§ 4. Vibrations of Rods free at Both Ends
Fig. 85.
Rods with both ends free are also capable of vibrating longitudinally, and producing musical tones. The investigation of this subject will lead us to exceedingly important results. Clasping a long glass tube exactly at its centre, and passing a wetted cloth over one of its halves, a clear musical sound is the result. A solid glass rod of the same length would yield the same note. In this case the centre of the tube is a node, and the two halves elongate and shorten in quick alternation. M. König, of Paris, has provided us with an instrument which will illustrate this action. A rod of brass, a b, Fig. 85, is held at its centre by the clamp s, while an ivory ball, suspended by two strings from the points, m and n, of a wooden frame, is caused to rest against the end, b, of the brass rod. Drawing gently a bit of resined leather over the rod near a, it is thrown into longitudinal vibration. The centre, s, is a node; but the uneasiness of the ivory ball shows you that the end, b, is in a state of tremor. I apply the rubber still more briskly. The ball, b, rattles, and now the vibration is so intense that the ball is rejected with violence whenever it comes into contact with the end of the rod.
§ 5. Fracture of Glass Tube by Sonorous Vibrations
When the wetted cloth is passed over the surface of a glass tube the film of liquid left behind by the cloth is seen forming narrow tremulous rings all along the rod. Now this shivering of the liquid is due to the shivering of the glass underneath it, and it is possible so to augment the intensity of the vibration that the glass shall actually go to pieces. Savart was the first to show this. Twice in this place I have repeated this experiment, sacrificing in each case a fine glass tube 6 feet long and 2 inches in diameter. Seizing the tube at its centre C, Fig. 86, I swept my hand vigorously to and fro along C D, until finally the half most distant from my hand was shivered into annular fragments. On examining these it was found that, narrow as they were, many of them were marked by circular cracks indicating a still more minute subdivision.
In this case also the rapidity of vibration is inversely proportional to the length of the rod. A rod of half the length vibrates longitudinally with double the rapidity, a rod of one-third the length with treble the rapidity, and so on. The time of a complete vibration being that required by the pulse to travel to and fro over the rod, and that time being directly proportional to the length of the rod, the rapidity of vibration must, of necessity, be in the inverse proportion.
Fig. 86.