Resonances of closed air columns

Closed Cylinder Air Column

封闭圆柱形空气柱

A closed cylindrical air column will produce resonant standing waves at a fundamental frequency and at odd harmonics. The closed end is constrained to be a node of the wave and the open end is of course an antinode. This makes the fundamental mode such that the wavelength is four times the length of the air column. The constraint of the closed end prevents the column from producing the even harmonics.

一个封闭的圆柱形空气柱会在基频和奇数倍谐波处产生共振的驻波。封闭端被约束为波的节点，而开放端当然是波的腹点。这使得基频模式的波长是空气柱长度的四倍。封闭端的约束阻止了该柱体产生偶数倍谐波。

Calculation

计算

The clarinet consists of an approximate closed cylinder, and this makes clarinet acoustics quite different from the other woodwind instruments. As can be seen from a sample waveform, the even harmonics missing from the tone, at least for the lower range of the instrument. The upper register of notes which may be played with this instrument start at the third harmonic of the air column rather than at the second harmonic as in the other woodwinds.

管乐由一个近似封闭的圆柱体组成，这使得管乐的声学特性与其他木管乐器有很大不同。从示例波形可以看出，音调中缺少偶次谐波，至少在乐器的低音区是如此。使用该乐器可以演奏的高音区的音符起始于空气柱的第三谐波，而不是像其他木管乐器那样起始于第二谐波。

Closed Cylinder Frequency

封闭圆柱体频率

In actual practice, the position of the antinode is slightly outside the open end, and an end correction of about 0.6 times the radius of the pipe should be added to the open end to get the effective acoustic length.

实际上，驻波的节点位置略在开口处之外，为得到有效的声学长度，应在开口处加上约0.6倍管径的端部修正。