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On the Vibrations of Eods, Plates, &o
As the musical instruments treated of in the present chapter are of comparatively less importance than those already studied, the principles which they involve will be more briefly touched on. We shall first consider the
Vibrations of Eods or Bars. A Eod is capable of vibrating in three ways (the last however being of little importance, musically speaking), viz.
1.    Longitudinally.
2.    Laterally.
3.    Torsionally.
1. Longitudinal vibrations again may be classified according as the rod is
(a)   Fixed at both ends.
(b)    Fixed at one end only, (e) Free at both ends.
(a) The Longitudinal vibrations of a rod or wire, fixed at both ends, may be studied on the monochord, by passing briskly along the wire, a cloth, which has been dusted with powdered resin. The sound produced is much higher in pitch than that obtained by causing the wire to vibrate transversely. On stopping the wire at the centre, and rubbing one of the halves, the upper octave of the sound first heard, is emitted. When the wire is stopped at one third its length, and this third excited, the fifth above the last is heard; and so on. Thus, as in the case of transverse vibrations, the vibration number varies inversely as the length of the wire. On altering the tension, the pitch will not be found to have varied ; that is, the pitch is independent of the tension.