CHAPTER XII.

SOUND.

248. =What Sound is.=--Sound is such a vibration of substances as can, on being transmitted to the ear, act upon the sense of hearing. I say _such_ a vibration, because there may be vibrations which will not produce the sensation of sound, Vibrations which are either very slow or very quick will not do it. Thus if a plate of metal or a string make less than 15 or more than 48,000 vibrations in a second, no effect is produced upon the ear. The capacity of hearing differs, however, in different persons, so that although few can hear vibrations which are beyond the range which I have mentioned, there are many whose capacity falls much within it either at one end or both ends of the scale. The range for animals is not the same as that for man. Thus the lion and the elephant can hear a sound when the vibrations are too infrequent to make any impression upon our ears; while small animals have a susceptibility in the organ of hearing for vibrations so quick that we can not hear them, and at the same time are not susceptible to the slower vibrations. How far the range varies in different animals has not been ascertained to any extent.

249. =The Vibration of Sounding Bodies Manifest to the Senses.=--If we place the hand upon a large bell that has been struck we can feel the vibration. If we strike one of the ends of a tuning-fork upon some hard body we can see the vibration, as represented in Fig. 182 by the dotted lines. If we look in upon the strings of a piano as it is played, the vibration of the larger strings is very observable to the eye. If we rub the edge of a drinking-glass so as to produce a musical sound, the water which is in it will be thrown into waves from the vibration of the glass.

250. =Wind Instruments.=--In wind instruments, as the flute, horn, etc., it is the vibration of the body of air in the instrument which causes the sound. In the common tin whistle or bird-call, Fig. 183, the sound is produced by the vibration imparted to the contained air by the impulse of the breath through the orifice, B.

251. =An Analogy.=--The vibration of a sounding body is much like that of a pendulum. The end of the tuning-fork, Fig. 182, on being struck passes to _b_, and in returning passes by the point of rest, A, as the pendulum does, and reaches _a_. So, also, if a string, A B, Fig. 184, be drawn aside to D, as it flies back to C it will by its inertia pass on to E, and so will continue to vibrate back and forth for some time. The same rule also applies to the extent of the vibrations here as in the case of the pendulum, § 209. The quickness of the vibration is not at all affected by its width. The farther the string, A B, is drawn to one side the greater will be the force with which it will return, and hence it will arrive at its position on the other side of the middle line as soon when drawn far away from this line as it would if drawn but little away. The same thing is true of the vibrations or waves of air, though it can not so easily be made plain to you.

252. =How the Sensation of Sound is Produced.=--The vibration of a sounding body is transmitted to the ear ordinarily through the air, and there strikes upon a little drum, a membrane at the bottom of the external cavity of the ear just like a common drum-head. Here the vibration of the air is communicated to this drum, and from this to a chain of very small bones. From the last of these bones it is transmitted to another very small drum, and from this to a fluid in some very complicated passages in the most solid bone in the body. These may be called the _halls of audience_. In the fluid contained in them are spread out the branches of the nerve of hearing, which receive the impression of the vibration, and transmit it to the brain, where the mind takes knowledge of it. Observe that the vibration, transmitted first through the air, then through the drum, then the chain of bones, then another drum to a fluid, stops at the fluid. What is transmitted from this to the brain by the nerve we know not, and so we call it an impression.

253. =Sound Transmitted through Various Substances.=--In ordinary hearing sound, as you have seen, is transmitted through various substances before the vibration arrives at the liquid in the halls of audience. But sound need not take this course in all cases to arrive at the nerve of hearing. If, for example, you place a watch between your teeth, the sound will go through the solid teeth and the bones of the jaw directly to the halls of audience by a short cut, instead of going round through the outer ear-passage to the drum, and so through the chain of bones. Fishes in hearing receive the vibration through water. If you place your ear at the end of a timber, while some one scratches with a pin at the other end, you hear the sound distinctly, for the vibration is transmitted through the timber; as in the case of the watch between the teeth, it goes through the solid bone.

