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HAND-BOOK OF ACOUSTICS. |
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both ends, and
n the vibration number of the note it emits when vibrating longitudinally ; then, if V denote the velocity of sound in the substance of which the rod or wire is composed,The overtones of a wire fixed at both ends follow the ordinary series, 1, 2, 3, 4, 5, &c, the wire vibrating in two segments, with a node in the centre to produce the first overtone, and so on.
(b) The longitudinal vibrations of rods fixed at one end, present considerable analogy with those in stopped organ pipes. Thus the vibration number varies inversely as the length of the rod, as may be easily shown by fixing varying lengths of rod in a vice, and exciting them with a resined cloth. Again, the time required for a complete vibration, is the time during which a pulse makes two complete journeys up and down the rod. Thus, these vibrations may be used to ascertain the velocity of sound in any substance, the method of proceeding being similar to that explained above, but the formula will beThe partials obtainable from these rods, are, like those of a stopped organ pipe, the odd partials of the complete series, 1,3, 5, 7, &c.; the first overtone requiring a node, at a point one-third the length of the rod from the free end; the second at one-fifth of the length, and so on.
The only musical instrument in which this kind of rod vibration is utilized is Marloye's harp. It consists of a series of wooden rods of varying lengths, vertically fixed on a sound-board below. The rods are excited, by rubbing up and down with the resined fingers.
(c) In rods or tubes free at both ends, the simplest longitudinal vibrations are set up, when the tube is clasped or clamped at the centre, and excited by longitudinally rubbing either half : the simplest form of vibration is therefore, with one node in the centre. Hods so treated are analogous with open organ pipes. For example, the vibration number varies inversely as the length of the rod; and the time of a complete vibration is the same as that required for a pulse to run to and fro over the rod; so that here again the velocity of sound in the substance of which the rod is composed, may be ascertained by multiplying the vibration number of the note produced, by twice the length of the rod.
As just stated, the simplest form in which these rods can vibrate, is with one node in the centre ; the next simplest, as in the case of |
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