A Course of Lectures on Natural Philosophy and the Mechanical Arts Volume 1 (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1845 Excerpt: ... the drum being almost the only instrument in which they are concerned; they do not however appear to differ materially in their properties from the vibrations of strings. A musical string or cord is supposed to be perfectly flexible, and of uniform thickness, to be stretched between two fixed points by a force incomparably greater than its own weight, and to vibrate in a single plane through a minute space on each side of its natural position. Its motions may then be traced through all their stages, by comparing the cord to a portion of an elastic medium of the same length, contained between two bodies capable of reflecting any impulse at each end; for example, to a portion of air situated between two walls, or inclosed in a pipe stopped at both ends; for the vibration of such a medium will be performed in the time occupied by any impulse in travelling through twice its length; and the vibration of the cord will be performed in the same time, supposing the height or depth of the medium equal to the length of a, portion of the cord, of which the weight is equivalent to the force applied to stretch it, and which may be called with propriety the modulus of the tension. If the cord be at first bent into a figure of any kind, and then set at liberty, the place of any part of it at every subsequent time, will' be such, that it will always be in a right line between two points moving along the figure each way with the appropriate velocity; but in order to pursue this determination, we must repeat the figure of the cord on each side of the fixed points in an inverted position, changing the ends as well as the sides. Hence it appears that, at the end of a single vibration, the whole cord will assume a similar figure on the opposite side of its natural place, but in...