254. =Sound not Transmitted through a Vacuum.=--As sound is a vibration of some substance it can not be transmitted through absolute space. This can be proved by an experiment with the air-pump, as represented in Fig. 185. The apparatus in the receiver is so arranged that the bell, _a_, can be struck by pressing down a sliding rod, _h_. If it be struck before the air is exhausted the sound is heard through the glass. But the more you exhaust the air the fainter will be the sound; and at length, if you keep on pumping, it can not be heard at all. The same experiment can be tried with a music-box. It is from the thinness of the air on high mountains, and at the great heights reached by balloons, that all sounds are so faint. The report of a pistol fired off on top of Mont Blanc is a mere crack compared with its report when fired in the valley below.

255. =Motion of the Heavenly Bodies without Noise.=--Sound is often heard at a very great distance on the earth. The sound of an eruption of a volcano has been heard in one case at the distance of 970 miles. But suppose that the same sound should occur at the same distance from the earth, that is, over 900 miles beyond the atmosphere that enrobes the earth, no inhabitant of our world could hear it, for the same reason that you do not hear the bell ringing in an exhausted receiver. If, therefore, any sound, however loud, should be given forth by any of the heavenly bodies we could not hear it. The course of these bodies in their orbits is noiseless, because they meet with no resistance from any substance. Bodies passing rapidly through our atmosphere cause sound, from the resistance which the air gives to their passage. The whizzing of a ball is an example of this. It is the passage of the electric fluid through the air which produces the thunder. But the heavenly bodies, having no such resistance, make no sound in their course, though their velocity be so immense. In the expressive language of the Bible, "their voice is not heard."

256. =Velocity of Sound.=--The velocity of sound varies in different media. Thus it passes through water four times as rapidly as it does through air. Dr. Franklin, with his head under water, heard distinctly the sound of two stones struck together in the water at the distance of more than half a mile. Sound passes through solids much more easily, and therefore more rapidly, than through liquids. Thus its velocity through copper is twelve times and through glass seventeen times greater than through air. If you place your ear against a long brick wall at one end, and let some one strike upon the other end, you will hear two reports, the first through the wall and the second through the air. Indians are in the habit of ascertaining the approach of their enemies by putting the ear to the ground. When the eruption of a volcano is heard at a great distance the sound comes through the solid earth rather than through the air. The ready transmission of sound through solids furnishes us with a very valuable means of examining diseases of the lungs and heart. The sounds occasioned by the movement of the air in the lungs and by the action of the heart are very distinctly heard through the solid walls of the chest.

257. =Measurement of Distances by Sound.=--It makes no difference with the velocity of sound whether it be loud or not. Thus the sounds of a band of music at a distance all reach your ear at the same time, the sounds of the instruments that can scarcely be heard keeping exact pace in the air with the sounds of the loudest. So, also, the velocity of sound is uniform throughout its whole course, being just as rapid when it is about to die away as it was when it began. It is from this uniformity in the velocity of sound that we can estimate the distance of the object by which any sound is made. We do it by a comparison between light and sound. Sound moves at the rate of 1120 feet in a second. Now light moves 192,000 miles a second, and therefore, for all ordinary distances on the earth, we need make no allowance of time for light in comparison with sound. If we see, then, the operation by which a sound is produced we can estimate its distance from us by the length of time which elapses between what we see and what we hear. In this way we can estimate very accurately the distance of a cannon that we see fired, or the distance of a flash of lightning.

258. =Loudness of Sound.=--The loudness of sound depends upon the width of the vibrations producing it. The harder you strike the end of the tuning-fork, Fig. 182, the farther will it vibrate the one way and the other, and the louder will be the sound. The same thing is true of the strings of a piano. A round bell, when it is struck, tends in its vibration to take an oval form, and the extent of its vibration back and forth as it does this governs the loudness of the sound. As sound passes from the sounding body the vibration gradually lessens, and at length dies away. It is like the successive vibrations or waves of water produced by dropping a stone in it. The louder the sound is the larger are the first vibrations, and the farther will the vibrations extend, as in water a large stone dropped into it will produce larger waves than a small one, and the waves will extend over a greater space.

