Closed tube

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In the field of acoustics, a tone is created by the periodic vibrations of air applied to a resonator. There are several ways in music to create such vibrations. One of these is to use a closed tube and to blow across the end. This creates a Bernoulli, or "siphon", effect just below the open end or embouchure causing an effect called a Von Karman vortex street. The tube will resonate at a specific frequency, dependent on the length of the tube, the internal diameter and the pressure/velocity of the airstream across the open hole/embouchure. The internal cubic volume is the primary factor though.

A closed tube is a tube which is closed at one end. The tube resonates at a single fundamental frequency or note but can have overblown notes. These overblown registers can be tuned by using different degrees of conical taper. A closed tube resonates at the same fundamental frequency as an open tube twice its length or 1/4th of the keynote frequency wavelength. In a closed tube, a node or point of no vibration, always appears at the closed end and an antinode, or point greatest vibration at the Phi point (length X 0.618) near the open end (Sometimes called "nodes and waves" to avoid confusion).

By overblowing a cylindrical closed tube, a note is obtained that is an approximate twelfth above the fundamental note of the tube. This is sometimes described as a fifth above the octave of the fundamental note. For example, if the fundamental note of a closed pipe is c1, then overblowing the pipe gives g2, which is a twelfth above c1. Alternatively we can say that g2 is a fifth above c2 - the octave above c1. Adjusting the taper of this cylinder for a decreasing cone can tune the second harmonic or overblown note close to the octave position or 8th. (ref: Horns,Strings and Harmony, by Arthur H. Benade. ) Opening a small "speaker hole" at the Phi point, or shared "wave/node" position will cancel the fundamental frequency and force the tube to resonate at a 12th above the fundamental. This technique is used in a Recorder by pinching open the dorsal thumb hole.

A closed tube is called a "stopped pipe" in the organ.

[edit] References

Kool, Jaap, Das Saxophon. J. J. Weber, Leipzig. 1931. Translated by Lawrence Gwozdz in 1987, discusses "open" and "closed" tubes. Arthur H. Benade "Horns,Strings and Harmony"