Traveling waves

# 20 Microscopic model

### “Still” air

“Still” air at room temperature and pressure is far from still. Air is crowded with lots of tiny particles (mostly nitrogen and oxygen molecules) blazing around in random directions. Each particle moves incredibly fast, but no particle actually gets anywhere very quickly because it is constantly being redirected by collisions. The situation is somewhat like a large glass cage crowded with blind, angry bees.

To get a true appreciation of air, consider some numbers. The distances in this paragraph are in nanometers (nm). For reference, a human red blood cell is huge- about 7000 nm across. A typical air molecule is a little less than half a nanometer across. Air molecules are also surprisingly close together (about 3 nm on average) and traveling really fast (about 1000 miles per hour on average). The result is that molecules only travel about 70 nm on average between collisions. (It’s actually amazing that they get even that far when you consider how close together air molecules are). Going at 1000 mph and traveling only 70 nm between collisions, the typical molecule suffers billions of collisions every second.

Sources of sound move in and out. As the speaker cone moves out into the air, it pushes on the air molecules closest to it, creating a pocket of slightly compressed air. As the cone moves back in, the atoms in the air spring back, creating a low pressure region. The process repeats and the result is a series of compressions and rarefactions that travels out from the source, like ripples on a pond. A very simplified animation of sound in air

When a wave passes, the particles in a the medium do not travel very far at all. If you watch a cork bobbing in the water, you’ll notice that the cork is not carried along with the wave- it simply bobs up and down. Sound works the same way. You can think of air as a box of tiny hard particles. The individual air particles do not travel with the sound. Each air molecule bumps into a neighbor and the neighbor bumps its neighbor and so on. Sound travels across the room quite quickly, but the individual air particles do not travel across the room very quickly at all. Think about a lecturer with really bad breath- you hear the words long before you detect the smell. That’s because the air particles from the lecturer’s mouth reach you long after the sound does.

### A (somewhat) more realistic picture

The microscopic model presented here is oversimplified. The model works fine for the purposes of this book, but it’s worth mentioning some things about air.

Moving surfaces (like the cone of a loudspeaker) create “bunched up” and “spread out” regions in this sea of chaos. The air molecules pass on the information onto their neighbors, but do not travel with the disturbance- they’re just too busy crashing into each other to make headway in any given direction. It is also important to recognize that individual molecules in “still” air do actually eventually cross the room, after suffering an unimaginably large number of collisions. (If this didn’t happen, we would never smell anything).

The pictures in this book (and most of the simulations on the web) grossly exaggerate the differences in pressure and density in a sound wave. The differences between compressions and rarefactions in everyday sound are actually incredibly small. Even for a sound loud enough to do instantaneous damage to hearing (a jet engine 100 feet away), the air at the center of a compression is less than 1% denser than the air at the center of a rarefaction. For common sounds, the difference is much smaller- less than 0.0001%.