is closed, a double passage is not sufficient to complete the cycle of changes. The original state cannot be recovered until two reflections have occurred from the open end, and the pulse has travelled over four times the length of the pipe. To make the unstopped tube in the above experiment yield the same note as the stopped, it would be necessary to give it double the length. This law is universal, and may easily be explained.
Vibration may be set up in the column of air otherwise than by the blow above described. If a gentle stream of breath from the lips be sent obliquely across the open end of either an open or a stopped tube, an audible note results; indeed a common instrument, the Pandean pipe, acts on this principle. [See Pandean Pipes.] This may be also seen in the Nay or Egyptian Flute figured under that heading. In the organ pipe, a more complicated arrangement occurs. From the wind-chest a tube leads into a cavity, the only outlet of which is a linear crack forming the foot of the pipe. Just over this fissure, the wood or metal is cut away so as to leave a feather-edged portion communicating with the interior of the pipe, and exactly splitting the stream of wind. An explanation has of late been tendered as to the action here set up. The flat plate of compressed air blown through the slit is compared to the elastic material of a vibrating reed. In passing across the upper orifice it momentarily produces a slight exhaustive or suctional effect, tending to rarify the air in the lower part of the pipe. This, by the elasticity of air, soon sets up a corresponding compression, and the two allied states react upon the original lamina of air issuing from the bellows, causing it to communicate its motion to that within the pipe. Schneebeli drove air rendered opaque by smoke through a moveable slit. When it passed entirely outside the pipe, no sound was produced, but appeared when the issuing sheet was gently blown on at right angles to its direction, continuing until a counter current was produced by blowing down the upper orifice of the pipe. Little or no smoke penetrated into the pipe. If the sheet of air passed entirely into the pipe there was also no sound, but on blowing into the upper end, it was produced. He concludes that the Luft-Lamelle or air-lamina acts a part analogous to that of the reed in reed-pipes.
In all cases the air may assume several modes of undulation. In the Open Pipe the embouchure at which the wind enters is obviously a place of greatest motion, corresponding to the ventral segment of a string. So also will be the open upper extremity. Half-way between these, at the point where the two opposite motions meet and neutralise each other, will be a node or place of rest. In this instance the pipe will give its lowest or fundamental note. If the force of the current be increased, a shorter wave may be set in action, a node being established at one-fourth of the whole length from the embouchure, and another at the same distance from the top. The pipe then speaks its first harmonic, the octave of the fundamental. By a further windpressure three nodes may form, the first onesixth from the mouth, the third at a similar distance from the top, and the second half-way between the two, the pipe giving its second harmonic, a twelfth above the foundation.
In Stopped Pipes a different law obtains; for the waves have clearly to traverse the length of the tube twice, instead of once, being reflected by the closed end. This fact influences the position of the nodes. When the fundamental note is struck, the only node is at the stopped end. In sounding the first possible harmonic, another node is set up at one-third of the length from the open end. With the second harmonic, the first node forms at one-fifth of the length from the open end, the second dividing the lower four-fifths into two equal parts. In any case the stopped end must be a node; so that the second form of vibration of the open pipe, and all others which would render the stopper the centre of a loop or ventral segment, are excluded. Hence the harmonics of a stopped pipe follow the series of odd numbers, 1, 3, 5, etc. These relations were discovered by Daniel Bernouilli, and are generally known as the Laws of Bernouilli. In both stopped and open pipes the distance from an open end to the nearest node is a quarter wave-length of the note emitted. In the open pipe there is no further limitation; but in the case of the stopped pipe, the nearest node to the mouth must also be distant an even number of quarter wave-lengths from the stopped end, which is itself a node.
These laws hold good with pipes of which the bore is cylindrical or prismatic with parallel sides. It was shown by Wheatstone that a pipe of conical bore, while giving out a similar fundamental note to one of the same length of cylindrical shape, differs as regards the position of the nodes when emitting harmonic sounds. The first node in a conical pipe is not in the middle, but some distance towards the smaller end. It appears from modern observations that the laws of Bernouilli require correction. If an open pipe be stopped at one end, its note is not exactly an octave below that given by it when open, but about a major seventh. According to theory, the hypothesis is made that the change from constraint to a condition of no constraint takes place suddenly at the point where the wave-system leaves the pipe. This is not the case, and practically the open pipe is equivalent to one a little longer than its actual length, by about .635 of the radius of the pipe for the open end, and .59 for the mouth. Kundt has made some valuable researches on the influence of the diameter of a pipe on the velocity of sound within it, which are beyond our present limits. They are however fully discussed in Lord Rayleigh's 'Theory of Sound,' vol. ii. p. 55.
[ W. H. S. ]
PIRATA, Il. Opera in two acts; libretto by Romani, music by Bellini. Produced at the Scala, Milan, in the autum of 1827 [App. p.749 "on Oct. 27"]; in Paris at Theatre Italien, Feb. 1, 1832; in London, at the King's Theatre, April 17, 1830.
[ G. ]
