§ 1 Longitudinal Vibrations of Wires and Rods: Conversion of Longitudinal Into Transverse Vibrations
We have thus far occupied ourselves exclusively with transversal vibrations; that is to say, vibrations executed at right angles to the lengths of the strings, rods, plates, and bells subjected to examination. A string is also capable of vibrating in the direction of its length, but here the power which enables it to vibrate is not a tension applied externally, but the elastic force of its own molecules. Now this molecular elasticity is much greater than any that we can ordinarily develop by stretching the string, and the consequence is that the sounds produced by the longitudinal vibrations of a string are, as a general rule, much more acute than those produced by its transverse vibrations. These longitudinal vibrations may be excited by the oblique passage of a fiddle-bow; but they are more easily produced by passing briskly along the string a bit of cloth or leather on which powdered resin has been strewed. The resined fingers answer the same purpose.
When the wire of our monochord is plucked aside, you hear the sound produced by its transverse vibrations. When resined leather is rubbed along the wire, a note much more piercing than the last is heard. This is due to the longitudinal vibrations of the wire. Behind the table is stretched a stout iron wire 23 feet long. One end of it is firmly attached to an immovable wooden tray, the other end is coiled round a pin fixed firmly into one of our benches. With a key this pin can be turned, and the wire stretched so as to facilitate the passage of the rubber. Clasping the wire with the resined leather, and passing the hand to and fro along it, a rich, loud musical sound is heard. Halving the wire at its centre, and rubbing one of its halves, the note heard is the octave of the last: the vibrations are twice as rapid. When the wire is clipped at one-third of its length and the shorter segment rubbed, the note is a fifth above the octave. Taking one-fourth of its length and rubbing as before, the note yielded is the double octave of that of the whole wire, being produced by four times the number of vibrations. Thus, in longitudinal as well as in transverse vibrations, the number of vibrations executed in a given time is inversely proportional to the length of the wire.
And notice the surprising power of these sounds when the wire is rubbed vigorously. With a shorter length, the note is so acute, and at the same time so powerful, as to be hardly bearable. It is not the wire itself which produces this intense sound; it is the wooden tray at its end to which its vibrations are communicated. And, the vibrations of the wire being longitudinal, those of the tray, which is at right angles to the wire, must be transversal. We have here, indeed, an instructive example of the conversion of longitudinal into transverse vibrations.