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V. § 54.] MOTION OF A SOUNDING STRING. 107
of vibration are inversely proportional to their lengths. The reader should observe that it has been throughout this discussion assumed that the material, thickness and tension of the tube, or tubes, in question were subject to no variation whatever. Any changes in these would correspondingly affect the rates of vibration produced.
54. We are now prepared to examine the motion of a sounding string. Its ends are fastened to fixed points of attachment and the string is excited at some intermediate point, by plucking it with the finger, as in the harp and guitar, by striking it with a soft hammer, as in the pianoforte, or by stroking it with a resined bow, as in the violin and other instruments of the same class. The impulses thus set up are reflected at the extremities of the string (in the violin at the bridge and at the finger of the performer) and behave towards each other exactly as in the case of the vibrating tube considered above. The results there at once obtained are accordingly applicable to the case before us. The string may vibrate in a single segment as in Fig. 26. This is the form of slowest vibration with a string of given length, material and tension. Accordingly, when thus vibrating, the string produces the deepest note of which, all other conditions remaining the same, it is capable. The string may also vibrate in the