ACOUSTICS. 



ACOUST1' 



great elasticity of the gum which are duwngaged by igniting the 

 gunpowder, forces the nir forward* out uf the gun, which the instant 

 afterwards ia allowed to return. If fenthers or dust be flonting in the 

 .-u'r, they hve bean obMrved to more forward*, and then back again, 

 just aa we have found the particles of air around them would do in 

 the ooime at a double wave. The intensity or loudness of the sound 

 seems to depend u|Hin the greatest absolute velocity of the particlex. 

 ml not at all upon the velocity of propagation, winch is found to he 

 the same for all sound*. TliitK in a musical chonl. spring m- ilniin. 

 the harder the metal or parchment is struck, tin- louder is the Bound, 

 but without any difference of tone, character, or velocity of propagation. 

 There is no instrument of which the nound may not be made louder 

 or weaker without any other change than giving greater velocity t the 

 immediate cause of sound. We will not enter further into this part 

 of the subject than to observe, that, generally speaking, we arc not 

 authorised to say that sound travels with equal loudnecx in all 

 directions. It might do HO in the case where it was communicated 

 by the sudden contraction and expansion of an elastic sphere, as above 

 supposed ; but this is a supposition which we cannot put in practice. 

 If a tuning fork be sounded and turned round in the hand while held 

 up before the ear, very perceptible diminutions and augmentations of 

 Kindness will be perceived. This is however explained othtrtmte on 

 the principle of Interference, by the fact that when the branches 

 coincide, or are equidistant from the ear, the waves of sound combine 

 their effects, while in all intermediate positions, as they reach the ear 

 in different phases of -vibration, they interfere, and produce partial 

 silence. 



The immediate communicator of sound ia the tympanum or drum of 

 the ear, an elastic membrane, which in set in vibration by the motion 

 of the particles of air against it, and vibrates in the same time with 

 them. From thin membrane vibrations are communicated to the fluid 

 filling the labyrinth of the ear, through the air in the tympanic cavity, 

 and probably not, as was formerly supposed, through the delicate chain 

 of bones connecting them. [EAR, in NAT. HIST. Drv. of ENG. CYC.] 

 We might expect, that when the wave of sound is of considerable 

 length, we should hear its different parts, that i, feel a difference be- 

 tween the beginning aud i-nd where the velocities and compressions 

 are small, and the middle where they are greatest. This happens to 

 a .-mall extent in the difference, for example, between the ' roar ' of a 

 camion and the ' report ' of a musket. No explanation can convey a 

 better idea of the difference than these two words. These simple 

 uncontinuing sounds are the result of few waves, there being no cause 

 for their continuance. 



We have not space in this article for any discussion of the manner 

 in which sounds are conveyed through other bodies besides air, for 

 which see VIBRATION. Noises conveyed through solid bodies travel in 

 general more quickly, and are heard better ; the scratch of a pin may 

 be distinctly perceived through a long spar of wood, though inaudible 

 by the person who makes it. With regard to gases, both theory and 

 experiment agree in enabling us to assert, that any two of the same 

 pressure and temperature, (that is, where the barometer aud the 

 thermometer would present similar indication* in each gas,) convey 

 nound with velocities which are inversely as their densities. Thus, air 

 being about fifteen times as heavy as hydrogen, the velocity of propa- 

 gation in the latter is about fifteen times that in the former. Such a 

 result cannot be directly submitted to experiment ; but, as we shall 

 see in the article Pips, there are methods equally certain for ascer- 

 taining the truth. 



The velocity of sound hail been determined by experiment before 

 the time of Newton, who gave the first mathematical solution of the 

 question, with the following result ; that if the atmosphere, instead of 

 decreasing in density as we ascend it, were all to be reduced to the 

 density at the earth's surface, but to be so diminished in height, that 

 the pressure at the earth's surface should not be altered, the velocity 

 -f propagation would be that acquired by a heavy body falling nnre- 

 xisted from half the height of this homogcMotu atmosphere. This 

 reasoning, however, gave the velocity nearly one-tizth too small ; and 

 the cause of the difference was afterwards supplied by the sagacity of 

 Laplace. This we shall try to explain. We know that air and all 

 gases resist compression, and will expand themselves if the pressure of 

 the superincumbent atmosphere be removed. This tendency is what 

 we mean by the elastic forre of the air or gas. If we take a column of 

 air reaching from the earth's surface to the top of the atmosphere, the 

 elastic force at any one stratum in equal to the weight of the superin- 

 cumbent column, since It balance* that weight. Moreover, it in 

 observed, that, at Oa mne Itmperntmrt*, the elastic forces of two 

 different strata are as their dtnuititt, that is, for air of half the density 

 of common air, the elastic force U only half as great, and so on. It is 

 also observed that any increase of temperature increases the elastic force 

 if the density remain the name, ami also that compression always increases 

 the temperature ; and rier vend. If, therefore, a vessel of air were 

 preesed into half iU dimensions, it would double its elastic force from 

 the condensation, which would also receive a further addition from 

 the increase of temperature. Again, 'if the same were rarefied into 

 double H first dimension*, the elastic force would be halved by the 

 rarefaction, and receive a further decrease from the diminution of tem- 

 perature. The increase or decrease arising from temperature would 

 not last long, since the altered mam would communicate heat < Hi- 



surrounding bodie* in the first case, and receive it from them in t h.- 

 second ; but in calculating such instantaneous effect* M the propaga- 

 tion of sound, it U evident they ought not to be neglected. Tl 

 position on which Newton went was, tliat the elastic force* . 

