[Ill.u.s.tration: FIG. 165.--The ball does not remain at rest]

These simple facts lead us to conclude that all sound is due to the motion of matter, and that a sounding body of any kind is in rapid motion.

251. Sound is carried by Matter. In most cases sound reaches the ear through the air; but air is not the only medium through which sound is carried. A loud noise will startle fish, and cause them to dart away, so we conclude that the sound must have reached them through the water. An Indian puts his ear to the ground in order to detect distant footsteps, because sounds too faint to be heard through the air are comparatively clear when transmitted through the earth. A gentle tapping at one end of a long table can be distinctly heard at the opposite end if the ear is pressed against the table; if the ear is removed from the wood, the sound of tapping is much fainter, showing that wood transmits sound more readily than air. We see therefore that sound can be transmitted to the ear by solids, liquids, or gases.

Matter of any kind can transmit sound to the ear. The following experiments will show that matter is necessary for transmission.

Attach a small toy bell to a gla.s.s rod (Fig. 166) by means of a rubber tube and pa.s.s the rod through one of two openings in a rubber cork.

Insert the cork in a strong flask containing a small quant.i.ty of water and shake the bell, noting the sound produced. Then heat the flask, allowing the water to boil briskly, and after the boiling has continued for a few minutes remove the flame and instantly close up the second opening by inserting a gla.s.s stopper. Now shake the flask and note that the sound is very much fainter than at first. As the flask was warmed, air was rapidly expelled; so that when the flask was shaken the second time, less air was present to transmit the sound. If the gla.s.s stopper is removed and the air is allowed to reenter the flask, the loudness of the sound immediately increases.

[Ill.u.s.tration: FIG. 166.--Sound is carried by the air.]

Since the sound of the bell grows fainter as air is removed, we infer that there would be no sound if all the air were removed from the flask; that is to say, sound cannot be transmitted through empty s.p.a.ce or a vacuum. If sound is to reach our ears, it must be through the agency of matter, such as wood, water, or air, etc.

252. How Sound is transmitted through Air. We saw in Section 250 that sound can always be traced to the motion or vibration of matter.

It is impossible to conceive of an object being set into sudden and continued motion without disturbing the air immediately surrounding it. A sounding body always disturbs and throws into vibration the air around it, and the air particles which receive motion from a sounding body transmit their motion to neighboring particles, these in turn to the next adjacent particles, and so on until the motion has traveled to very great distances. The manner in which vibratory motion is transmitted by the atmosphere must be unusual in character, since no motion of the air is apparent, and since in the stillness of night when "not a breath of air" is stirring, the shriek of a railroad whistle miles distant may be heard with perfect clearness. Moreover, the most delicate notes of a violin can be heard in the remotest corners of a concert hall, when not the slightest motion of the air can be seen or felt.

In our study of the atmosphere we saw that air can be compressed and rarefied; in other words, we saw that air is very elastic. It can be shown experimentally that whenever an elastic body in motion comes in contact with a body at rest, the moving body transfers its motion to the second body and then comes to rest itself. Let two billiard b.a.l.l.s be suspended in the manner indicated in Figure 167. If one of the b.a.l.l.s is drawn aside and is then allowed to fall against the other, the second ball is driven outward to practically the height from which the first ball fell and the first ball comes to rest.

[Ill.u.s.tration: FIG. 167.--Elastic b.a.l.l.s.]

[Ill.u.s.tration: FIG. 168.--Suspended billiard b.a.l.l.s.]

If a number of b.a.l.l.s are arranged in line as in Figure 168 or Figure 169, and the end ball is raised and then allowed to fall, or if _A_ is pushed against _C_, the last ball _B_ will move outward alone, with a force nearly equal to that originally possessed by _A_ and to a distance nearly equal to that through which _A_ moved. But there will be no _visible_ motion of the intervening b.a.l.l.s. The force of the moving ball _A_ is given to the second ball, and the second ball in turn gives the motion to the third, and so on throughout the entire number, until _B_ is reached. But _B_ has no ball to give its motion to, hence _B_ itself moves outward, and moves with a force nearly equal to that originally imparted by _A_ and to a distance nearly equal to that through which _A_ fell. Motion at _A_ is transmitted to _B_ without any perceptible motion of the b.a.l.l.s lying between these points. Similarly the particles of air set into motion by a sounding body impart their motion to each other, the motion being transmitted onward without any perceptible motion of the air itself. When this motion reaches the ear, it sets the drum of the ear into vibration, and these vibrations are in turn transmitted to the auditory nerves, which interpret the motion as sound.

