3.1 Standing waves and wind instruments

Introduction

A wind instrument makes a tone when a standing wave of air is created inside it. In most wind instruments, a vibration that the player makes at the mouthpiece is picked up and amplified and given a pleasant timbre by the air inside the tube-shaped body of the instrument. The shape and length of the inside of the tube give the sound wave its pitch as well as its timbre.

You will find below a discussion of what makes standing waves in a tube , wind instruments and the harmonic series , and the types of tubes that can be used in musical instruments . This is a simplified discussion to give you a basic idea of what's going on inside a wind instrument. Mathematical equations are avoided, and all the complications - for example, what happens to the wave when there are closed finger holes in the side of the tube - are ignored. Actually, the physics of what happens inside real wind instruments is so complex that physicists are still studying it, and still don't have all the answers. If you want a more in-depth or more technical discussion, there are some recommendations below .

If you can't follow the discussion below, try reviewing Acoustics for Music Theory , Standing Waves and Musical Instruments , Harmonic Series I , and Wind Instruments: Some Basics

What makes the standing waves in a tube

As discussed in Standing Waves and Musical Instruments , instruments produce musical tones by trapping waves of specific lengths in the instrument. It's pretty easy to see why the standing waves on a string can only have certain lengths; since the ends of the strings are held in place, there has to be a node in the wave at each end. But what is it that makes only certain standing waves possible in a tube of air?

To understand that, you'll have to understand a little bit about what makes waves in a tube different from waves on a string. Waves on a string are transverse waves . The string is stretched out in one direction (call it "up and down"), but when it's vibrating, the motion of the string is in a different direction (call it "back and forth"). Take a look at this animation . At the nodes (each end, for example), there is no back and forth motion, but in between the nodes, the string is moving back and forth very rapidly. The term for this back-and-forth motion is displacement . There is no displacement at a node; the most displacement happens at an antinode .

Transverse motion on a string

The standing waves of air in a tube are not transverse waves. Like all sound waves, they are longitudinal . So if the air in the tube is moving in a certain direction (call it "left and right"), the vibrations in the air are going in that same direction (in this case, they are rushing "left and right").

But they are like the waves on a string in some important ways. Since they are standing waves, there are still nodes - in this case, places where the air is not rushing back and forth. And, just as on the string, in between the nodes there are antinodes, where the displacement is largest (the air is moving back and forth the most). And when one antinode is going in one direction (left), the antinodes nearest it will be going in the other direction (right). So, even though what is happening is very different, the end result of standing waves "trapped" in a tube will be very much like the end result of standing waves "trapped" on a string: a harmonic series based on the tube length.