Waves: Moving Without Going Anywhere

At the tail end of Tuesday’s post about wind and temperature, I asked a “vaguely related fun bonus question:”

If the air molecules that surround us are moving at 500 m/s anyway, why isn’t the speed of sound more like 500 m/s than 300 m/s?

This is another one that people are sometimes surprised by. The answer is simply that in a sound wave, the air molecules don’t really go anywhere. When something creates a sound– say a foolish dog barking at a perfectly harmless jogger going by outside, to choose an example completely at random– there isn’t any actual thing that travels from the noisy dog to your ear. The sound wave is a disturbance in the air, not a physical thing.

We think of air as an extremely tenuous substance, but in fact it packs quite a few particles into a small space– the nominal density of air is on the order of 10¹⁹ molecules per cubic centimeter (if you don’t like scientific notation, that’s 10,000,000,000,000,000,000). If you ask how far a randomly chosen air molecule will move before it hits something– a quantity known as the mean free path, it turns out to be only a few tens of nanometers. Air molecules are zipping around at very high speeds, but they don’t really go all that far in any one direction before they hit something and change direction.

So, what’s a sound wave, then? A sound wave is a disturbance in the air caused by the collective motion of vast numbers of molecules moving back and forth by small amounts. You can get the basic idea from this image I snagged from hyperphysics (which, by the way, is an excellent source for very compact physics explanation):

When you start to create a sound wave– say by barking like an idiot, if you’re a dog– you begin by pushing a bunch of molecules forward, as if you were going to shoot them across the room to someone else. The molecules don’t go very far before they hit other molecules, though, and bounce back toward you. The molecules that were hit are now moving across the room, though, at least until they hit other molecules, and so on. This creates a little pulse of higher density (where moving molecules are colliding with ones that were minding their own business) that moves in the direction you want the waves to go.

Shortly after setting the first batch of molecules in motion in the desired direction, whatever you’re using to push the molecules forward pulls back to set up for the next push, which creates a bit of a void for the molecules that are bouncing back from the initial collisions to rush into. Which they do, to be met by the push for the next oscillation of the wave. And so on.

The result, as you see from the picture, is a pattern of areas where the molecules are temporarily somewhat closer together and areas where they are temporarily somewhat farther apart. These repeat with some characteristic frequency and wavelength, making up the sound wave. The individual air molecules, though, just oscillate back and forth more or less where they are, only moving a small distance forward and back. The disturbance in the otherwise mostly uniform distribution of air molecules propagates through the air, to annoy a nearby human who’s trying to get work done, but the individual molecules don’t go anywhere.

So that’s why the speed of sound isn’t the same as the speed of the molecules in air. The two are related– if you look at the speed of sound in air at different temperatures, you’ll see that it increases with temperature. Which makes sense, because the speed of sound waves is naturally going to depend on how quickly the molecules can move back to where they started for the next wave. They’re not identical, because the speed of sound also depends on the density and other factors.

This, by the way, is a very general property of waves. Waves are disturbances in some medium, but the medium itself generally doesn’t move very far, even though the waves themselves do. The canonical tool for demonstrating this is a Slinky– get a long spring, and stretch it out to its full length. You can then create two different types of waves. If you take one end of the Slinky, and move it back and forth by a small amount along the direction of the extension of the spring, you’ll set up a longitudinal wave like a sound wave in air– a pattern of areas where the coils are closer together and areas where the coils are farther apart. If you move the end side to side by a small amount, you’ll set up a transverse wave, which you’ll see as a sort of curve in the path of the spring.

In either case, the Slinky itself doesn’t move any significant distance. The individual coils move in and out or back and forth, creating a moving disturbance, but the spring as a whole stays put.

Water waves, like you see if you’re lucky enough to live close to a good ocean beach, are a sort of combination of the two. The water molecules making up a region of water that a wave is passing through describe little loops, moving both back and forth and up and down as they go through the oscillation. When we see waves breaking on a beach, what we’re seeing is, in a sense, the interruption of this circular oscillation by the bottom of the ocean as it rises to become the shore (it’s a little more complicated than that, because the speed of the wave changes as the depth decreases, but it will serve as a kind of shorthand for the full process).