[Ill.u.s.tration: FIG. 169.--Elastic b.a.l.l.s transmit motion.]

[Ill.u.s.tration: FIG. 170.--When a ball meets more than one ball, it divides its motion.]

253. Why Sound dies away with Distance. Since the last ball _B_ is driven outward with a force nearly equal to that possessed by _A_, it would seem that the effect on the ear drum should be independent of distance and that a sound should be heard as distinctly when remote as when near. But we know from experience that this is not true, because the more distant the source of sound, the fainter the impression; and finally, if the distance between the source of sound and the hearer becomes too great, the sound disappears entirely and nothing is heard.

The explanation of this well-known fact is found in a further study of the elastic b.a.l.l.s (Fig. 170). If _A_ hits two b.a.l.l.s instead of one, the energy possessed by _A_ is given in part to one ball, and in part to the other, so that neither obtains the full amount. These b.a.l.l.s, having each received less than the original energy, have less to transmit; each of these b.a.l.l.s in turn meets with others, and hence the motion becomes more and more distributed, and distant b.a.l.l.s receive less and less impetus. The energy finally given becomes too slight to affect neighboring b.a.l.l.s, and the system comes to rest. This is what occurs in the atmosphere; a moving air particle meets not one but many adjacent air particles, and each of these receives a portion of the original energy and transmits a portion. When the original disturbance becomes scattered over a large number of air particles, the energy given to any one air particle becomes correspondingly small, and finally the energy becomes so small that further particles are not affected; beyond this limit the sound cannot be heard.

If an air particle transmitted motion only to those air particles directly in line with it, we should not be able to detect sound unless the ear were in direct line with the source. The fact that an air particle divides its motion among all particles which it touches, that is, among those on the sides as well as those in front, makes it possible to hear sound in all directions. A good speaker is heard not only by those directly in front of him, but by those on the side, and even behind him.

254. Velocity of Sound. The transmission of motion from particle to particle does not occur instantaneously, but requires time. If the distance is short, so that few air particles are involved, the time required for transmission is very brief, and the sound is heard at practically the instant it is made. Ordinarily we are not conscious that it requires time for sound to travel from its source to our ears, because the distance involved is too short. At other times we recognize that there is a delay; for example, thunder reaches our ears after the lightning which caused the thunder has completely disappeared. If the storm is near, the interval of time between the lightning and the thunder is brief, because the sound does not have far to travel; if the storm is distant, the interval is much longer, corresponding to the greater distance through which the sound travels.

Sound does not move instantaneously, but requires time for its transmission. The report of a distant cannon is heard after the flash and smoke are seen; the report of a near cannon is heard the instant the flash is seen.

The speed with which sounds travels through the air, or its velocity, was first measured by noting the interval (54.6 seconds) which elapsed between the flash of a cannon and the sound of the report. The distance of the cannon from the observer was measured and found to be 61,045 feet, and by dividing this distance by the number of seconds, we find that the distance traveled by sound in one second is approximately 1118 feet.

High notes and low notes, soft notes and shrill notes, all travel at the same rate. If ba.s.s notes traveled faster or slower than soprano notes, or if the delicate tones of the violin traveled faster or slower than the tones of a drum, music would be practically impossible, because at a distance from the source of sound the various tones which should be in unison would be out of time--some arriving late, some early.

255. Sound Waves. Practically everyone knows that a hammock hung with long ropes swings or vibrates more slowly than one hung with short ropes, and that a stone suspended by a long string swings more slowly than one suspended by a short string. No two rocking chairs vibrate in the same way unless they are exactly alike in shape, size, and material. An object when disturbed vibrates in a manner peculiar to itself, the vibration being slow, as in the case of the long-roped swing, or quick, as in the case of the short-roped swing. The time required for a single swing or vibration is called the _period_ of the body, and everything that can vibrate has a characteristic period.

Size and shape determine to a large degree the period of a body; for example, a short, thick tuning fork vibrates more rapidly than a tall slender fork.

[Ill.u.s.tration: FIG. 171.--The two hammocks swing differently.]

Some tuning forks when struck vibrate so rapidly that the p.r.o.ngs move back and forth more than 5000 times per second, while other tuning forks vibrate so slowly that the vibrations do not exceed 50 per second. In either case the distance through which the p.r.o.ngs move is very small and the period is very short, so that the eye can seldom detect the movement itself. That the p.r.o.ngs are in motion, however, is seen by the action of a pith ball when brought in contact with the p.r.o.ngs (see Section 250).

