SOUND. 



the fimpleft fources of a mufical found ; the walls being 

 parallel, the impulfe is reflefted backwards and forwards 

 continually, at equal intervals of time, fo as to produce the 

 effeft of a mufical found. When we blow obliquely and uni- 

 formly into a cylindrical pipe clofed at one end, the impulfe 

 or condenfation mult probably travel to the bottom and 

 back, before the refiftance is increafed ; the current of our 

 breath will then be diverted from the mouth of the pipe, 

 for an equal time, which will be required for the diminu- 

 tion of the refiftance by the difcharge of the condenfed air, 

 fo that the whole time of a vibration will be equal to the 

 time occupied by an impulfe of any kind in pafling through 

 four times the length of the pipe. An open pipe may be 

 confidered nearly as if it confiited of two fuch pipes, united 

 at their clofed ends ; the portions of air contained by them 

 being agitated by contrary motions, fo as always to afford 

 each other a refiftance fimilar to that which the bottom of 

 the ftopped pipe would have furnifhed. It is probable, 

 fays Dr. Young, that when an open pipe is once filled with 

 air a little condenfed, the oblique current is diverted, until 

 the effeft of the difcharge, beginning at the remoter end, 

 has returned to the inflated orifice, and allowed the cur- 

 rent to re-enter the pipe. Where the diameter of the pipe 

 is different at different parts of its length, the inveftigation 

 of the found becomes much more intricate ; but it has been 

 purfued by M. Daniel Bernouilli with confiderable fuccefs, 

 although upon fuppofitions, fays Young, not llriftiy con- 

 flftent with the aftual ilate of the motions concerned. 



In the fame manner as an open pipe is divided by an 

 imaginary bafis, fo as to produce the fame found with a 

 ftopped pipe of half the length, a pipe of any kind is 

 capable of being fubdivided into any number of fuch pipes, 

 fuppofed to meet each other's correfponding ends only ; 

 and in general the more violently the pipe is inflated, the 

 greater is the number of parts into which it fubdivides 

 itfelf, the frequency of the vibrations being always pro- 

 portional to that number. Thus, an open pipe may be 

 divided not only into two, but alfo into four, fix, eight, or 

 more portions, producing the fame founds as a pipe of one- 

 half, one-third, one-fourth, or any other aliquot part of 

 the length ; but a ftopped pipe cannot be divided into any 

 even number of fimilar parts ; its fecondary founds being 

 only thofe of a pipe of which the proportion is determined 

 by the odd numbers, its length being, for example, one- 

 third, one-fifth, or one-feventh of the original length. 

 Thefe fecondary notes are fometimes called harmonics ; 

 they are not only produced in fucceffion from the fame 

 pipe, but they are alfo often faintly heard together, while 

 the fundamental note of the pipe continues to found. When 

 the pipe has a large cavity connefted with it, or confifts 

 principally of fuch a cavity, with a fmall openine, its vibra- 

 tions are ufually much lefs frequent, and it is generally in- 

 capable of producing a regular feries of harmonics. 



It is obvious, from this ftatement of the analogy between 

 the velocity of found and the vibrations of the air in pipes, 

 that they muft be affefted in a fimilar manner by all altera- 

 tions of temperature. Thus, the frequency of the vibra- 

 tions of a pipe muft be increafed nearly in the ratio of 33 

 to 34 by an elevation of 30 degrees of Fahrenheit's ther- 

 mometer ; and if this change be accompanied by a tranfition 

 from dampnefs to fimple moifture, the found will be ftiU 

 more altered. 



Dr. Chladai has difcovered that folids of all kinds, when 

 of a proper form, are capable of longitudinal vibrations, 

 cxaAly refembhng in their nature thofe of the air in an 

 organ-pipe, having alfo their fecondary or harmonic notes 

 related to them in a fimilar manner. Thefe vibrations are 



always far more frequent than thofe of a column of air of 

 equal length, the velocity with which an impulfe is tranf- 

 mitted by a folid of any kind, being ufually from 5 to 16 

 times as great as the velocity of found in air ; fo that the 

 longitudinal founds are always extremely acute, when they 

 are produced by fubftances of moderate length. Thefe 

 founds afford perhaps the moft accurate mode of deter- 

 mining the velocity of the tranfmiffion of an impulfe through 

 any elaftic fubftance, and of obtaining from that velocity 

 the exaA meafure of its elafticity : they may be eafily ex- 

 hibited by holding a long bar or wire of iron or brafs in 

 the middle, and ftriking it at one end with a fmall hammer 

 in the direftion of its length. 



The vibrations by which folid bodies moft ufually pro- 

 duce found, are, however, not longitudinal, but lateral, 

 and they are governed either by a tenfion, derived from the 

 operation of a weight, or of fome other external force, or 

 by the natural elafticity of the fubftance. The vibrations 

 of extended fubftances referable molt in their properties 

 thofe of elaftic fluids, and they occur the moft frequently 

 in praftice, although the vibrations produced by the elafti- 

 city of the fubftance may be confidered as the moft natural. 

 See String and Vibration. 



Sound is the objeft of mufic ; which is nothing but the 

 art of applying founds, under fuch circumftances of tone 

 and time, a^ to raife agreeable fenfations. 



The principal affeftion of found, by which it becomes 

 fitted to have this end, is that by which it is dillinguifhed 

 into acuti and grave. 



This difference depends on the nature of the fonorous 

 body ; the particular figure and quantity of it ; and even, 

 in fome cafes, on the part of the body where it is ftruck ; 

 and this is that which conftitutes what we call different 

 tones. 



The caufe of this difference appears to be no other than 

 the different velocities of the vibrations of the founding 

 body. In effeft, the tone of a found is found, by abun- 

 dance of experiments, to depend on the nature of thofe 

 vibrations, whofe difference we can conceive no otherwile 

 than as having different velocities : and fince it is proved, 

 that the fmall vibrations of the fame chord or (tring are 

 all performed in equal time, and that the tone of a found, 

 which continues for fome time after the ftroke, is the fame 

 from firit to laft, it follows, that the tone is neceffarily 

 connefted with a certain quantity of time in making each 

 vibration or each wave ; or that a certain number of vibra- 

 tions or waves, accomplifhed in a given time, conftitute a 

 certain and determinate tone. From this principle are all 

 the phenomena of tune deduced. 



If the vibrations be ifochronous, the found is called 

 mufical, and is faid to continue at the fame pitch ; and 

 is faid to be acuter, fharper, or higher, than any other 

 found, whofe vibrations are flower and graver, and flatter 

 or lower, than any other whofe vibrations are quicker. See 

 Unison. 



From the fame principle arifc what we call concords, &c. 

 which are nothing but the refults of frequent unions and 

 coincidences of the vibrations of two fonorous bodies, and 

 confequently of the waves and undulating motions of the 

 air occationed by them. 



On the contrary, the refult of lefs frequent coincidences 

 of thofe vibrations is what we call a S/cord. 



Another confiderable diftinftion of found, with regard 



to mufic, is that by which they are denominated long and 



Jhort ; not with regard to the fonorous body's retaming a 



motion, once received, a longer or a lefs time, though 



gradually growing weaker, but to the continuation of the 



impulfe 



