PIPE. A column of air contained in it tube and maintained in a state of vibration yields a musical sound, depending upon its length and ( slightly) upon the state of the atmosphere. Our object in the present article is to give such an account of the theory of a musical pipe as may, with the articles Acorsries, Conn, Ileneoeles, SCALE, TEMPERAM ENT, lec., complete the statement of the leading principles of sound and the doctrines of music.
In this subject a distinct line should be drawn between those eir curnstances which are of easy and difficult explanation : for example, to a person who thoroughly under-kande the composition of waves moving In opposite directions [Aeourries ], it is not difficult to point out what the state of a pipe must be when in musical vibration; but to explain how the action of a current of air, as in the common flute, or the joint action of the air and a reed, as in the clarionet or reed•stops of an organ, produces and maintains this state of vibration, is quite another thing.
We shall first consider the pipe in a state of continued sonorous vibration (uo matter how produced), yielding the lowest note which it will give : let it be a simple pipe open at both ends, and let it be sounding, say the C of the treble clef, which note requires 258 double vibrations per second. If we now remember that the air at the two extremities is in communication with the outer air, we see that no condensation or rarefaction can take place at those extremities, or only very small ones compared with those which take place in the interior of the tube. To get approximately at the conditions of vibration, let us suppose that no condensation or rarefaction takes place at the extremities. We then see [Acousncs] that the state of the pipe, its two extremities never being condensed or rarefied, is as it would be if two waves of sound were travelling in opposite directions, every particle of the interior being affected by the joint condensations and velocities of both. Moreover, the distance between two uncondensed particles is always the whole length of the wave of condensation or that of rare faction, or a multiple of this length ; that is, the pipe must be either the half-length of a double wave or a multiple of this half-length. When the pipe sounds the lowest note, it must give the longest wave ; that is, the length of the pipe must be that of the simple wave of con. densation or rarefaction. Hence, the lowest note which a pipo can yield, which is called its fundamental note, is that belonging to a double wave of sound which is double of its length. Each double wave
answers to a complete or double vibration of a string.
To compare this result with practice, let us suppose sound to travel at the rate of 1125 feet per second (temperature 62° Fahr.). The note C having 253 double vibrations per second, this 1125 feet must contain 258 double waves, or each double wave must be 4 36 feet. The single wave then is 2.18 feet, or 2 feet 2 inches and '16 of an inch, which is the theoretical length of the pipe. Now the organ-builders say 2 feet (Onanis, Coxsracc-rion os) but this of course is a rough description, since the French organ-builders also say 2 feet (according to Biot), and the French foot is longer than the English. Further on in the article referred to we see 2 feet 2 inches given as the length of this o in an open pipe (the dulciana), and 1 foot 1 inch in a stopped pipe (the stopped diapason), which, as we shall presently see, ought to be half as long as an open pipe. The common flute, when everything is stopped, gives this same c, and the length from the embouchure (or mouth-hole) to the end of the instrument is a little more than 2 feet, but certainly never 2 feet 2 inohes. It moat be remembered however that this instrument is made up of the flute (so called) and the player, whose lips, when they come over the embouchure, confine the air, and are equivalent to a slight lengthening of the pipe. It is not the man ner of blowing which does this, but the approach of the lips, as may be thus shown. Take a common flute, and without holding it to the lips, strike the uppermost hole with the finger; a faint sound will be heard. Now approach the lips to the embouchure, but without blow ing, and then strike the same hole with the finger; another faint sound will be heard, decidedly flatter than the furinar. It is well known to those who pinyon this instrument (to those who play in tune at least) that drawing the lips back, so as not so much to confine the air contiguous to the embouchure, sharpens the tone, and what some persons call humouring the instrument means continual alteration of the position of the lips, so as to shorten or lengthen the pipe by turns, according to the note to be sounded. It I. also well known to players that this humouring can be carried to a much greater extent with the high notes than with the low notes ; but so little were the practical musicians in connection with the theoretical in the time of Daniel Bernoulli (who first gave the mathematical theory of this subject), that this eimple fact was only discovered by him from a new and some what complicated experiment.