Text: In order that a column of air, in cylindrical tube open at both ends, may vibrate in unison with a given sound, the length of the tube must be approximately one half the length of the corresponding sound wave. If the tube be closed at one end, its length must be one fourth that of the sound wave. In both cases the diameter of the tube should not exceed one sixth the length. (The vibration number of the sound produced by an open pipe, may be found, by dividing the velocity of sound by twice the length of the pipe; that of a stopped pipe, by dividing by four times its length. In the latter case the internal length must be measured, as "length of pipe" really means, the length of the vibrating column of air.) [Handbook on Acoustics, page 99]

See Also: ACOUSTICS §14, 15, 16

Source: 68