100 HAND-BOOK OF ACOUSTICS.
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.
The pitch of a pipe is also affected by the pressure of the wind. The above rule supposes this pressure to be capable of supporting a column of water nches high. If this pressure be reduced to the vibration number diminishes by about 1 in 300; if increased to 4, it rises by about 1 in 440. The pitch is also affected by the size of the wind slit and the orifice at the foot: by the shape and shading of the embouchure; and by the pressing in or pressing out of the edges of its open end, as by the "tuning cone."
As already stated, the velocity of sound in air, at 0° Centigrade, or 32° Fahrenheit, is 1,090 feet per second, increasing about two feet for every rise of temperature of 1° C. and about one foot for 1° F. The velocity of sound at any temperature may be more accurately determined from the formula
where t is the centigrade temperature and a = the coefficient
of expansion of gases. Now, as the vibration numbers of the sounds emitted from stopped and open pipes may be approximately found by dividing the velocity of sound by four times and twice their lengths respectively, it is evident that such vibration numbers will vary with the temperature; the higher the temperature, the sharper the pitch, and vice versa. Furthermore, the length of the