Text: 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. The rule just given, although approximately true in the case of narrow pipes, cannot be depended upon, when the diameter of the pipe is any considerable fraction of its length. The following rule quoted from Ellis' "History of Musical Pitch" is much more accurate. Divide 20,080 when the dimensions are in inches, and 510,000 when the dimensions are in millimetres, by:- (1). Three times the length, added to five times the diameter, for cylindrical open pipes. (2). Six times the length, added to ten times the diameter, for cylindrical stopped pipes. (3). Three times the length, added to six times the depth (internal from front to back), for square open pipes. (4). Six times the length, added to twelve times the depth, for square stopped pipes. As a matter of fact, however, the note produced by a stopped pipe is not exactly the octave of an open pipe of the same length: in fact, it varies from it by about a semitone." [Handbook of Acoustics, page 99]

See Also:

Source: