Sound

The process may be rudely represented by the propagation of motion through a row of glass balls, such as are employed in the game of solitaire. Placing the balls along a groove thus, Fig. 1, each of them touching its neighbor, and urging one of them against the end of the row: the motion thus imparted to the first ball is delivered up to the second, the motion of the second is delivered up to the third, the motion of the third is imparted to the fourth; each ball, after having given up its motion, returning itself to rest. The last ball only of the row flies away. In a similar way is sound conveyed from particle to particle through the air. The particles which fill the cavity of the ear are finally driven against the tympanic membrane, which is stretched across the passage leading from the external ear toward the brain. This membrane, which closes outwardly the “drum” of the ear, is thrown into vibration, its motion is transmitted to the ends of the auditory nerve, and afterward along that nerve to the brain, where the vibrations are translated into sound. How it is that the motion of the nervous matter can thus excite the consciousness of sound is a mystery which the human mind cannot fathom.

The propagation of sound may be illustrated by another homely but useful illustration. I have here five young assistants, A, B, C, D, and E, Fig. 2, placed in a row, one behind the other, each boy’s hands resting against the back of the boy in front of him. E is now foremost, and A finishes the row behind. I suddenly push A, A pushes B, and regains his upright position; B pushes C; C pushes D; D pushes E; each boy, after the transmission of the push, becoming himself erect. E, having nobody in front, is thrown forward. Had he been standing on the edge of a precipice, he would have fallen over; had he stood in contact with a window, he would have broken the glass; had he been close to a drumhead, he would have shaken the drum. “We could thus transmit a push through a row of a hundred boys, each particular boy, however, only swaying to and fro. Thus, also, we send sound through the air, and shake the drum of a distant ear, while each particular particle of the air concerned in the transmission of the pulse makes only a small oscillation.

But we have not yet extracted from our row of boys all that they can teach us. When A is pushed he may yield languidly, and thus tardily deliver up the motion to his neighbor B. B may do the same to C, C to D, and D to E. In this way the motion might be transmitted with comparative slowness along the line. But A, when pushed, may, by a sharp muscular effort and sudden recoil, deliver up promptly his motion to B, and come himself to rest; B may do the same to C, C to D, and D to E, the motion being thus transmitted rapidly along the line. Now this sharp muscular effort and sudden recoil is analogous to the elasticity of the air in the case of sound. In a wave of sound, a lamina of air, when urged against its neighbor lamina, delivers up its motion and recoils, in virtue of the elastic force exerted between them; and the more rapid this delivery and recoil, or in other words the greater the elasticity of the air, the greater is the velocity of the sound.

A very instructive mode of illustrating the transmission of a sound-pulse is furnished by the apparatus represented in Fig. 3, devised by my assistant, Mr. Cottrell. It consists of a series of wooden balls separated from each other by spiral springs. On striking the knob A, a rod attached to it impinges upon the first ball B, which transmits its motion to C, thence it passes to E, and so on through the entire series. The arrival at D is announced by the shock of the terminal ball against the wood, or, if we wish, by the ringing of a bell. Here the elasticity of the air is represented by that of the springs. The pulse may be rendered slow enough to be followed by the eye.

Scientific education ought to teach us to see the invisible as well as the visible in nature, to picture with the vision of the mind those operations which entirely elude bodily vision; to look at the very atoms of matter in motion and at rest, and to follow them forth, without ever once losing sight of them, into the world of the senses, and see them there integrating themselves in natural phenomena. With regard to the point now under consideration, we must endeavor to form a definite image of a wave of sound. We ought to see mentally the air-particles, when urged outward by the explosion of our balloon, crowding closely together; but immediately behind this condensation we ought to see the particles separated more widely apart. We must, in short, to be able to seize the conception that a sonorous wave consists of two portions, in the one of which the air is more dense, and in the other of which it is less dense than usual. A condensation and a rarefaction, then, are the two constituents of a wave of sound. This conception shall be rendered more complete in our next lecture.

§ 2. Experiments in Vacuo, in Hydrogen, and on Mountains

That air is thus necessary to the propagation of sound was proved by a celebrated experiment made before the Royal Society, by a philosopher named Hawksbee, in 1705.9 He so fixed a bell within the receiver of an air-pump that he could ring the bell when the receiver was exhausted. Before the air was withdrawn the sound of the bell was heard within the receiver; after the air was withdrawn the sound became so faint as to be hardly perceptible. An arrangement is before you which enables us to repeat in a very perfect manner the experiment of Hawksbee. Within this jar, G G′, Fig. 4, resting on the plate of an air-pump is a Fig. 4. bell, B, associated with cloc-kwork.10 After the jar has been exhausted as perfectly as possible, I release, by means of a rod, r r′, which passes air-tight through the top of the vessel, the detent which holds the hammer. It strikes, and you see it striking, but only those close to the bell can hear the sound. Hydrogen gas, which you know is fourteen times lighter than air, is now allowed to enter the vessel. The sound of the bell is not augmented by the presence of this attenuated gas, though the receiver is now full of it. By working the pump, the atmosphere round the bell is rendered still more attenuated. In this way we obtain a vacuum more perfect than that of Hawksbee, and this is important, for it is the last traces of air that are chiefly effective in this experiment. You now see the hammer pounding the bell, but you hear no sound. Even when the ear is placed against the exhausted receiver not the faintest tinkle is heard. Observe also that the bell is suspended by strings, for if it were allowed to rest upon the plate of the air-pump the vibrations would be communicated to the plate, and thence transmitted to the air outside. Permitting the air to enter the jar with as little noise as possible, you immediately hear a feeble sound, which grows louder as the air becomes more dense, until finally every person in this large assembly distinctly hears the ringing of the bell.11

Sir John Leslie found hydrogen singularly incompetent to act as the vehicle of the sound of a bell rung in the gas. More than this, he emptied a receiver like that before you of half its air, and plainly heard the ringing of the bell. On permitting hydrogen to enter the half-filled receiver until it was wholly filled, the sound sank until it was scarcely audible. This result remained an enigma until it received a simple and satisfactory explanation at the hands of Prof. Stokes. When a common pendulum oscillates it tends to form a condensation in front and a rarefaction behind. But it is only a tendency; the motion is so slow, and the air is so elastic, that it moves away in front before it is sensibly condensed, and fills the space behind before it can become sensibly dilated. Hence waves or pulses are not generated by the pendulum. It requires a certain sharpness of shock to produce the condensation and rarefaction which constitute a wave of sound in air.

The more elastic and mobile the gas, the more able will it be to move away in front and to fill the space behind, and thus to oppose the formation of rarefactions and condensations by a vibrating body. Now hydrogen is much more mobile than air; and hence the production of sonorous waves in it is attended with greater difficulty than in air. A rate of vibration quite competent to produce sound-waves in the one may be wholly incompetent to produce them in the other. Both calculation and observation prove the correctness of this explanation, to which we shall again refer.

At great elevations in the atmosphere sound is sensibly diminished in loudness. De Saussure thought the explosion of a pistol at the summit of Mont Blanc to be about equal to that of a common cracker below. I have several times repeated this experiment; first, in default of anything better, with a little tin cannon, the torn remnants of which are now before you, and afterward with pistols. What struck me was the absence of that density and sharpness in the sound which characterize it at lower elevations. The pistol-shot resembled the explosion of a champagne bottle, but it was still loud. The withdrawal of half an atmosphere does not very materially affect our ringing bell, and air of the density found at the top of Mont Blanc is still capable of powerfully affecting the auditory nerve. That highly attenuated air is able to convey sound of great intensity is forcibly illustrated by the explosion of meteorites at elevations where the tenuity of the atmosphere must be almost infinite. Here, however, the initial disturbance must be exceedingly great.

The motion of sound, like all other motion, is enfeebled by its transference from a light body to a heavy one. When the receiver which has hitherto covered our bell is removed you hear how much more loudly it rings in the open air. When the bell was covered the aërial vibrations were first communicated to the heavy glass jar, and afterward by the jar to the air outside; a great diminution of intensity being the consequence. The action of hydrogen gas upon the voice is an illustration of the same kind. The voice is formed by urging air from the lungs through an organ called the larynx, where it is thrown into vibration by the vocal chords which thus generate sound. But when the lungs are filled with hydrogen, the vocal chords on speaking produce a vibratory motion in the hydrogen, which then transfers the motion to the outer air. By this transference from a light gas to a heavy one the voice is so weakened as to become a mere squeak.12

The intensity of a sound depends on the density of the air in which the sound is generated, and not on that of the air in which it is heard.13 Supposing the summit of Mont Blanc to be equally distant from the top of the Aiguille Verte and the bridge at Chamouni; and supposing two observers stationed, the one upon the bridge and the other upon the Aiguille: the report of a cannon fired on Mont Blanc would reach both observers with the same intensity, though in the one case the sound would pursue its way through the rare air above, while in the other it would descend though the denser air below. Again, let a straight line equal to that from the bridge at Chamouni to the summit of Mont Blanc be measured along the earth’s surface in the valley of Chamouni, and let two observers be stationed, the one on the summit and the other at the end of the line: the report of a cannon fired on the bridge would reach both observers with the same intensity, though in the one case the sound would be propagated through the dense air of the valley, and in the other case would ascend through the rarer air of the mountain. Finally, charge two cannon equally, and fire one of them at Chamouni and the other at the top of Mont Blanc: the one fired in the heavy air below may be heard above, while the one fired in the light air above is unheard below.

§ 3. Intensity of Sound. Law of Inverse Squares

In the case of our exploding balloon the wave of sound expands on all sides, the motion produced by the explosion being thus diffused over a continually augmenting mass of air. It is perfectly manifest that this cannot occur without an enfeeblement of the motion. Take the case of a thin shell of air with a radius of one foot, reckoned from the centre of explosion. A shell of air of the same thickness, but of two feet radius, will contain four times the quantity of matter; if its radius be three feet, it will contain nine times the quantity of matter; if four feet, it will contain sixteen times the quantity of matter, and so on. Thus the quantity of matter set in motion augments as the square of the distance from the centre of explosion. The intensity or loudness of sound diminishes in the same proportion. We express this law by saying that the intensity of the sound varies inversely as the square of the distance.

Let us look at the matter in another light. The mechanical effect of a ball striking a target depends on two things—the weight of the ball, and the velocity with which it moves. The effect is proportional to the weight simply; but it is proportional to the square of the velocity. The proof of this is easy, but it belongs to ordinary mechanics rather than to our present subject. Now what is true of the cannon-ball striking a target is also true of an air-particle striking the tympanum of the ear. Fix your attention upon a particle of air as the sound-wave passes over it; it is urged from its position of rest toward a neighbor particle, first with an accelerated motion, and then with a retarded one. The force which first urges it is opposed by the resistance of the air, which finally stops the particle and causes it to recoil. At a certain point of its excursion the velocity of the particle is its maximum. The intensity of the sound is proportional to the square of this maximum velocity.

The distance through which the air-particle moves to and fro, when the sound-wave passes it, is called the amplitude of the vibration. The intensity of the sound is proportional to the square of the amplitude.

§ 4. Confinement of Sound-waves in Tubes

This weakening of the sound, according to the law of inverse squares, would not take place if the sound-wave were so confined as to prevent its lateral diffusion. By sending it through a tube with a smooth interior surface we accomplish this, and the wave thus confined may be transmitted to great distances with very little diminution of intensity. Into one end of this tin tube, fifteen feet long, I whisper in a manner quite inaudible to the people nearest to me, but a listener at the other end hears me distinctly. If a watch be placed at one end of the tube, a person at the other end hears the ticks, though nobody else does. At the distant end of the tube is now placed a lighted candle, c, Fig. 5. When the hands are clapped at this end, the flame instantly ducks down at the other. It is not quite extinguished, but it is forcibly depressed. When two books, B B′, Fig. 5, are clapped together, the candle is blown out.14 You may here observe, in a rough way, the speed with which the sound-wave is propagated. The instant the clap is heard the flame is extinguished. I do not say that the time required by the sound to travel this tube is immeasurably short, but simply that the interval is too short for your senses to appreciate it.

That it is a pulse and not a puff of air is proved by filling one end of the tube with the smoke of brown paper. On clapping the books together no trace of this smoke is ejected from the other end. The pulse has passed through both smoke and air without carrying either of them along with it.

An effective mode of throwing the propagation of a pulse through air has been devised by my assistant. The two ends of a tin tube fifteen feet long are stopped by sheet India-rubber stretched across them. At one end, e, a hammer with a spring handle rests against the India-rubber; at the other end is an arrangement for the striking of a bell, c. Drawing back the hammer e to a distance measured on the graduated circle and liberating it, the generated pulse is propagated through the tube, strikes the other end, drives away the cork termination a of the lever a b, and causes the hammer b to strike the bell. The rapidity of propagation is well illustrated here. When hydrogen (sent through the India-rubber tube H) is substituted for air the bell does not ring.

The celebrated French philosopher, Biot, observed the transmission of sound through the empty water-pipes of Paris, and found that he could hold a conversation in a low voice through an iron tube 3,120 feet in length. The lowest possible whisper, indeed, could be heard at this distance, while the firing of a pistol into one end of the tube quenched a lighted candle at the other.

§ 5. The Reflection of Sound. Resemblances to Light

The action of sound thus illustrated is exactly the same as that of light and radiant heat. They, like sound, are wave-motions. Like sound they diffuse themselves in space, diminishing in intensity according to the same law. Like sound also, light and radiant heat, when sent through a tube with a reflecting interior surface, may be conveyed to great distances with comparatively little loss. In fact, every experiment on the reflection of light has its analogy in the reflection of sound. On yonder gallery stands an electric lamp, placed close to the clock of this lecture-room. An assistant in the gallery ignites the lamp, and directs its powerful beam upon a mirror placed here behind the lecture-table. By the act of reflection the divergent beam is converted into this splendid luminous cone traced out upon the dust of the room. The point of convergence being marked and the lamp extinguished, I place my ear at that point. Here every sound-wave sent forth by the clock and reflected by the mirror is gathered up, and the ticks are heard as if they came, not from the clock, but from the mirror. Let us stop the clock, and place a watch w, Fig. 7, at the place occupied a moment ago by the electric light. At this great distance the ticking of the watch is distinctly heard. The hearing is much aided by introducing the end f of a glass funnel into the ear, the funnel here acting the part of an ear-trumpet. We know, moreover, that in optics the positions of a body and of its image are reversible. When a candle is placed at this lower focus, you see its image on the gallery above, and I have only to turn the mirror on its stand to make the image of the flame fall upon any one of the row of persons who occupy the front seat in the gallery. Removing the candle, and putting the watch, w, Fig. 8, in its place, the person on whom the light falls distinctly hears the sound. When the ear is assisted by the glass funnel, the reflected ticks of the clock in our first experiment are so powerful as to suggest the idea of something pounding against the tympanum, while the direct ticks are scarcely if at all, heard.

One of these two parabolic mirrors, n n′, Fig. 9, is placed upon the table, the other, m m′, being drawn up to the ceiling of this theatre; they are five-and-twenty feet apart. When the carbon-points of the electric light are placed in the focus a of the lower mirror and ignited, a fine luminous cylinder rises like a pillar to the upper Fig. 9. mirror, which brings the parallel beam to a focus. At that focus is seen a spot of sunlike brilliancy, due to the reflection of the light from the surface of a watch, w, there suspended. The watch is ticking, but in my present position I do not hear it. At this lower focus, a, however, we have the energy of every sonorous wave converged. Placing the ear at a, the ticking is as audible as if the watch were at hand; the sound, as in the former case, appearing to proceed, not from the watch itself, but from the lower mirror.15

Curved roofs and ceilings and bellying sails act as mirrors upon sound. In our old laboratory, for example, the singing of a kettle seemed, in certain positions, to come, not from the fire on which it was placed, but from the ceiling. Inconvenient secrets have been thus revealed, an instance of which has been cited by Sir John Herschel.16 In one of the cathedrals in Sicily the confessional was so placed that the whispers of the penitents were reflected by the curved roof, and brought to a focus at a distant part of the edifice. The focus was discovered by accident, and for some time the person who discovered it took pleasure in hearing, and in bringing his friends to hear, utterances intended for the priest alone. One day, it is said, his own wife occupied the penitential stool, and both he and his friends were thus made acquainted with secrets which were the reverse of amusing to one of the party.

When a sufficient interval exists between a direct and a reflected sound, we hear the latter as an echo.

Sound, like light, may be reflected several times in succession, and, as the reflected light under these circumstances becomes gradually feebler to the eye, so the successive echoes become gradually feebler to the ear. In mountain regions this repetition and decay of sound produce wonderful and pleasing effects. Visitors to Killarney will remember the fine echo in the Gap of Dunloe. When a trumpet is sounded in the proper place in the Gap, the sonorous waves reach the ear in succession after one, two, three, or more reflections from the adjacent cliffs, and thus die away in the sweetest cadences. There is a deep cul-de-sac, called the Ochsenthal, formed by the great cliffs of the Engelhörner, near Rosenlaui, in Switzerland, where the echoes warble in a wonderful manner.

The sound of the Alpine horn, echoed from the rocks of the Wetterhorn or the Jungfrau, is in the first instance heard roughly. But by successive reflections the notes are rendered more soft and flute-like, the gradual diminution of intensity giving the impression that the source of sound is retreating further and further into the solitudes of ice and snow. The repetition of echoes is also in part due to the fact that the reflecting surfaces are at different distances from the hearer.

In large, unfurnished rooms the mixture of direct and reflected sound sometimes produces very curious effects. Standing, for example, in the gallery of the Bourse at Paris, you hear the confused vociferation of the excited multitude below. You see all the motions—of their lips as well as of their hands and arms. You know they are speaking—often, indeed, with vehemence—but what they say you know not. The voices mix with their echoes into a chaos of noise, out of which no intelligible utterance can emerge. The echoes of a room are materially damped by its furniture. The presence of an audience may also render intelligible speech possible where, without an audience, the definition of the direct voice is destroyed by its echoes. On the 16th of May, 1865, having to lecture in the Senate House of the University of Cambridge, I first made some experiments as to the loudness of voice necessary to fill the room, and was dismayed to find that a friend, placed at a distant part of the hall, could not follow me because of the echoes. The assembled audience, however, so quenched the sonorous waves that the echoes were practically absent, and my voice was plainly heard in all parts of the Senate House.

Sounds are also said to be reflected from the clouds. Arago reports that, when the sky is clear, the report of a cannon on an open plain is short and sharp, while a cloud is sufficient to produce an echo like the rolling of distant thunder. The subject of aërial echoes will be subsequently treated at length, when it will be shown that Arago’s conclusion requires correction.

Sir John Herschel, in his excellent article “Sound,” In the “Encyclopædia Metropolitana,” has collected with others the following instances of echoes. An echo in Woodstock Park repeats seventeen syllables by day and twenty by night; one, on the banks of the Lago del Lupo, above the fall of Terni, repeats fifteen. The tick of a watch may be heard from one end of the abbey church of St. Albans to the other. In Gloucester Cathedral, a gallery of an octagonal form conveys a whisper seventy-five feet across the nave. In the whispering-gallery of St. Paul’s, the faintest sound is conveyed from one side to the other of the dome, but is not heard at any intermediate point. At Carisbrook Castle, in the Isle of Wight, is a well two hundred and ten feet deep and twelve wide. The interior is lined by smooth masonry; when a pin is dropped into the well it is distinctly heard to strike the water. Shouting or coughing into this well produces a resonant ring of some duration.17

§ 6. Refraction of Sound

Another important analogy between sound and light has been established by M. Sondhauss.18 When a large lens is placed in front of our lamp, the lens compels the rays of light that fall upon it to deviate from their direct and divergent course, and to form a convergent cone behind it. This refraction of the luminous beam is a consequence of the retardation suffered by the light in passing through the glass. Sound may be similarly refracted by causing it to pass through a lens which retards its motion. Such a lens is formed when we fill a thin balloon with some gas heavier than air. A collodion balloon, B, Fig. 10, filled with carbonic-acid gas, the envelope being so thin as to yield readily to the pulses which strike against it, answers the purpose.19 A watch, w, is hung up close to the lens, beyond which, and at a distance of four or five feet from the lens, is placed the ear, assisted by the glass funnel f f′. By moving the head about, a position is soon discovered in which the ticking is particularly loud. This, in fact, is the focus of the lens. If the ear be moved from this focus the intensity of the sound falls; if, when the ear is at the focus, the balloon be removed, the ticks are enfeebled; on replacing the balloon their force is restored. The lens, in fact, enables us to hear the ticks distinctly when they are perfectly inaudible to the unaided ear.

How a sound-wave is thus converged may be comprehended by reference to Fig. 11. Let m o n o″ be a section of the sound-lens, and a b a portion of a sonorous wave approaching it from a distance. The middle point, o, of the wave first touches the lens, and is first retarded Fig. 11. by it. By the time the ends a and b, still moving through air, reach the balloon, the middle point o, pursuing its way through the heavier gas within, will have only reached o′. The wave is therefore broken at o; and the direction of motion being at right angles to the face of the wave, the two halves will encroach upon each other. This convergence of the two halves of the wave is augmented on quitting the lens. For when o′ has reached o″, the two ends a and b will have pushed forward to a greater distance, say to a′ and b′. Soon afterward the two halves of the wave will cross each other, or in other words come to a focus, the air at the focus being agitated by the sum of the motions of the two waves.20

§ 7. Diffraction of Sound: illustrations offered by great Explosions

When a long sea-roller meets an isolated rock in its passage, it rises against the rock and embraces it all round. Facts of this nature caused Newton to reject the undulatory theory of light. He contended that if light were a product of wave-motion we could have no shadows, because the waves of light would propagate themselves round opaque bodies as a wave of water round a rock. It has been proved since his time that the waves of light do bend round opaque bodies; but with that we have nothing now to do. A sound-wave certainly bends thus round an obstacle, though as it diffuses itself in the air at the back of the obstacle it is enfeebled in power, the obstacle thus producing a partial shadow of the sound. A railway train passing through cuttings and long embankments exhibits great variations in the intensity of the sound. The interposition of a hill in the Alps suffices to diminish materially the sound of a cataract; it is able sensibly to extinguish the tinkle of the cowbells. Still the sound-shadow is but partial, and the marker at the rifle-butts never fails to hear the explosion, though he is well protected from the ball. A striking example of this diffraction of a sonorous wave was exhibited at Erith after the tremendous explosion of a powder magazine which occurred there in 1864. The village of Erith was some miles distant from the magazine, but in nearly all cases the windows were shattered; and it was noticeable that the windows turned away from the origin of the explosion suffered almost as much as those which faced it. Lead sashes were employed in Erith Church, and these, being in some degree flexible, enabled the windows to yield to pressure without much fracture of the glass. As the sound-wave reached the church it separated right and left, and, for a moment, the edifice was clasped by a girdle of intensely compressed air, every window in the church, front and back, being bent inward. After compression, the air within the church no doubt dilated, tending to restore the windows to their first condition. The bending in of the windows, however, produced but a small condensation of the whole mass of air within the church; the recoil was therefore feeble in comparison with the pressure, and insufficient to undo what the latter had accomplished.

§ 8. Velocity of Sound: relation to Density and Elasticity of Air

Two conditions determine the velocity of propagation of a sonorous wave; namely, the elasticity and the density of the medium through which the wave passes. The elasticity of air is measured by the pressure which it sustains or can hold in equilibrium. At the sea-level this pressure is equal to that of a stratum of mercury about thirty inches high. At the summit of Mont Blanc the barometric column is not much more than half this height; and, consequently, the elasticity of the air upon the summit of the mountain is not much more than half what it is at the sea-level.

If we could augment the elasticity of air, without at the same time augmenting its density, we should augment the velocity of sound. Or, if allowing the elasticity to remain constant we could diminish the density, we should augment the velocity. Now, air in a closed vessel, where it cannot expand, has its elasticity augmented by heat, while its density remains unchanged. Through such heated air sound travels more rapidly than through cold air. Again, air free to expand has its density lessened by warming, its elasticity remaining the same, and through such air sound travels more rapidly than through cold air. This is the case with our atmosphere when heated by the sun.

The velocity of sound in air, at the freezing temperature, is 1,090 feet a second.

At all lower temperatures the velocity is less than this, and at all higher temperatures it is greater. The late M. Wertheim has determined the velocity of sound in air of different temperatures, and here are some of his results:

At a temperature of half a degree above the freezing-point of water the velocity is 1,089 feet a second; at a temperature of 26·6 degrees, it is 1,140 feet a second, or a difference of 51 feet for 26 degrees; that is to say, an augmentation of velocity of nearly two feet for every single degree centigrade.

With the same elasticity the density of hydrogen gas is much less than that of air, and the consequence is that the velocity of sound in hydrogen far exceeds its velocity in air. The reverse holds good for heavy carbonic-acid gas. If density and elasticity vary in the same proportion, as the law of Boyle and Mariotte proves them to do in air when the temperature is preserved constant, they neutralize each other’s effects; hence, if the temperature were the same, the velocity of sound upon the summits of the highest Alps would be the same as that at the mouth of the Thames. But, inasmuch as the air above is colder than that below, the actual velocity on the summits of the mountains is less than that at the sea-level. To express this result in stricter language, the velocity is directly proportional to the square root of the elasticity of the air; it is also inversely proportional to the square root of the density of the air. Consequently, as in air of a constant temperature elasticity and density vary in the same proportion, and act oppositely, the velocity of sound is not affected by a change of density, if unaccompanied by a change of temperature.

There is no mistake more common than to suppose the velocity of sound to be augmented by density. The mistake has arisen from a misconception of the fact that in solids and liquids the velocity is greater than in gases. But it is the higher elasticity of those bodies, in relation to their density, that causes sound to pass rapidly through them. Other things remaining the same, an augmentation of density always produces a diminution of velocity. Were the elasticity of water, which is measured by its compressibility, only equal to that of air, the velocity of sound in water, instead of being more than quadruple the velocity in air, would be only a small fraction of that velocity. Both density and elasticity, then, must be always borne in mind; the velocity of sound being determined by neither taken separately, but by the relation of the one to the other. The effect of small density and high elasticity is exemplified in an astonishing manner by the luminiferous ether, which transmits the vibrations of light—not at the rate of so many feet, but at the rate of nearly two hundred thousand miles a second.

Those who are unacquainted with the details of scientific investigation have no idea of the amount of labor expended in the determination of those numbers on which important calculations or inferences depend. They have no idea of the patience shown by a Berzelius in determining atomic weights; by a Regnault in determining coefficients of expansion; or by a Joule in determining the mechanical equivalent of heat. There is a morality brought to bear upon such matters which, in point of severity, is probably without a parallel in any other domain of intellectual action. Thus, as regards the determination of the velocity of sound in air, hours might be filled with a simple statement of the efforts made to establish it with precision. The question has occupied the attention of experimenters in England, France, Germany, Italy, and Holland. But to the French and Dutch philosophers we owe the application of the last refinements of experimental skill to the solution of the problem. They neutralized effectually the influence of the wind; they took into account barometric pressure, temperature, and hygrometric condition. Sounds were started at the same moment from two distant stations, and thus caused to travel from station to station through the self-same air. The distance between the stations was determined by exact trigonometrical observations, and means were devised for measuring with the utmost accuracy the time required by the sound to pass from the one station to the other. This time, expressed in seconds, divided into the distance expressed in feet, gave 1,090 feet per second as the velocity of sound through air at the temperature of 0° centigrade.

The time required by light to travel over all terrestrial distances is practically zero; and in the experiments just referred to the moment of explosion was marked by the flash of a gun, the time occupied by the sound in passing from station to station being the interval observed between the appearance of the flash and the arrival of the sound. The velocity of sound in air once established, it is plain that we can apply it to the determination of distances. By observing, for example, the interval between the appearance of a flash of lightning and the arrival of the accompanying thunder-peal, we at once determine the distance of the place of discharge. It is only when the interval between the flash and peal is short that danger from lightning is to be apprehended.

§ 9. Theoretic Velocity calculated by Newton Laplace’s Correction

We now come to one of the most delicate points in the whole theory of sound. The velocity through air has been determined by direct experiment; but knowing the elasticity and density of the air, it is possible, without any experiment at all, to calculate the velocity with which a sound-wave is transmitted through it. Sir Isaac Newton made this calculation, and found the velocity at the freezing temperature to be 916 feet a second. This is about one-sixth less than actual observation had proved the velocity to be, and the most curious suppositions were made to account for the discrepancy. Newton himself threw out the conjecture that it was only in passing from particle to particle of the air that sound required time for its transmission; that it moved instantaneously through the particles themselves. He then supposed the line along which sound passes to be occupied by air-particles for one-sixth of its extent, and thus he sought to make good the missing velocity. The very art and ingenuity of this assumption were sufficient to throw doubt on it; other theories were therefore advanced, but the great French mathematician Laplace was the first Fig. 12. to completely solve the enigma. I shall now endeavor to make you thoroughly acquainted with his solution.

Into this strong cylinder of glass, T U, Fig. 12, which is accurately bored, and quite smooth within, fits an air-tight piston. By pushing the piston down, I condense the air beneath it, heat being at the same time developed. A scrap of amadou attached to the bottom of the piston is ignited by the heat generated by compression. If a bit of cotton wool dipped into bisulphide of carbon be attached to the piston, when the latter is forced down, a flash of light, due to the ignition of the bisulphide of carbon vapor, is observed within the tube. It is thus proved that when air is compressed heat is generated. By another experiment it may be shown that when air is rarefied cold is developed. This brass box contains a quantity of condensed air. I open the cock, and permit the air to discharge itself against a suitable thermometer; the sinking of the instrument immediately declares the chilling of the air.

All that you have heard regarding the transmission of a sonorous pulse through air is, I trust, still fresh in your minds. As the pulse advances it squeezes the particles of air together, and two results follow from this compression. First, its elasticity is augmented through the mere augmentation of its density. Secondly, its elasticity is augmented by the heat of compression. It was the change of elasticity which resulted from a change of density that Newton took into account, and he entirely overlooked the augmentation of elasticity due to the second cause just mentioned. Over and above, then, the elasticity involved in Newton’s calculation, we have an additional elasticity due to changes of temperature produced by the sound-wave itself. When both are taken into account, the calculated and the observed velocities agree perfectly.

But here, without due caution, we may fall into the gravest error. In fact, in dealing with Nature, the mind must be on the alert to seize all her conditions; otherwise we soon learn that our thoughts are not in accordance with her facts. It is to be particularly noted that the augmentation of velocity due to the changes of temperature produced by the sonorous wave itself is totally different from the augmentation arising from the heating of the general mass of the air. The average temperature of the air is unchanged by the waves of sound. We cannot have a condensed pulse without having a rarefied one associated with it. But in the rarefaction, the temperature of the air is as much lowered as it is raised in the condensation. Supposing, then, the atmosphere parcelled out into such condensations and rarefactions, with their respective temperatures, an extraneous sound passing through such an atmosphere would be as much retarded in the latter as accelerated in the former, and no variation of the average velocity could result from such a distribution of temperature.