[Ill.u.s.tration: FIG. 172.--The pitch given out by a fork depends upon its shape.]

The disturbance created by a vibrating body is called a wave.

256. Waves. While the disturbance which travels out from a sounding body is commonly called a wave, it is by no means like the type of wave best known to us, namely, the water wave.

If a closely coiled heavy wire is suspended as in Figure 173 and the weight is drawn down and then released, the coil will a.s.sume the appearance shown; there is clearly an overcrowding or condensation in some places, and a spreading out or rarefaction in other places. The pulse of condensation and rarefaction which travels the length of the wire is called a wave, although it bears little or no resemblance to the familiar water wave. Sound waves are similar to the waves formed in the stretched coil.

[Ill.u.s.tration: FIG. 173.--Waves in a coiled wire.]

Sound waves may be said to consist of a series of condensations and rarefactions, and the distance between two consecutive condensations and rarefactions may be defined as the wave length.

257. How One Sounding Body produces Sound in Another Body. In Section 255 we saw that any object when disturbed vibrates in a manner peculiar to itself,--its natural period,--a long-roped hammock vibrating slowly and a short-roped hammock vibrating rapidly. From observation we learn that it requires but little force to cause a body to vibrate in its natural period. If a sounding body is near a body which has the same period as itself, the pulses of air produced by the sounding body will, although very small, set the second body into motion and cause it to make a faint sound. When a piano is being played, we are often startled to find that a window pane or an ornament responds to some note of the piano. If two tuning forks of exactly identical periods (that is, of the same frequency) are placed on a table as in Figure 174, and one is struck so as to give forth a clear sound, the second fork will likewise vibrate, even though the two forks may be separated by several feet of air. We can readily see that the second fork is in motion, although it has not been struck, because it will set in motion a pith ball suspended beside it; at first the pith ball does not move, then it moves slightly, and finally bounces rapidly back and forth. If the periods of the two forks are not identical, but differ in the slightest degree, the second fork will not respond to the first fork, no matter how long or how loud the sound of the first fork. If we suppose that the fork vibrates 256 times each second, then 256 gentle pulses of air are produced each second, and these, traveling outward through the air, reach the silent fork and tend to set it in motion. A single pulse of air could not move the solid, heavy p.r.o.ngs, but the acc.u.mulated action of 256 vibrations per second soon makes itself felt, and the second fork begins to vibrate, at first gently, then gradually stronger, and finally an audible tone is given forth.

[Ill.u.s.tration: FIG. 174.--When the first fork vibrates, the second responds.]

The c.u.mulative power of feeble forces acting frequently at definite intervals is seen in many ways in everyday life. A small boy can easily swing a much larger boy, provided he gives the swing a gentle push in the right direction every time it pa.s.ses him. But he must be careful to push at the proper instant, since otherwise his effort does not count for much; if he pushes forward when the swing is moving backward, he really hinders the motion; if he waits until the swing has moved considerably forward, his push counts for little. He must push at the proper instant; that is, the way in which his hand moves in giving the push must correspond exactly with the way in which the swing would naturally vibrate. A very striking experiment can be made by suspending from the ceiling a heavy weight and striking this weight gently at regular, properly timed intervals with a small cork hammer.

Soon the pendulum, or weight, will be set swinging.

[Ill.u.s.tration: FIG. 175.--The hollow wooden box reenforces the sound.]

258. Borrowed Sound. Picture frames and ornaments sometimes buzz and give forth faint murmurs when a piano or organ is played. The waves sent out by a sounding body fall upon all surrounding objects and by their repeated action tend to throw these bodies into vibration. If the period of any one of the objects corresponds with the period of the sounding body, the gentle but frequent impulses affect the object, which responds by emitting a sound. If, however, the periods do not correspond, the action of the sound waves is not sufficiently powerful to throw the object into vibration, and no sound is heard. Bodies which respond in this way are said to be sympathetic and the response produced is called _resonance_. Seash.e.l.ls when held to the ear seem to contain the roar of the sea; this is because the air within the sh.e.l.l is set into sympathetic vibrations by some external tone. If the seash.e.l.l were held to the ear in an absolutely quiet room, no sound would be heard, because there would be no external forces to set into vibration the air within the sh.e.l.l.