 strata of air are always in the same i 'i. -, win. h 



is not true, unless the temperatures are the same. We may also here 

 remark, that an alteration in the Inrtnaeler only, produces no alteration 

 '"' <!" if the barometer rise, though the pres- 



sure of tl,,. aii is imrea.-ed. yet the density is increased in the same 

 proportion; that to, the force which is to set each maw in motion 

 receives no greater increase in proportion than the mass which i 

 moved. But a rise in the thermometer, accompanied by no change 

 in the barometer, increases the velocity of sound, for there is an 

 increase in the elastic foroe, without any' increase in tin- .li-n-ity. A 

 very good measure of this vel,., it y made near Paris in 1 ^'J, under thr 

 directions of the Academy of Sciences, gave 1118 feet per second at 

 the temperature of 61 of Fahrenheit. Ivnlier px|M>rinient had givm 

 1180 feet, which, if the French measure is assumed as accurate, repre- 

 sents the velocity at a somewhat higher temperature. The number 

 which we have adopted, viz., 1125 feet per second, at 62 of Fahren- 

 heit, is shown by Sir John Herschel, in his masterly treatise on ' Sound ' 

 in the ' Encycloptcdia Metropolitans,' to accord very nearly with tin- 

 mean of the best experiments. The formula for calculating thi 

 city is now given as follows : 



V = 1090-8 { (1 + 0-003665 x /) (1 + 0-375 1)1$. 

 where I is the centigrade temjwrature, T the density of vapour, and n 



when the air is at the freezing point. We may add, that in the 

 present state of our knowledge of the manner in which 1 1 

 ture and elastic force of the atmosphere are connected, observation and 

 theory give results Vhich differ from one another by about a hundredth 

 part of the whole. 



When the exciting cause of sound is continued, as for example, ulien 

 a board is scratched with a pin, we have a continued sound, caused by 

 the succession of waves which the ear receives, which waves we h 

 reason to believe are all of the same length. But whenever the exciting 

 cause is one, the vibrations of which can be shown to be performed in 

 exactly the same time, so that the waves caused by them are all of the 

 same length, we perceive a sound which gives pleasure to the ear, and 

 has the name of harmonious or musiral. This, however, only happen- 

 when the vibrations are at least thirty in a second, or the wave of * 

 sound at most about 38 feet t long. This fact is so well estal 

 that we may consider it an certain that the pleasure arising from 

 musical sounds is a consequence of the perfectly equal times of thr 

 vibrations which produce them, and of its result," the equal lengths of 

 the sonorous waves propagated from them through the 

 This will not appear go extraordinary, if we consider the very . . 

 nature of our organ of hearing. A person of tolerable cm 

 guish between two Bounds, which only differ in that the 00 

 consequence of 400 vibrations in a second, and the other of 405. We 

 must therefore grant to the ear a much higher power of perception an 

 to sounds than the eye has to length or surface. Some increase of the. 

 perceptive power may arise from the very great number of vilu 

 since a result in come degree corresponding in observed in vision. If 

 we look at a large number of parallel lines ruled clow together at equal 

 distances, any little deviation from parallelism or equidisuncc- i.- much 

 more sensibly seen than when the number of lines is small. And even 

 to the eye, any moderately rapid succession of objects of the sain 

 is much more pleasing when they follow at equal distances and periods 

 of time. 



The difference between two musical sounds, which w express by 

 saying that one is higher or lower than the other, is a eonsequ. i 

 the different numhci -of vibrations performed by the two in ih 

 time, and the. sound which wo call higher has the greater niimlier of 

 vibrations. And Rome sounds, when made together, produce an effect 

 utterly unbearable, while others can be tolerated ; others again arc 

 extremely pleasant, while some, though very dill'm-nt in pitch, appear 

 w> alike, that we call them the same, only higher. It ix found !>y 

 experiment that two sounds arc more or less contminni. when heard 

 together, according as the relation between their vibrations is more or 

 less simple. Thus, when two vibrations of the first ore made in one 

 vibratiou of the second (which is the simplest ratio possible, when the 

 sounds ore really different), that similarity is observed to which we 

 have just alluded; the first sound is called the oclart of the second, 

 and both are denoted in music by the same letter. When the number 

 of vibrations of the two are as 8 to 2, the one which vibrates three 

 times while the other vibrates two, in called a fifth above the 

 because in the inimical scale of notes 



C D E F A B C' 1)' Ac. 



the vibrations of c and o arc in this proportion, and <.; is the fifth 

 ound reckoned from c. If the ratio of the vibrations be thnt of 8 to 

 4, that i, if the higher note makes four vibration*, while the lower 



