1.1 Standing waves and wind instruments  (Page 2/4)

There will be more on that harmonic series in the next section . First, let's talk about why only some standing waves will "fit" in a tube of a particular length. If the tube were closed on both ends, it's easy to see that this would be a lot like the wave on the string. The air would not be able to rush back and forth at the ends, so any wave trapped inside this tube would have to have nodes at each end.

Fully closed tube

Now, a closed tube wouldn't make a very good musical instrument; it wouldn't be very loud. Most of the sound you hear from an instrument is not the standing wave inside the tube; the sound is made at the open ends where the standing waves manage to create other waves that can move away from the instrument. Physicists sometimes study the acoustics of a tube closed at both ends (called a Kundt tube ), but most wind instruments have at least one open end. An instrument that is open at both ends may be called open-open , or just an open tube instrument. An instrument that is only open at one end may be called open-closed , or a closed tube or stopped tube instrument (or sometimes semi-closed or half-closed ). This is a little confusing, since such instruments ( trumpets , for example) still obviously have one open end.

Now, there's nothing stopping the air from rushing back and forth at the open end of the tube. In fact, the waves that "fit" the tube are the ones that have antinodes at the open end, so the air is in fact rushing back and forth there, causing waves (at the same frequency as the standing wave) that are not trapped in the instrument but can go out into the room.

Open-open and open-closed tubes

What is it that requires the waves to have an antinode at an open end? Look again at the animation of what is happening to the air particles in the standing wave. The air at the nodes is not moving back and forth, but it is piling up and spreading out again. So the air pressure is changing a lot at the nodes. But at the antinodes, the air is moving a lot, but it is moving back and forth, not piling up and spreading out. In fact, you can imagine that same wave to be an air pressure wave instead of an air displacement wave. It really is both at the same time, but the pressure wave nodes are at the same place as the displacement antinodes, and the pressure antinodes are at the same place as the displacement nodes.