ACOUSTICS. 



ACOUSTIC 



en 



Let tuning-fork be sounded, and while yrt in vibration, l.-t it 

 be stopped by the finger. A sensation will be felt for an instant, for 

 which we have no name in our language, wining from the prong of the 

 fork rapidly, but gently, striking the finger, and very different from 

 that which is produced by merely touching the fork when at rest. 

 Now, blow into a common flute, and at the same time stop gently ! 

 r three of the higher holes. The me sort of Mneation, though in a 

 much smaller degree, will be felt on that part of the finger*' end- lii- 1. 

 U in communication with the interior air. For this purpose the fingers 

 should be warm, but if the observer be not used to the instrument, 

 the effect is made more certain by tuning the string of a violoncello to 

 the note which is to be fingered on the flute, and then sounding the 

 former strongly, while the Utter is held over it, with the fingers placed 

 as before. The column of air in the flute will be made to vibrate by 

 the motions of the string, forming a case of what is called sympathetie 

 norafi'o*. That any very violent and sudden noise produces a con- 

 cussion in the air even farther than the sound can be heard, is proved 

 by the fact, that the explosion of a large powder-mill will shake the 

 window* in their frames for nearly twenty miles around. 



We now proceed to describe, as far as can be simply done, the inoti.ni 

 which takes place in tjie air when the impression of sound U com- 

 municated; and here we stop to explain a method which may be 

 adopted in many cases, of making the eye assist the reason. Suppose 

 we wish to register what takes place in the vibration of a spring, of 

 which the position of rest is A B (fg. 1), but which, having been set in 

 motion, passes through all the positions between A c and A D. The 



fig. 2. 



spring being drawn aside by the finger or other disturbing cause to A c, 

 and then released, the elasticity of the metal makes continued efforts to 

 restore it to ita first position A B, by which it is made to move, and 

 with continual accession to its velocity, until it actually does arrive at 

 A B, where, if the velocity were suddenly destroyed, it would remain at 

 rest. But the velocity still continuing, the spring continues to move 

 towards A D, with a change of circumstances, inasmuch as the elasticity, 

 new opposing ito motion, gradually destroys the velocity by the same 

 steps as it was before gradually created ; so that when the spring 

 comes to A D, it will be again at rent, but will not continue so, since 

 the elasticity will cause the same phenomena to be repeated, and the 

 pring will move back again towards A c. But for friction and the 

 resistance of the air it would again reach A c ; it does not, however, get 

 no far, owing to these causes, which always diminish, and never increase, 

 velocity. This alternation will go on until the spring is reduced to a 

 state of rest. Similar phenomena occur in the motion of a pendulum, 

 of the string of a harpsichord, and generally, wherever small vibrations 

 are excited in a body, which remove it, but not much, from its position 

 of rest. We might, perhaps, conclude, that each successive oscillation 

 is performed in a shorter time than the preceding, seeing that a lew 

 space is described by the spring. But this is not the fact ; it can be 

 observed, as well as demonstrated, that the oscillations which take 

 place before a body recovers the effect* of a small disturbance and 

 resumes the state of rest, are severally performed, if not in the same 

 i:in--. yet so nearly in the same time, that the difference may he 

 entirely neglected in most practical application*. Such being the caw, 

 we may omit the effects of friction and resistance, so far as the Hate 

 of vibration is concerned, and consider the spring as describing exactly 

 the same path in each successive vibration. Let D c (fy. 2) be the 

 line described by the top of the spring, which we may call a straight 

 line, since it U very nearly so, and while the spring moves from t> to c, 

 imagine a curve D y c to be drawn, in such a way that, the spring being 

 nt f, the perpendicular x y is the rate per second at which the top of 

 the spring is then moving. A little attention will K!IO\V that the curve 

 whirh we have drawn represents the various changes of motion just 

 alluded to : thus T B, the greatest perpendicular, in over the )H>int B, 

 where the spring moves fastest ; and at D and c there is no |M>r]>en- 

 ilicular, because the spring comes tn rest when It reaches those points. 

 During the return from c to D, in which the motion is the same, but 

 in contrary direction, let a similar branch c t D be drawn, on the 

 other side of o D. We will call the whole curve D T c f D the type of 

 the double vibration of the spring, the two branches Iwing the type of 

 ito two halves. Now, suppose a column of air inclosed in a thin tulie 

 A B Of-/. 3), which is indefinitely extended towards B, but closed at A 

 by a piston which can be moved backwards and forwards from A to c, 

 and from c to A, after the manner of a spring, the type of its motion 

 being represented by the curves on A c. And first let the piston be 

 pushed forward from A to c. If the air wore solid, we should .ay that 

 a column of sir A c in length would ) pushed out of the end B of the 

 tube in the time in which the piston in driven in, but we certainly can 

 have no notion that such an effect would be produced upon a column of 

 elastic fluid like the air. Experiment, as well as mathematical demon- 

 stration, show ni that though every particle of th<- fluid will finally In- 



put in motion, vet that those particles which are nearer the disturbing 

 piston receive their first impression sooner than those which are more 







distant ; and we find that this successive , ., an it is called, of 



the disturbance, goes on uniformly at th<- rate of about 1125 feet in a 

 second, the temperature being 2" of Fahi . ram pie, a second 



must elapse before those particles, which are 1125 feet distant fi 

 will have their first news, so to speak, of what is going on at A, aivl in 

 the same proportion for other distances. It is also shown t!: 

