ACOUSTICS suddenly drops down and roars. The sensitive point is at the orifice. Lord Rayleigh {Sound, ii. § 370), using as a source a “ bird-call,” a whistle of high frequency, formed a series of stationary waves by reflection at a flat surface. Placing the sensitive flame at different parts of this train, he found that it was excited, not at the nodes where the pressure varied, but at the loops where the motion was the greatest and where there was little pressure change. In his Sound (ii. chapter xxi.) he has given a theory of the sensitiveness. When the velocity of the jet is gradually increased there is a certain range of velocity for which the jet is unstable, so that any deviation from the straight rush-out tends to increase as the jet moves up. If then the jet is just on the point of instability, and is subjected at its base to alternations of motion, the sinuosities impressed on the jet become larger and larger as it flows out, and the flame is as it were folded on itself. Another form of sensitive jet is very easily made by putting a piece of fine wire gauze 2 or 3 inches above a pinhole burner and igniting the gas above the gauze. On adjusting the gas so that it burns in a thin column, just not roaring, it is extraordinarily sensitive to some particular range of notes, going down and roaring when a note is sounded. If a tube be placed over such a flame it makes an excellent singing tube. If a jet of water issues at an angle to the horizontal from a round pinhole orifice under a few inches pressure, it travels out as an apparently smooth cylinder for a short distance, and then breaks up into drops which travel at different rates, collide, and scatter. But if a tuning-fork of appropriate frequency be set vibrating with its stalk in contact with the holder of the pipe from which the jet issues, the jet appears to go over in one continuous thread. Intermittent illumination, however, with frequency equal to that of the fork shows at once that the jet is really broken up into drops, one for each vibration, and that these move over in a steady procession. The cylindrical form of jet is unstable if its length is more than tt times its diameter, and usually the irregular disturbances it receives at the orifice go on growing, and ultimately break it up irregularly into drops which go out at different rates. But, if quite regular disturbances are impressed on the jet at intervals of time which depend on the diameter and speed of outflow (they must be somewhat more than tt times its diameter apart), these disturbances go on growing and break the stream up into equal drops, which all move with the same velocity one after the other. An excellent account of these and other jets is given in Boys’ Soap Bubbles, Lecture III. The formation of beats (as described in O. A. § 102) may be illustrated by considering the disturbance at any point due to two trains of waves of equal amplitude a and of nearly equal frequencies nl n.2. If we Beats. measure the time from an instant at which the two are in the same phase the resultant disturbance is iets.eSaa later by Barrett {Phil. Mag. xxxiii. 1867, p. y = a sin 2™^ + a sin 2~n.,t 216). Barrett found that the best form of = Za cos tr{n^ - n2)t sm 2tt t, burner for ordinary gas pressure might be made of glass tubing about § inch in diameter contracted to an orifice which may be regarded as a harmonic disturbance of freyV inch in diameter, the orifice being nicked by a pair of quency (re + ^ )/2 but with amplitude 2a cos n2)t 1 2 scissors into a V-shape. The flame rises up from.the slowly varying with the time. Taking the square of the burner in a long thin column, but when an appropriate amplitude to represent the intensity or loudness of the note is sounded it suddenly drops down and thickens. sound which would be heard by an ear at the point, this is Barrett further showed by using smoke jets that the flame 4a2 cos2 7r(re1 — n^)t is not essential. Tyndall {Sound, Lecture YI. § 7 <?£ seq.) 2 = 2a {1 + cos 2-7r{n1 — n2)t}, describes a number of beautiful experiments with jets at higher pressure than ordinary, say 10 inches of water, a value which ranges between 0 and 4u2 with frequency issuing from a pinhole steatite burner. The flame may be nY - n2. The sound swells out and dies down - n2 16 inches high, and on receiving a suitably high sound it times per second, or there are - n2 beats per second. pipe open at both ends is vibrating in its simplest mode, the air is alternately closing into and out from the centre. During the quarter swing ending with greatest nodal pressure, the kinetic energy is changed to potential energy manifested in the increase of pressure. This becomes again kinetic in the second quarter swing, then in the third quarter it is changed to potential energy again, but now manifested in the decrease of pressure. In the last quarter it is again turned to the kinetic form. Now suppose that at the end of the first quarter swing, at the instant of greatest pressure, heat is suddenly given to the air. The pressure is further increased and the potential energy is also increased. There will be more kinetic energy formed in the return journey and the vibration tends to grow. But if the heat is given at the instant of greatest rarefaction, the increase of pressure lessens the difference from the undisturbed pressure, and lessens the potential energy, so that during the return less kinetic energy is formed and the vibration tends to die away. And what is true for Jthe extreme points is true for the half periods of which they are the middle points; that is, heat given during the compression half aids the vibration, and during the extension half damps it. Now let us apply this to the singing tube. Let the gas jet tube be of somewhat less than half the length of the singing tube, and let the lower end of the jet tube be in a wider tube or cavity so that it may be regarded as an “open end.” When the air in the singing tube is singing, it forces the gas in the jet tube to vibrate in the same period and in such phase that at the nozzle the pressure in both tubes shall be the same. The lower end of the jet tube, being open, is a loop, and the node may be regarded as in an imaginary prolongation of the jet tube above the nozzle. It is evident that the pressure condition will be fulfilled only if the motions in the two tubes are in the same direction at the same time, closing into and opening out from the nodes together. When the motion is upwards gas is emitted; when the motion is downwards it is checked. The gas enters in the half period from least to greatest pressure. But there is a slight delay in ignition, partly due to expulsion of incombustible gas drawn into the jet tube in the previous half period, so that the most copious supply of gas and heat is thrown into the quarter period just preceding greatest pressure, and the vibration is maintained. If the jet tube is somewhat longer than half the sounding tube there will be a node in it, and now the condition of equality of pressure requires opposite motions in the two at the nozzle, for their nodes are situated on opposite sides of that point. The heat communication is then chiefly in the quarter vibration just preceding greatest rarefaction, and the vibration is not maintained. When a flame is just not flaring, any one of a certain range of notes sounded near it may make it flare while the note is sounding. This was first noticed by Sensitive Leconte {Phil. Mag. xv. 1858, p. 235), and
