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):

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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).

Comments

  1. #1 Andy Perrin
    August 19, 2010

    It’s true that for sounds that aren’t “too” loud that the gas doesn’t drift after the sound wave passes, but not true for really loud sounds. At high enough sound intensities there is a small drift velocity. This is also true for water waves– the water particles don’t describe perfect circles for big enough waves.

  2. #2 Omega Centauri
    August 19, 2010

    I used to have a nice view of the opposite phenomena. I used to live downrange of a mountain, with good views of the rotor cloud. Essentially this is the place where the wind wave downstream of the mountain has its first rarefraction. There would often be a pretty impressive looking cloud right there. You could tell the air was moving really fast, and the finescale detail of the cloud would move with the flow -but the overall cloud would remain stationary for hours.

  3. #3 Peter Morgan
    August 19, 2010

    “Waves are disturbances in some medium” … except, perhaps, if they are light waves, or anything quantum mechanical. Insofar as the standard story is that there is no Stuff, perhaps even that there is no ding an sich. If there are no turtles under your atomic turtles, that you say make the dog noises, are there atomic turtles at all?

  4. #4 Sophie
    August 19, 2010

    Wait, if waves are generally disturbances in some medium, then do light waves – which don’t need a medium (now that we’ve ruled out luminiferous ether) – still fit the traditional “waves” definition ? Or are those quantum mechanical waves that Peter mentions distinct from the waves that propagate through a medium?

    Also, do you know if there’s a picture/video representing what happens when water waves get cut off by the shore and then break? I know that’s what happens, but I’ve always had trouble visualizing it.