259. =Diffusion of Sound.=--When there is no hindrance sound spreads equally in all directions. It is in this respect with the vibrations or waves of air as it is with the waves of water when a stone is dropped into it. Light is also diffused in the same manner, as you will see in another chapter.

260. =Reflection of Sound.=--As waves of water striking against any object bound off, so it is with the vibrations or waves of sound. And the same is true of this as of all motion, as stated in § 206, that the angle of incidence is equal to the angle of reflection. The reflection of sound is the cause of _echoes_. In order that an echo be perfect the sound must be reflected back to the ear from some plane surface of some size. Sometimes when there are successive plane surfaces of rocks along a river there are successive echoes. Thus in Fig. 186 (p. 200) is represented a locality on the Rhine where a sound is reflected at successive places, 1, 2, 3, 4. The rolling of thunder, though sometimes caused by the different distances of parts of the same flash of lightning, is commonly owing to reflections of the sound among the clouds. From this cause the report of a cannon is more apt to be a rolling sound when there are clouds above than when the sky is clear. Sound is continually reflected in every variety of direction from obstacles with which it meets. Thus in a room it is reflected from the walls and from all the objects in the room; and the more varied are the surfaces the more varied and confused are the reflections. You know that a voice has a very different sound in a room when it is empty from what it has when the room is filled with an audience. Indeed, a blind speaker can estimate very nearly the size of his audience by the sound of his own voice. The explanation is, that with a full audience the surfaces for reflection are vastly multiplied, and so deprive the sound of the sharp and ringing character which is given to it by reflection from comparatively few surfaces which are plane and firm. The effect produced by an audience upon the voice of the speaker is quite analogous to that of muffling upon the sound of a drum.

261. =Whispering Galleries.=--The reflection of sound from curved surfaces gives us some interesting phenomena. The waves of sound in being reflected from a concave surface are gathered together to some point. If the surface be a perfectly spherical one, and the sound issue from the centre, the reflection will be from all points to the centre. But suppose the concave surface have the curve of an ellipse, as represented in Fig. 187. This, instead of having a centre, has two foci, _c_ and _g_. Now if a sound proceed from one focus, _c_, the waves of sound, as represented by the lines _c d_, _c e_, _c f_, _c h_, will all be reflected to the other focus, _g_; so that if a person speak in a very low tone or even whisper at _c_, he may be heard distinctly by another at _g_, though persons at other points may hear nothing. We may have this result with a curved wall extending even several hundred feet; and such structures are called whispering galleries. If in one of these galleries a person standing in one focus speak loudly he will be heard by others at any point by the _direct_ waves of sound; but the reflected sound will be added to the direct in the case of one standing at the other focus.

262. =Concentration of Sound.=--It is by the reflection of sound that it can be concentrated in various ways. Thus in using a speaking-trumpet the waves of sound, instead of moving in all directions as soon as they escape from the mouth, are reflected by the sides of the instrument toward a central line as represented in Fig. 188. The waves or vibrations, being thus concentrated have more intensity and are thrown to a greater distance than if they issued directly from the mouth. So a speaking-tube, confining the vibrations, carries the voice to distant parts of a building. For the same reason the voice can be heard much farther through a narrow street than in an open space. So, also, a speaker can be heard more distinctly in a hall than when addressing an audience of the same size in the open air. The "sounding-board," once so fashionable in churches, was really of considerable service in preventing the escape of the vibrations of the voice of the preacher upward, and directing them downward upon the audience. In the hearing-trumpet, Fig. 189, the vibrations are collected in the broad open end of the instrument, and by reflection are thrown together into a narrow compass before they enter the ear to strike upon the drum. We often instinctively make the palm of the hand act as an ear-trumpet when we do not hear distinctly. Many animals have the external ears movable, so that they can direct their concave surface toward the point from which they wish to hear. Such ears are movable ear-trumpets.

