ON THE SOURCES AND EFFECTS OF SOUND. 297 



sound and the vibrations of the air in pipes, that they must he affected in 

 a swiilar manner by all alterations of temperature. Thus the frequency of 

 the vibrations of a pipe must be increased nearly in the ratio of 33 to 34 by 

 an elevation of 30 degrees of Fahrenheit's thermometer ; and if this change 

 be accompanied by a transition from dampness to simple moisture, the sound 

 will be still more altered. 



Dr. Chladni has discovered that solids of all kinds, when of a proper form, 

 are capable of longitudinal vibrations, exactly resembling in their nature 

 those of the air in an organ pipe, having also their secondary or harmonic 

 noter* related to them in a similar manner. These vibrations are always far 

 more frequent than those of a column of air of equal length, the velocity 

 with which an impulse is transmitted by a solid of any kind being usually 

 from 5 to 16 times as great as the velocity of sound in air, so that the 

 longitudinal sounds are always extremely acute when they are produced by 

 substances of moderate length. These sounds afford, perhaps, the most ac- 

 curate mode of determining the velocity of the transmission of an impulse 

 through any elastic substance, and of obtaining from that velocity the exact 

 measure of its elasticity ; they may be easily exhibited by holding a long 

 bar or wire of iron or brass in the middle, and striking it at one end with a 

 small hammer in the direction of its length. 



The vibrations by which solid bodies most usually produce sound are, 

 however, not longitudinal, but lateral, and they are governed either by a 

 tension derived from the operation of a weight, or of some other external 

 force, or by the natural elasticity of the substance. The vibrations of ex- 

 tended substances resemble most in their properties those of elastic fluids, 

 and they occur the most frequently in practice, although the vibrations 

 produced by the elasticity of the substance may be considered as the most 

 natural. 



Vibrations derived from tension are either those of cords or musical 

 strings, or those of membranes : but the vibrations of membranes afford 

 little variety, and have not hitherto been very accurately investigated, 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 