 velocity of communication in not affected liy the grater or less degree 

 of violence with which the air is struck, but remains the same for 

 every sort of disturbance. With gin-h .1 \vl.>rity, we may see that the 

 column of air made up of all the particles which feel, or have felt. th. 

 effects of the disturbance, must be very long when compared v. . 

 the extent of an almost insensible vibration ; so that it will lead to 110 

 sensible error if we suppose that the effect of the piston at every point 

 of ito course is propagated instantaneously to c, and thence ouly, with 

 the velocity of 1125 feet per second. We will now consider what this 

 effect is. Divide the whole length A c, fij. 4, into a large number of 

 very small parts, described in equal time*, and instead of the piston 

 moving continuously, and with imperceptible changes of velocity, along 

 A c, let it move by starts from each point to the next, with the proper 

 increase or decrease of velocity. In the figure we have divided A c into 

 ten parts, but the same reasoning applies to any greater numlier. We 

 have much enlarged A c (Jig. 41, to give room for the figure : the reader 



Fig. 4. 



A1SJ4 3 67C r Q K s 



may help his ideas by supposing that A c U viewed through a powerful 

 microscope, and the rest of the tube by the naked eye. Whatever may 

 be the common time of moving through each of the parts A 1.12, Ac., 

 the portions of the column affected by the starts of the piston will ! 

 of the same length, and each will be as much of 1125 feet as the time 

 of each start is of one second. Set off the lengths c P, P Q, Q R, Ac. . 

 each equal to this length, and for the present let us agree to c 

 common time in which the piston starts through A 1 , 1 2, Ac., an inttant. 

 The reader must bear in mind throughout thai we intend to carry the 

 supposition of dividing A c into parts to ito utmost limit, by which wr 

 shall have to suppose CP, PQ, Ac., to be very small, though >-till great 

 when compared with A 1, 1 2, Ac. We also think it right to repeat, 

 that all the figure on the left of c is immensely magnified, and that the 

 propagation is supposed to be instantaneous from 1, 2, Ac., to 

 the first instant, the piston moves through A 1, with the velocity p 1 per 

 second, and forces the column of air A 1 into c P, which therefore has 

 ito density increased, or is compressed, the air which was held in c r 

 and A 1 together being now confined in c p. As the propagation haw 

 not travelled farther than P, the effect U just the same as if there hod 

 been a solid obstacle at P during the first instant. The portion c P i/> 

 then compressed, strictly speaking, unequal/it; tluii t* near 



to c are more compressed than those near to P; but on account of the 

 small length of c P, and the rapidity of the transmission, we may sup- 

 pose all the parts to be equally compressed. Again, the particles near 

 o begin to move towards p, and for a similar reason we may suppose 

 the velocities of all the particles to be the same ; tin- 

 that of A during the first instant. The reader must not confou 

 absolute velocity of the several particles, which is always SMI. ill. with 

 the rate at which they transmit their velocities and compressions, which 

 is very great. We will use the phrase that the portion r i' has i 

 ito frit comprettion. If the piston were stopped at the end of t! 

 instant, the whole effect upon CP would be transferred to PQ in the 

 second instant, both as to compression and velocity, and the ]>n- 

 i 1 i- would relurn to Ihcir first state, and receive no further modili 

 But in the second in-tani.the portion' CP receives ito Kcond compreuion, 

 which U greater than the first, since a column 1 2 longer than A 1 i- 

 forced into it. Similarly, the \ increased, being 2 q per second 



instead of 1 j>. If the sjning were then stopped, the third instant 

 would sec the ]>ortion PQ transmit ito velocity and compression to Q n, 

 c i- to P Q, and c P would resume ito natural state. But in this instant, 

 c p receives ito third compression, which is greater than the former 

 two, and the same process goes on, each portion transmitting ito \ 

 and compression to the ntctteilin;i one. receiving in its turn more than 

 it parted with, from the /nviW/'/i;/. Thi- continues until the, piston has 

 reached the middle point of A c, after which the compression of c P still 

 continues, but becomes less and less in successive instants, because 5 6, 

 8 7, Ac., down to 9c, decrease hi length, in the same way as A 1, 1 2, 

 Ac., increased. When the piston begins to return through c 8, in the 

 li instant, the portion c p. receives Ito fret rarefactim . lor the 

 air in C P now occupies c p and c 9 ; the particles in c P therefore move 

 towards c instead of from it, and the ^receding modi i o sue- 



