Thus far plates of glass have been employed held by a clamp at the centre. Plates of metal are still more suitable for such experiments. Here is a plate of brass, 12 inches square, and supported on a suitable stand. Damping it with the finger and thumb of my left hand at two points of its edge, and drawing the bow with my right across a vibrating portion of the opposite edge, the complicated pattern represented in Fig. 67 is obtained.
Fig. 68.
The beautiful series of patterns shown on page 182 were obtained by Chladni, by damping and exciting square plates in different ways. It is not only interesting but startling to see the suddenness with which these sharply-defined figures are formed by the sweep of the bow of a skilful experimenter.
§ 8. Wheatstone’s Analysis of the Vibrations of Square Plates
And now let us look a little more closely into the mechanism of these vibrations. The manner in which a bar free at both ends divides itself when it vibrates transversely has been already explained. Rectangular pieces of glass or of sheet metal—the glass strips of
Fig. 69. the harmonica, for example—also obey the laws of free rods and bars. In Fig. 69 is drawn a rectangle a, with the nodes corresponding to its first division marked upon it, and underneath it is placed a figure showing the manner in which the rectangle, looked at edgewise, bends up and down when it is set in vibration.[42] For the sake of plainness the bending is greatly exaggerated. The figures b and c indicate that the vibrating parts of the plate alternately rise above and fall below the average level of the plate. At one moment, for example, the centre of the plate is above the level and its ends below it, as at b; while at the next moment its centre is below and its two ends above the average level, as at c. The vibrations of the plate consist in the quick successive assumption of these two positions. Similar remarks apply to all other modes of division.
Now suppose the rectangle gradually to widen, till it becomes a square. There then would be no reason why the nodal lines should form parallel to one pair of sides rather than to the other. Let us now examine what would be the effect of the coalescence of two such systems of vibrations.