Musical instruments
28 Vibrating air columns
Wind instruments
Wind instruments, like the flute and the trombone are made of tubes or pipes. How do these instruments work? What material is vibrating? What is the function of the pipe? How does the length of a pipe affect the pitch of the sound it produces?
A quick look at the orchestra reveals that instruments with longer pipes generally produce lower notes- compare the trumpet and the tuba, for instance. What’s actually happening?
Vibrating air columns
The air inside the pipes of a wind instrument vibrates. The tubing in a wind instrument confines the motion of the air inside it- the air particles must wiggle parallel to the walls of the pipe. The result is a longitudinal standing wave in the air column inside the pipe. The ends, whether open or closed, create nodes or antinodes.
On a string, the reason for nodes at the ends of standing wave on a string is obvious. Something (a person, the nut of a string instrument, etc.) holds the string and prevents it from vibrating. The cap on the closed end of a pipe does essentially the same thing by preventing air from leaving (or entering) the pipe. Air particles at the closed end don’t move at all, creating a displacement node. At displacement nodes, the density and the pressure of the air fluctuates wildly molecules crowd together and spread apart. As a result, displacement nodes are sometimes called pressure antinodes. The open end of a tube also acts a sort of clamp. Near the open end of a pipe, air molecules can enter or leave the tube easily. However, the pressure near the end of the tube must match the pressure in the room (which doesn’t fluctuate at all). As a result, particles near the end of the tube oscillate back and forth with large amplitude. The result is a displacement antinode. At displacement antinodes, the density of particles remains constant as the particles slosh back and forth across the equilibrium position. So, displacement antinodes are also pressure nodes. To see how this works, the reader is strongly encouraged to visit Dan Russell’s web page on standing waves in air columns [1] while rereading this paragraph, focusing on the animations that show the motion of air particles.
Different representations
Longitudinal waves are hard to draw, so many books show diagrams for air column standing waves that look like transverse waves. Instead of showing how the air particles are moving, these diagrams show graphs of displacement versus position along the direction of the column. Here’s what the diagrams usually look like:
The diagram summarizes the connections among particle motion, displacement and pressure for standing waves in air columns. All three diagrams show the fundamental mode of a pipe closed at one end. The bottom picture shows how the molecules move at different locations in the tube. Particles don’t move near the closed end of the tube, while particles near the open end vibrate back and forth. The next diagram up is called