ON THE VIBRATIONS OF RODS, PLATES, ETC. 121
the open organ pipe, is "with two nodes; the next, with three, and so on; the partials produced being those of the complete series, 1, 2, 3, 4, 5, &c.
2. Coming now to the lateral vibrations of rods, we find these may also be classified according as the rods are,—
(a) Fixed at both ends,
(b) Fixed at one end only,
(c) Free at both ends.
(a) A rod fixed at both ends, vibrates laterally in exactly the same manner as a string; that is, it may vibrate as a whole, forming one vential segment; or with a node in the centre, and two ventral segments; or, with two nodes, and three ventral segments, &c. The relative vibration rates are, however, very different, as may be seen from the following table :—
(b) In laterally vibrating rods fixed at one end, the vibration number varies inversely as the square of the length. Chladni endeavoured to utilize this fact, in ascertaining the vibration number of a musical sound. He first obtained a strip of metal of such a length, that its vibrations were slow enough to be counted. Suppose, for example, a strip is taken, 36 inches long, and that it vibrates once in a second. Seducing it to one-third that length, according to the above law, it will vibrate nine times per second. Reducing it to six inches, it will make 36 vibrations per second; to three inches, 144 vibrations; to one inch, 1,296 vibrations. By a little calculation, it is easy to find the vibration number of any intermediate length.
The relative rates of vibration of the partial tones of such rods, are very complex; the second partial is more than two octaves above the fundamental, and the others are correspondingly distant from one another. Examples of instruments, in which these lateral vibrations of rods fixed at one end are utilized, may be found in the musical box and the bell piano.
(c) The simplest mode in which a rod free at both ends can vibrate laterally, may be experimentally observed by grasping a lath some six feet long, with both hands, at about one foot from either end, and striking or shaking it in the centre. It will be found that there are two nodes, as shown in tig. 61, A- The next