Sound – Bartosz Ciechanowski

Invisible and relentless, sound is seemingly just there, traveling through our surroundings to carry beautiful music or annoying noises. In this article I’ll explain what sound is, how it’s created and propagated. Throughout this presentation you will be hearing different sounds, which you will often play yourself on little keyboards like the one below. You can either click its keys with your mouse or use WER keys on your computer keyboard, but before you do so make sure your system volume is at a reasonable level:You can press its keys with your fingers, but before you do so make sure your system volume is at a reasonable level. You may also need to unmute your device: We’ll eventually understand how these sounds are created and how they get to your ears, but we have to start by talking about the medium that is most commonly associated with sound – air. Air You’re probably aware that at microscopic level air consists of individual, tiny particles. Let’s look at the behavior of those molecules up close. In the demonstration below, I parceled out a tiny cube of air – notice how the molecules freely enter and leave this space. You can drag the cube around to change the viewing angle and you can also control the speed of the flow of time with the slider: I need to note that this visualization simplifies things a little. The air consists primarily of nitrogen and oxygen – their particles contain two atoms bound together, but for simplicity I’m drawing all molecules as simple spheres. Each particle of air travels through space with some velocity in a more or less random direction. While some molecules are faster, and some are slower, at room temperature the average velocity of a particle is a staggering 1510 ft/s460 m/s so to make the particles visible I’m showing their motion significantly slowed down. As a side note, I’m using imperialmetric units here, but you can switch to the metricthe imperial system if you prefer. With all the commotion in the previous simulation it may have been hard to see that the air particles collide with each other. In the demonstration below, I’m flashing the particles red and making them a little bigger right after they collide. To make these events easier to see you can control the speed of time with the slider: Naturally, those particles can also collide with other things in the environment. In the simulation below I put up walls around that parcel of air. While at this scale we could also see the individual atoms constituting the walls of the box, I’m not showing them here to make things clearer. The particles of air are bouncing off these sides and every time that happens I’m drawing a little blue glow on the wall: When an air particle bounces off, it imparts a small force on the wall. Although a single collision doesn’t do that much, with enough particles present the walls experience a constant barrage of collisions which exert expanding pressure on the container. The magnitude of that pressure is the sum of all these forces of impacts divided by the area of the box. Intuitively, for a box of a fixed size, the more particles there are, the heavier they are, and the faster they move, the higher the pressure. Let’s see what happens if we resize this box a little while keeping the number of particles constant. In the demonstration below, you can drag the slider to change the length of the box, the plot in the bottom tracks the number of collisions per area of the box in a unit of time: The number of collisions per area, and thus the pressure, increases as we squeeze particles closer together, and it decreases as we let them loose. Remember that we’re observing a significantly slowed down simulation. Because of the speeds involved here, I’m only letting you resize the box at a limited pace. That limitation prevents the walls from moving at enormous speeds, which would create some truly extreme pressure conditions. It may not be immediately clear, but the experience of pressure is not limited to the walls of the box we built. Molecules in any open region of gas also experience compressing forces exerted by collisions with molecules from the neighboring regions. Those collisions aren’t as neatly aligned in space, but in aggregate it makes no difference if particles are bouncing off a wall or off particles from the neighboring area – the pressure is still there. All the collisions between particles also have other consequences, but to look at them I need to adjust the scale at which we’ll be looking at – you can do this with a slider below: The small cube of air from the previous demonstration is now just part of a larger volume. While this large cube is 20 times larger in each dimension, its sides measure only 1 micrometer – a few times smaller than a width of spider silk. Unfortunately, it would be both chaotic to display and taxing to correctly simulate the over 26 million air particles that one could find in this area. Instead, I’ll just visualize the motion of a single molecule as it travels through this space. In the demonstration below, I enlarged that particle to make it visible, you can also control the flow of time with the slider: Due to collisions with other molecules, it may take a while for this particle to travel a significant distance and get out of this larger volume. You probably experienced this yourself – when someone sprays perfume in a distant part of a room the scent doesn’t instantly get to you. It’s only after some lucky aromatic particles manage to bounce into the vicinity of your nose that you get to experience the smell. If it wasn’t for the collisions with other molecules, those fragrant particles could travel the distance to your nose in a fraction of a second. The important point is that, while the air particles move very fast, the collisions with other particles keep them mostly contained inside their local area. Over a longer period of time they will eventually all mix up, but at the short timeframes we’ll be interested in here, each reasonably sized parcel of air contains mostly the same particles. All the microscopic behavior of individual particles we’ve observed ends up contributing to properties of air at larger scales. From this point on, we’ll move past looking at individual molecules and instead we’ll focus on regions of air that more closely match the sizes we’re used to. Those particles are still there, and they’re what actually end up distributing changes in gases, but we need to aggregate a huge collection of the molecules to end up with more discernible motions. Let’s witness some of this large scale behavior when a section of air in a tube gets pushed on by a moving plate. In the demonstration below, I divided the air next to that circular plate into individual slices, which I’m drawing with thin lines. Although these boundaries are imaginary, they let us see what happens to different sections of air as you move the plate around with the slider: Notice that the individual parcels of air move only a little from their initial position, but the disturbance caused by the motion of the plate seems to propagate through them with some speed. Moreover, that disturbance moves away from the plate regardless of the direction of the plate’s motion. If you recall our experiment with a resized cube of air having more or less available space, you’ll notice that a very similar situation happens here inside each slice – this tells us that we’re witnessing some changes in pressure. Let’s look at this situation from the side, which will make it easier to see how these pressure changes propagate. In the following demonstration I’m coloring each slice of air red when it’s compressed and the pressure increases, and I’m coloring it blue when it’s expanded and the pressure decreases: When the plate moves to the right, it compresses the air particles in its vicinity, which increases the pressure in this region. Those particles then push and expand into particles in the neighboring slice of air, which then push onto the next slice and so on. All of this results in an area of higher pressure propagating away from the plate. On the flip side, when the plate moves to the left, it creates an area of depletion, or rarefaction, which the neighboring slice of air rushes to fill in. This then reduces the pressure in the vicinity of the next slice and so on. While the slices move towards the receding plate, the pressure disturbance still moves away from the plate. What we’ve just seen more clearly were pressure waves propagating through the air. When those pressure waves reach our ears we perceive them as sound. By moving the plate we’ve effectively created a very crude speaker that emits sounds as its moving element changes position. While this simple demonstration helps to build an intuitive understanding of the propagation of pressure waves, the relation between the vibration of the object and the pressure disturbances it generates is much more complicated. We’ll soon explore some of those details, but for now we’ll focus on the relation between the movement of that vibrating element and the sound it produces. Making Sounds Let’s begin by introducing a simple musical instrument. By pressing a key down, you can request the plate to rapidly change its position. When you let that key go, the plate will move back by the same amount. Notice that each of the three keys moves the plate by a different amount, with red marker showing the total offset: Despite its simplicity, this device lets us observe a few things. Firstly, a sudden jump of a plate creates a popping sound. It also doesn’t matter if the object has jumped forwards or backwards – the effect sounds the same. Secondly, the loudness of that pop depends on the magnitude of the jump – the larger the jump the louder the pop. Finally, this plate can jump forwards or backwards from any position – you can verify this by holding one of the keys and then pressing some other key. That pop sounds exactly the same as the sound