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 leading to 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.

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 least vibration, always appears at the closed end and an antinode, or point greatest vibration at 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, Arthur H.Benade. )

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"