,

and then striking them with a spoon or something, you'll see that the sounds that you get are different pitches, which represents different frequencies at which they're vibrating. And you strike them in this exact same way, and they'll vibrate at different frequencies, because they have different masses, and therefore different natural frequencies. Now, resonance refers to the phenomenon whereby periodic application of small amounts of force at or near the system's natural frequency over time greatly increases the amplitude of vibration. So the analogy that's always used with resonance is the example of a child on a swing. So the natural frequency in a sense of the child on the swing is that the sort of natural time

based on gravity in the child's masses on that it takes for them to swing forward and then come down and back to, say, behind the swing where the parent's standing pushing. them. So that's the frequency, or I guess we'd say that the frequency would be the number of times they do that in a minute or whatever. The number of swings they make in a minute. That would differ between child, but for a child it's going to be basically the same. Now, when you're pushing them, basically, you're going to want to push them either once per swing or once every two swings or once every three swings, some whole multiple of the period, basically. But you're not going to want to push them every three quarters of a cycle or every third cycle. Because if you do that,

basically what happens is you're going to be, sometimes you're going to be pushing them when they're, or for example, take the three-quarters example, the first time you push them when they're right in front of you, which is where you've normally pushed them, but then the next time you push them when they're sort of halfway back down coming towards you, then the next time you push them sort of halfway when they're going away from you, and then the third time you push them again when they're down right in front of you. So you're pushing them at different times. Clearly, if you did that, it would become a mess, because sometimes you're pushing them when they're going away from you, sometimes you're pushing them when they're coming towards you,

sometimes you're pushing them when they're sort of, and they're sort of just halfway in between. So sometimes the energy adds to the energy that they already have, adds to the motion that the child already has. Sometimes it subtracts from it, and it kind of gets in a mess. Basically, if you're trying to do that, you just get into a chaotic motion, and a motion will rather die out or will just kind of not really go anywhere.

And it becomes very hard to maintain that sort of motion. That would be non-resonant addition of force. So you can do that. You can push them in those intervals if you want to, but that's not resonance. your push your energy wouldn't be resonating with the natural frequency, and therefore you're not going to really get anywhere. What resonance does is that it only applies the forces

basically in time with the natural frequency at which it's vibrating. So in this case, it's only pushing the chart when they're right in front of you, when they swung back towards you, just ready to be pushed again in a sense. Whole multiples of that. If you push whole multiple, say every second swing or a tenth swing, the less frequently you do it, the less energy is going to be added. However, as long as you do it at a whole multiple of the frequency, you'll still maintain that resonant motion.

You won't get the chaotic motion that would happen if you did it every third period or something. Basically, when you do that, when you add the energy only on those sort of frequency intervals in line with the natural frequency, the amplitude will gradually increase. Not forever, because there's friction, for example, regardless of what the system is, there's always some kind of friction, second law of thermodynamics, there's some kind of loss of energy. So eventually you'll reach an equilibrium where the amount of energy you're putting in is equal to the amount of energy that's leaving, and so the system will reach a steady state there.

But up until that point, you'll gradually increase the energy. So there's an example you may have heard. of a bridge that collapsed because of essentially wind, which was blowing in some complicated way, on the bridge in line with its natural vibration frequency. So although the force of the wind wasn't actually very strong, it was gusting in such a way, or maybe it was the waves or something. I can't exactly remember what the story is, but I think it was the wind. It was gusting in such a way, blowing in such a way, that it was adding energy in line with the natural

frequency of the bridge. And so the bridge started swaying or vibrating only a small amount, but it gradually built up over time as that energy was added in a sort of consistent way in resonance with the natural frequency of the bridge, and the amplitudes of the vibration of the bridge got larger and larger control the bridge tore itself apart and collapsed. Now I look this up and it seems that the actual case is a bit more complicated than that, and there were more complicated physics going on. I don't really care exactly about that. I'm just trying to illustrate the point of what resonance can do.

Resonance can indeed make things happen or sort of store energy in a way that's not possible if you just add the energy in at sort of random intervals. Another example of that would perhaps be on a seesaw. One person needs to push up at the right time relative to the other person. If each person just pushes at random times, you're not going to get a nice coherent motion there. You're not going to get very high either. Pedaling a bicycle might also be example. You need to push the pedals down at the right times.

If you just do it at random times, you're not going to get the resonance in, you're not going to get the speed up in the wheels there, and the bicycle is not really going to go anywhere. So resonance is a very important concept. But fundamentally it refers to adding energy into a system consistent with, or basically at the same time as its fundamental frequency. or at least whole multiples of that. All right, that was resonance. Now I want to talk about reflection.