Tuning forks do not produce strong tones unless mounted on hollow wooden boxes (Fig. 175), whose size and shape are so adjusted that resonance occurs and strengthens the sound. When a human being talks or sings, the air within the mouth cavity is thrown into sympathetic vibration and strengthens the otherwise feeble tone of the speaker.

259. Echo. If one shouts in a forest, the sound is sometimes heard a second time a second or two later. This is because sound is reflected when it strikes a large obstructing surface. If the sound waves resulting from the shout meet a cliff or a mountain, they are reflected back, and on reaching the ear produce a later sensation of sound.

By observation it has been found that the ear cannot distinguish sounds which are less than one tenth of a second apart; that is, if two sounds follow each other at an interval less than one tenth of a second, the ear recognizes not two sounds, but one. This explains why a speaker can be heard better indoors than in the open air. In the average building, the walls are so close that the reflected waves have but a short distance to travel, and hence reach the ear at practically the same time as those which come directly from the speaker. In the open, there are no reflecting walls or surfaces, and the original sound has no reenforcement from reflection.

If the reflected waves reach the ear too late to blend with the original sound, that is, come later than one tenth of a second after the first impression, an echo is heard. What we call the rolling of thunder is really the reflection and re-reflection of the original thunder from cloud and cliff.

Some halls are so large that the reflected sounds cause a confusion of echoes, but this difficulty can be lessened by hanging draperies, which break the reflection.

260. Motion does not always produce Sound. While we know that all sound can be traced to motion, we know equally well that motion does not always produce sound. The hammock swinging in the breeze does not give forth a sound; the flag floating in the air does not give forth a sound unless blown violently by the wind; a card moved slowly through the air does not produce sound, but if the card is moved rapidly back and forth, a sound becomes audible.

Motion, in order to produce sound, must be rapid; a ball attached to a string and moved slowly through the air produces no sound, but the same ball, whirled rapidly, produces a distinct buzz, which becomes stronger and stronger the faster the ball is whirled.

261. Noise and Music. When the rapid motions which produce sound are irregular, we hear noise; when the motions are regular and definite, we have a musical tone; the rattling of carriage wheels on stones, the roar of waves, the rustling of leaves are noise, not music. In all these ill.u.s.trations we have rapid but irregular motion; no two stones strike the wheel in exactly the same way, no two waves produce pulses in the air of exactly the same character, no two leaves rustle in precisely the same way. The disturbances which reach the ear from carriage, waves, and leaves are irregular both in time and strength, and irritate the ear, causing the sensation which we call noise.

The tuning fork is musical. Here we have rapid, regular motion; vibrations follow each other at perfectly definite intervals, and the air disturbance produced by one vibration is exactly like the disturbance produced by a later vibration. The sound waves which reach the ear are regular in time and kind and strength, and we call the sensation music.

To produce noise a body must vibrate in such a way as to give short, quick shocks to the air; to produce music a body must not only impart short, quick shocks to the air, but must impart these shocks with unerring regularity and strength. A flickering light irritates the eye; a flickering sound or noise irritates the ear; both are painful because of the sudden and abrupt changes in effect which they cause, the former on the eye, the latter on the ear.

The only thing essential for the production of a musical sound is that the waves which reach the ear shall be rapid and regular; it is immaterial how these waves are produced. If a toothed wheel is mounted and slowly rotated, and a stiff card is held against the teeth of the wheel, a distinct tap is heard every time the card strikes the wheel.

But if the wheel is rotated rapidly, the ear ceases to hear the various taps and recognizes a deep continuous musical tone. The blending of the individual taps, occurring at regular intervals, has produced a sustained musical tone. A similar result is obtained if a card is drawn slowly and then rapidly over the teeth of a comb.

[Ill.u.s.tration: FIG. 176.--A rotating disk.]

That musical tones are due to a succession of regularly timed impulses is shown most clearly by means of a rotating disk on which are cut two sets of holes, the outer set equally s.p.a.ced, and the inner set unequally s.p.a.ced (Fig. 176).

If, while the disk is rotating rapidly, a tube is held over the outside row and air is blown through the tube, a sustained musical tone will be heard. If, however, the tube is held, during the rotation of the disk, over the inner row of unequally s.p.a.ced holes, the musical tone disappears, and a series of noises take its place. In the first case, the separate puffs of air followed each other regularly and blended into one tone; in the second case, the separate puffs of air followed each other at uncertain and irregular intervals and the result was noise.