The Syren is an ingenious instrument, devised by M. Cagniard de la Tour, for ascertaining the number of pulsations in a second, corresponding to each pitch: the notes are produced by jets of air passing through small apertures, arranged at regular distances in a circle on the side of a box, before which a disc revolves pierced with the same number of holes. During a revolution of the disc the currents are alternately intercepted and allowed to pass as many times as there are apertures in it, and a sound is produced whose pitch depends on the velocity of rotation.
A glass or metallic rod, when struck at one end, or rubbed in the direction of its length with a wet finger, vibrates longitudinally, like a column of air, by the alternate condensation and expansion of its constituent particles, producing a clear and beautiful musical note of a high pitch, on account of the rapidity with which these substances transmit sound. Rods, surfaces, and, in general, all undulating bodies, resolve themselves into nodes. But in surfaces the parts which remain at rest during their vibrations are lines which are curved or plane according to the substance, its form, and the mode of vibration. If a little fine dry sand be strewed over the surface of a plate of glass or metal, and if undulations be excited by drawing the bow of a violin across its edge, it will emit a musical sound, and the sand will immediately arrange itself in the nodal lines, where alone it will accumulate and remain at rest, because the segments of the surface on each side will be in different states of vibration, the one being elevated while the other is depressed; and, as these two motions meet in the nodal lines, they neutralise one another. These lines vary in form and position with the part where the bow is drawn across, and the point by which the plate is held. The motion of the sand shows in what direction the vibrations take place. If they be perpendicular to the surface, the sand will be violently tossed up and down till it finds the points of rest. If they be tangential, the sand will only creep along the surface to the nodal lines. Sometimes the undulations are oblique, or compounded of both the preceding. If a bow be drawn across one of the angles of a square plate of glass or metal held firmly by the centre, the sand will arrange itself in two straight lines parallel to the sides of the plate, and crossing in the centre so as to divide it into four equal squares, whose motions will be contrary to each other. Two of the diagonal squares will make their excursions on one side of the plate, while the other two make their vibrations on the other side of it. This mode of vibration produces the lowest tone of the plate (N. 183). If the plate be still held by the centre, and the bow applied to the middle of one of the sides, the vibrations will be more rapid, and the tone will be a fifth higher than in the preceding case: now the sand will arrange itself from corner to corner, and will divide the plate into four equal triangles, each pair of which will make their excursions on opposite sides of the plate. The nodal lines and pitch vary not only with the point where the bow is applied, but with the point by which the plate is held, which being at rest necessarily determines the direction of one of the quiescent lines. The forms assumed by the sand in square plates are very numerous, corresponding to all the various modes of vibration. The lines in circular plates are even more remarkable for their symmetry, and upon them the forms assumed by the sand may be classed in three systems. The first is the diametrical system, in which the figures consist of diameters dividing the circumference of the plate into equal parts, each of which is in a different state of vibration from those adjacent. Two diameters, for example, crossing at right angles, divide the circumference into four equal parts; three diameters divide it into six equal parts; four divide it into eight, and so on. In a metallic plate, these divisions may amount to thirty-six or forty. The next is the concentric system, where the sand arranges itself in circles, having the same centre with the plate; and the third is the compound system, where the figures assumed by the sand are compounded of the other two, producing very complicated and beautiful forms. Galileo seems to have been the first to notice the points of rest and motion in the sounding-board of a musical instrument; but to Chladni is due the whole discovery of the symmetrical forms of the nodal lines in vibrating plates (N. 184).