This one's, compared to polarization phase and resonance, this one's actually quite simple. Well, really, reflection and absorption. I'll take these two together because they kind of go together. Reflection basically refers to the fact that when a wave hits a barrier or more accurately a boundary between two different media. So, for example, it could be air moving to a wall, or a sound wave moving from water to air,

or electromagnetism moving from air to water, or from brick to air or whatever, but any change of medium like that. Some of the wave will be reflected, so we'll essentially bounce off and travel back in the direction it came from, and some of the wave will be transmitted through the medium, so we'll keep going through it, and some of the wave energy will be absorbed by the new medium that it's traveling in.

Really, all mediums will absorb some of the energy. This is basically just the friction that I was talking about internal to the medium. So, for example, water molecules rubbing up against each other, or air molecules bouncing off against each other, ways that are not consistent with the overall wave motion, that will sort of leak energy away from the wave itself and therefore gradually diminish amplitude over time. That's why sound actually travels very well in water, because water has a very low viscosity, and that's very important to not

essentially leaking away energy. So water will travel actually hundreds of kilometers through water, even thousands, really, if it's loud enough and it's not disrupted by something. So that's the absorption aspect. Reflection occurs, as I said, when the wave moves across the boundary from going from one medium to another. And essentially the reason it happens is because different mediums will have, will be differently conducive, or conducive to different degrees, to the transference of that wave.

So, for example, sound waves travel more or less easily in water compared to air, or compared to brick or wood or whatever. And so, when that energy is approaching the boundary, when it reaches the boundary, the energy, the vibrations will essentially just travel in the path of least resistance, just like water running downhill or whatever. Some of them will continue through the wall, some of them will bounce back and continue through the air,

depending on which is easier. If it's much easy to travel through air than it is through brick, as indeed it is, for sound waves, or most sound waves, then most of the energy will bounce back

and will push the molecules sort of back in the opposite direction that came from, and then the wave propagates back in the direction it came from. That's basically an echo, but a small amount will travel through the brick

and the sound is transmitted through the brick. If you have air and water, sound travels much better and water than a dozen bricks, so less of the energy will reflect back and more of it will continue,

will transmit through into the new medium. So that's basically really all that affects the, I shouldn't say that. That's one of the two important properties that determines how much reflection, how much of the wave is reflected. It's the relative properties or the relative ease with which the wave can travel through the two mediums. Now I want to move on and talk about refraction. Now don't get confused. Refraction is not the same as reflection. They're quite different to each other, although they're sort of related. So refraction and reflection, reflection is bouncing off. Refraction is the change in direction of a wave due to a change in its space.

when a wave changes from one medium to another. So, for example, if a wave is travelling from air into water, that's changing medium. Water, waves travel, it could be a sound wave or a light wave, doesn't really matter in this case, but they'll travel at different speeds in the two different mediums, and so as it changes speed, it also changes direction when it passes from one minute into the other. However, refraction does not always occur. It only occurs when the wave strikes the division, or strikes the boundary between the two mediums, at an angle, not 90 degrees or zero degrees,

degrees or zero degrees, but at some angle in between those. So a 45 degree angle or 20 degree angle or something. Now, the best way to understand why this happens is just to look at a picture or diagram, but essentially imagine a squad of soldiers marching abreast, and they're all holding each other's hands or whatever, so that they're all connected and they're all marching shoulder to shoulder next to each other at a slight angle or at some angle to a boundary. And say this boundary, say they're walking through grass, and they're about to emerge onto a paved area. And you can, can move, let's say, long grass cut to a pavement area. And so once the soldier

gets onto the paved area, they'll be able to walk faster than they were walking on the grass. And so because the line of soldiers, the squad of soldiers is travelling as an angle relative to the boundary, one soldier, at whichever end, depending on which way it's angled, one soldier will reach the paved area before or the others. And so they'll

start walking more quickly before the others start walking more quickly. And then the second guy, and then as the squad moves a bit further forward, that the second soldier reaches the paved area and then they start moving more quickly, but there's still a bunch of the rest of the squad that haven't reached it yet. And so by the time the final soldier reaches the paid area, all of the other ones have been traveling at that faster speed for a while already,

and the very first guy who reached the paved area has been traveling at that faster speed for substantially longer than the final guy has. That doesn't sound, this sounds kind of obvious, and it is, when the soldiers are connected, sort of holding hands or abreast to each other in the way that we said they were, essentially representing a wave front, when you have that and have the changing speeds, as we said, changing speeds at different times because of the angle, you get a change in direction of the wave. There's really no way I can explain this other than just to say look at a picture, and that's what happens.

And whether the degree to which the wave change direction depends upon the difference in speeds and also the angle at which the wave hits the boundary, you can see why this only happens when there is an angle, because say that the bunch of soldiers, was walking towards the boundary sort of, suppose their direction of travel was perpendicular to the boundary so that if you drew a line across the squad of soldiers, that line would be parallel to the boundary line.

