[freixas]

Please read The Compressibility of Air and Mass Flow, Speed, and Pressure before proceeding.

I said that air is incompressible. If you put 1 liter of air into a melodica, 1 liter of air will come out—guaranteed. Well…plus or minus a few molecules. We’re going to spend some time with those rebel molecules.

Let me first define two words commonly used as synonyms. We’ll define the term speed to mean how fast something moves regardless of its direction and the term velocity when we need to know the direction as well. 

If you examine air microscopically, it is a collection of air molecules zipping around in random directions at random speeds. They can do this all day; after all, from their point of view, they are traveling in a vacuum until they collide with another molecule. At that point (in a perfect world) energy is transferred, but not lost.

When we blow into a melodica’s mouthpiece, we are imparting kinetic energy to molecules of air. The molecules are still zipping about in random directions and at random speeds but, taken as a whole, the average direction is into the mouthpiece and the average velocity is what we consider to be the airflow.

There is a lot of empty space between the molecules. As the stream of molecules from our breath enters the mouthpiece, most molecules will zip on in without any problems. Eventually, the molecules flowing in will collide with the molecules already in the mouthpiece and will transfer their kinetic energy to those molecules. These, in turn (and on average), start flowing further into the melodica, transferring the kinetic energy further down.

No individual molecule will go very far. It is the kinetic energy that is transferred.

The region around where the molecules of different average velocity meet tends to form a small area with a slightly different fluid density than the surrounding air. The air is still generally incompressible, but we have created a tiny region of compression (or rarefication, the opposite). This results in a slightly different pressure in this region, so the movement of the compression is called a pressure wave.

Sound travels as a series of pressure waves, some compressing and others rarefying the air. These pressure waves travel at (naturally) the speed of sound. The speed of sound is not a fixed speed, it is (by definition) the speed of a pressure wave through a medium.

And, in our case, it is much faster than the velocity of the air flowing in.

Let’s say you blow into at 1 meter tube at a velocity of 1 m/s. You might at first think that air flows out the other end 1 second later. A moment of reflection tells you this can’t be right—there is air already in the tube, so that air will flow out first. But how soon? In dry air at around 20° C, it takes less than 3 milliseconds for the airflow to begin.

This diagram shows what happens if you blow a very quick puff of air into a 1 meter tube:

Check the tube at the 1 millisecond mark. There is a fine vertical line near the yellow arrow. It represents the point we might think air traveling at 0.1 m/s might have reached in 1 millisecond (this line is not to scale—it is probably much closer to the tube’s entrance). Yet the pressure wave has traveled about 1/3 the length of the tube and the region of air behind it will all have a velocity of 0.1 m/s (colors correspond to velocities).

This seems almost magical. The complete explanation is quite technical, but you can get the gist with just a few concepts.

The molecules in air have an average speed of around 500 m/s (about 1800 km/hr!). Because they are as likely to zip one way as another, their average velocity might be 0. The average speed of the molecules is not the speed of sound, but can be used to derive the speed of sound (about 343 m/s), which then tells us how fast the added 0.1 m/s velocity can be transmitted to molecules down the tube. 

The added velocity, whether it’s 0.1 m/s or 10 m/s,  doesn’t affect the speed of sound. You’ll have to trust me on this as that is one of the more technical parts, involving terms like Maxwell–Boltzmann distribution curves and root mean squared velocities. The point is that speed of the pressure wave is the same regardless of the velocity that it is transferring down the tube. It’s good it works this way or else sounds waves would be distorted by distance (the peaks of the sound waves would travel faster than the troughs and the wave’s shape would change).

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