ON THE VIBRATIONS OF RODS, PLATES, ETC. 119 |
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The longitudinal vibrations of a wire fixed at both ends, somewhat resemble those that take place in an open organ pipe. In both cases, the time of a complete vibration is the time taken by a pulse to move through the length of the wire or pipe, and back again. In the case of the latter, we have seen, that the vibration number of the note produced by any given pipe, may be ascertained by dividing the velocity of sound in air, by twice the length of the pipe. Conversely, if we know the vibration number of the pipe, we can ascertain the velocity of sound in air, by multiplying this number by twice the length of the pipe. This principle may be employed to determine the velocity of sound in other gases. Thus, fill and blow the pipe with hydrogen, instead of air, and ascertain the pitch of the note produced: its vibration number multiplied by twice the length of the pipe, will give the velocity of sound in hydrogen. Or we may proceed thus; blow one pipe with air, and another with hydrogen, the latter pipe being furnished with telescopic sliders, so that its length can be altered at pleasure. Now while both pipes are sounding, gradually lengthen the pipe, till both are in unison. When this is the case, let
I denote the length of the air sounding pipe, andthe length of the other: then if V be the velocity of sound in air, and its velocity in hydrogen, it is evident that—from whichmay be readily calculated. In this way, the velocity of sound in the various gases has been ascertained.
Now from what has been said above, it will be seen, that this same method may be applied, in order to ascertain the velocity of sound in solids. For example, suppose we wish to ascertain the velocity of sound in iron. Stretch some twenty feet of stout iron wire between two fixed points, one of which is movable: a vice, the jaws of which are lined with lead answers very well. Rub the wire with a resined piece of leather, and gradually shorten it till the sound produced is in unison with a C tuning-fork, the vibration number of which is, say, 512. "When the unison point is reached, measure the length of wire : say it is 16| feet. Then the time of a complete vibration is the time required for the pulse to run through 2 X =33 feet of the wire. But there are 512
vibrations or pulses per second : therefore sound travels along the iron wire at the rate of 512 X 33 = 16,896 feet in a second. Generally, let I denote the length, in feet, of a wire or rod fixed at |
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