In that case, all the soldiers will reach the paved area at the same time, and so there is no difference in speed, and so there's no change in direction there. You only get that different timing of the one soldier compared to the other when there's some angle, and the greater the angle is essentially the greater the difference in time is, and so the greater the one soldier walks compared to the other,

and therefore the greater the change in direction. direction is. Yeah, really recommend looking at an image or even better animation of that to get your head around how that works exactly, because it's a little bit confusing. But that's why refraction occurs. Whenever you have a wave moving across a boundary, into a new medium where it travels a different speed, and it hits it at some angle, it will change direction. The greater the angle, the more direction will change. Refraction is a very important phenomenon for light, and it's partly responsible, well, largely responsible for the phenomenon of rainbows, for example. We'll talk about that when I cover light in a future episode. One thing I just want to quickly mention, I'll bring this up in much more detail when we talk about light. This is the concept of diffraction. Diffraction basically is the spreading out of waves when they pass, excuse me, when it passes through a small aperture, or passes around the side of a small obstacle. The obstacle has to be relatively small, and gap has to be relatively small relative to the wavelength,

otherwise you don't really notice it. So technically all objects have a wavelength, your car has a wavelength, in terms of quantum physics, I think we talked about this, but the wavelength is extraordinarily small, you can't notice it. So, you know, technically you could observe diffraction of billiard balls, but it would be ridiculously small, and it wouldn't look like anything. When we talk about things as small as electrons, though, we can see, and photons, we can see the diffraction occurring,

we can see the spreading out occur when we pass them through narrow slits or around small objects. But this is much more obviously if you just talk about waves in water. If you have a wave that's sort of a flat wave that's just moved down and you pass it through an aperture, it will spread out and go in a nice, circle for you there. Once again, pictures of that on the internet. I won't go into detail exactly why that happens. We'll talk about that later, but it's just an important concept.

I just want to put it in here to, for completeness basically, because it kind of goes along with reflection and refraction and polarization and some of these other things. And it's an important concept, particularly in electromagnetism. One final thing that I want to talk about, and I'll go into this more detail again when we talk about sound, because this is particularly important when it comes to sound, but this is the concept of a standing wave. This is quite counterintuitive, really. It's a way, a standing wave is basically a wave that doesn't move. It stands in the same place. Now, but I've just defined wave

as essentially a movement of vibrations transferring energy from one place to another, so it would seem contradictory. How can you have a stationary movement of energy? Well, basically the reason you can have a stationary movement of energy is because the energy is sort of moving, but it's moving backwards and forwards within a fixed position. And so there's

no net motion. Kind of like moving in a, not really like moving in a circle, more like bouncing backwards and forwards between one wall or another. It's sort of moving, but it's sort of stuck in the same place. And there's more to it than that, though, because remember the concept of interference. If you have a peak lining up with a peak, then they superimposed and you get a higher peak, or if you have a peak lining up with the trough, they cancel out destructive interference, and you essentially get nothing there.

If you have one wave coming in one direction and another identical wave going in the other direction, so same frequency and all that, same amplitude as well, but they're just traveling in opposite directions. Basically, what will happen is, first of all, well, is it one time, the peak will line up with the peak and you will get constructive interference, and then later on they'll sort of move away from that and get to a situation. situation where peak lines up with trough and you'll get complete cancelling out. And if you have those two waves travelling backwards and forwards essentially bouncing between the between two walls or between two obstacles, bouncing like that, they're constantly

interfering constructively and then destructively and then constructively and then constructively again in a fixed pattern in that way. And as I said, if they have the same frequency, it'll look like you've essentially got a string just vibrating in position. And that's what we call a standing wave. Once again, I recommend looking up an animation on this. It sounds kind of weird that you can have one wave moving in one direction and then bouncing off and another wave moving the out direction bouncing off and that they cancel each other at and produce a behavior that looks like you've just got a string vibrating there, but in fact that is exactly what happens. So it doesn't look like anything's actually moving. It just looks like the string or the medium or whatever it is

is vibrating. It could be air or water, but strings are a good example to take from it. But in fact, what's, you've got waves there, they're just sort of constantly constructively and then destructively interfering with each other in a regular pattern, which then produces a behavior that looks like a vibration. So it's a wave that stands in position. And it's basically, as I said, the result of interference. And this is also when the concept of being in phase is relevant, because the two waves need to be, well, they're not always in phase, but they at least need to have the same frequency if you're going to get a nice regular standing wave pattern like that. Staining waves are very important in music. We can show that much of the complicated behavior

or sounds that we hear in music is actually a combination of some very basic principles of basically pitch, which corresponds to frequency, loudness which corresponds to amplitude, and superposition of waves, one on top of the other, producing standing waves. with the principle of interference, but we'll talk about that in more detail when I do it in an episode on sound and music. Okay, so that's all I wanted to cover today. This podcast has already gone on longer than I had hoped. Hopefully that was relatively clear. If you have any suggestions about how to improve the podcast or topics that you'd like to hear or anything like that or any other feedback, I'd be happy to hear from you. My email address is Fodds12 at gmail.com.

Thanks for listening, and I'll talk to you next time.