263. =Difference Between a Musical Sound and a Noise.=--The difference between a musical sound and a noise is very analogous to the difference between a crystal and the same substance destitute of the crystalline arrangement. In both there are vibrations, but in the musical sound they have perfect regularity, while in a noise the vibrations are irregular, and there is confusion. Indeed so regular are the vibrations of musical sounds that the rules and principles of music have all the rigid exactness of mathematics.

264. =How Different Notes are Produced.=--The quicker is the vibration the higher is the note. Thus a short and small string on a violin or in a piano gives a higher note than a long and large string, because its vibrations are quicker. The tension of the string also has an influence, the note being raised by increasing the tension. In tuning a violin the right pitch is given to each string by lessening or increasing the tension by means of the screws to which the strings are attached. In playing upon it various notes are made upon each string by shortening the vibrating portion more or less by pressure of the finger.

In wind instruments the note depends on the length and size of the column of air contained in them. This may be illustrated by an organ-pipe, Fig. 190 (p. 203). It is one of the pipes of what is called the flute-stop. It is constructed very much like a boy's willow whistle. The air from the bellows of the organ enters at P, and causes a vibration of the whole column of air in the pipe, the sound issuing at _t_. In the upper end is a movable plug, _s_, by which, in tuning, the note of the pipe is regulated. If the note be too grave this plug is pushed downward, so as to shorten the column of air.

It is from difference in rapidity of vibration that a large bell gives a graver note than a small one. So, too, when musical sounds are produced by passing the moistened fingers over the edges of glass vessels, the larger the vessel the graver is its note. A tumbler will give a graver note than a wine-glass.

265. =Human Voice.=--The principles which I have developed in relation to musical instruments apply to the voice. The musical instrument of man, by which the voice is produced, is contained in a very small compass. It is that box at the top of the throat commonly called Adam's apple. Across this, from front to rear, stretch two sheets of membrane, leaving a space between their edges. In our ordinary breathing these membranes are relaxed, and the space between their edges is considerable, to allow the air to pass in and out freely. But when we speak or sing these membranes, or vocal chords, as they are termed, are put into a tense state by muscles pulling upon them, and the opening between them is lessened. The voice is produced by the air that is forced out from the lungs, which, striking on the chords, causes them to vibrate. The nearer their edges are together, and the more tense they are, the higher is the note. The sounds are produced precisely as those of the Æolian harp are, the air causing in the one case a vibration of strings, and in the other of edges of membranes.

266. =Harmony.=--When notes, on being sounded at the same time, are agreeable to the ear, they are said to harmonize. Now this harmony depends on a certain relation between the vibrations. The more simple is the relation the greater is the harmony. For example, if we take the first note, termed the fundamental note, of what is called the scale in music, it harmonizes better with the octave than with any other of the eight notes, because for every vibration in it there are just two in the octave. Take in contrast with the octave the second note. Here to every eight vibrations of the first note we have nine of the second, and the consequence is a discord when they are sounded together. The difference between the two cases is this: In the first case the commencement of every vibration in the fundamental note coincides with the commencement of every second vibration in the octave. But in the other case there is a coincidence at only every eighth vibration of the first note with every ninth of the second. Next to the octave, the most agreeable harmony with the fundamental note is that of the fifth note of the scale. Here we have three vibrations to every two of the first note, and so every second vibration in the first note coincides with every third vibration of the fifth. Next comes the harmony of the fourth, there being here a coincidence at every third vibration of the fundamental note. The more frequent, you see, are the coincidences between the vibrations the greater is the harmony. In the three cases just stated the coincidence is in the first at the commencement of _every_ vibration of the fundamental note, in the second case at the commencement of every _second_ vibration, and in the third at the commencement of every _third_ vibration.

267. =The Diatonic Scale.=--In order that you may see the relative numbers of the vibrations for each of the notes I will give them for the whole scale. They are as follows:

1 9/8 5/4 4/3 3/2 5/3 15/8 2 C D E F G A B C.

According to this the note D has nine vibrations to every eight vibrations of C, E has five to every four of C, etc., the octave C having just twice the number of vibrations that the fundamental note C has. You have here expressed the _proportion_ between the numbers of vibrations in the different notes. Suppose, then, that you know the number of vibrations in a second that C, the fundamental note, has, you can readily calculate the number of vibrations of each of the other notes. It is done by multiplying the number which C has by the fractions over the other notes. Thus if the number of vibrations in a second in the fundamental note be 128, by this process we make the vibrations of all the notes to be thus:

C D E F G A B C 128 144 160 170 192 213 240 256.

There are really but seven notes in what is called the diatonic scale, the eighth note, C, being truly the first of seven other notes above, having relations to each other similar to those of the notes below, and constituting another octave. So we may have several octaves, one above another.

It is interesting to observe that the proportionate lengths of strings required to produce the eight notes of the scale have an exact numerical relation, but the _reverse_ of that of the numbers of the vibrations. Thus if you have eight strings of the same size, their vibrating lengths required for the notes are as follows:

C D E F G A B C 1 8/9 4/5 3/4 2/3 3/5 8/15 1/2.

For the notes of the octave above the lengths are thus:

C D E F G A B C 1/2 4/9 2/5 3/8 1/3 3/10 4/15 1/4.

268. =Unison.=--In tuning instruments so as to make them harmonize the result is obtained when the corresponding parts of the instruments have the same number of vibrations. Thus the string in one violin that gives any particular note must vibrate just the same number of times in a second that the strings giving the same note in other violins do, or it will not be in perfect unison with them. The same is true of other strings for other notes, and also of the corresponding parts of all kinds of instruments which are to be played together. When, in tuning instruments together, it is said that a string of a violin, for example, is too _flat_, the difficulty is that it does not vibrate with sufficient rapidity, and it is therefore screwed up to make its note _sharp_ enough, as it is expressed, to be in unison with the note of the corresponding strings or parts of other instruments.

269. =Mysteries of Sound and Hearing.=--There are many things of a mysterious character in relation both to sound and the manner in which it causes the sensation of hearing. I will barely notice but two of these. The effect, or rather the chain of effects, resulting in hearing is wholly mechanical, until we come to the nerve of hearing, which branches out with minute fibrils in the halls of audience of the internal ear. It is merely a series of vibrations. Now how it is that the mere agitation of a fluid inclosed in hard bone can communicate through fine white fibres to the brain, and through that to the mind, the idea that we have of all the various sounds that are produced, is a great mystery. All that we know is that the nerve is the medium of the communication, but of the manner in which it performs its office we know absolutely nothing. Again, while it is sufficiently mysterious that this information can thus be given to the mind when one sound after another communicates its vibration to the liquid in the ear, the mystery is greatly enhanced when various sounds come to the ear at one and the same time. To get a distinct idea of the very compound and wonderful character of the process of hearing in such a case we will suppose that a full band of music is playing, and at the same time mingled with its sounds there are various other sounds heard, some of them perhaps discordant. What a diversity of vibrations we have here! We have the slow vibrations produced in the grave notes, and the quick vibrations of the higher ones, all traveling together through the air to the ear, and each preserving its distinctive character. And more than this, after they arrive at the ear they are communicated unaltered through the drum, the chain of bones, the second drum, and the liquid where the nerve is, so that a correct report of each of all the notes is given through the nerve to the mind. Then, too, if there be any discord its vibration travels along with the rest, and so do the vibrations of other sounds, as the roaring of the wind, the report of cannon, and the noise of the people. And besides all this, in the multiplicity of the vibrations thus transmitted through so many different substances the mind gets a true report of the comparative loudness of the sounds, and even of their character, so that the sounds of drum, fife, trumpet, etc., are all accurately distinguished. In view of such wonders how significant is the question, "He that planted the ear, shall he not hear?"