Popular Science Monthly/Volume 13/May 1878/How Sound and Words are Produced

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THE recent appearance of those remarkable devices the telephone and the phonograph has given such a new interest to the general subject of voice, music, and sound, and the conditions and mechanisms by which they are produced, that a familiar explanation of some of the points involved may be useful at the present time.

Prof. Tyndall, in his work "On Sound," speaking of a tremendous powder-explosion which occurred at Erith, England, in 1864, shattering the windows on every side, though the village was some miles from the magazine, says: "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. Every window in the church, front and back, was bent inward. In fact, 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, which forced all its windows inward."

Now, was this "sound-wave" of compressed air, that struck the church, a wind-storm from the place of explosion? If not, whence all this force? That there was no wind is plain from the fact no dust was raised, nor a leaf stirred from its place. We must look for another explanation.

Suppose that, in the middle of a closely-packed crowd, "room" were suddenly made by pushing back the by-standers. These, thus suddenly losing their balance, would fall back on those behind them, and these in turn on others, and so on to the outsiders. It is easy to see that each one would recover his own balance by pushing against the one behind him, and so the fall-back movement would be seen to pass like a wave through the crowd, each one passing it on as it reached him. In like manner, the push of the expanding gases, at the explosion, was transmitted to the church, the intervening air only passing the push along. If the windows of the church had been elastic, they would have swayed with the air; as it was, they were pushed in, but had no back-spring.

The impulse which struck the church struck many ears in the same way, but their drums taking up the air-push and its back-snap, sent it to the brain, where it was put down as a tremendous sound. Sound, then, is only the beating of air-waves in the ear.

Now, a sound is either a noise or a musical tone. We take a noise to be the blow of a single wave, or an irregular succession of waves striking the ear, while a tone is the sound made by the beating of the same kind of a wave, at regular intervals, in such rapid succession as to form a sound-blend in the ear akin to the spoke-blend presented to the eye by the spokes of a fast-turning wheel.

We have divided sound into noise and musical tones, and have spoken of a tone, distinguished from noise, as being a sound-blend

Fig. 1.

made in the ear by the beating of the same kind of a wave, at regular intervals, in rapid succession. Let us prove this. We will strike middle C on a piano. We get a musical tone from its string, which is set a-vibrating, as shown in Fig. 1. But how shall we determine the number of vibrations, for we cannot begin to count them? We will take a tuning-fork, D, Fig. 2, that gives the same tone as middle C, thus having the same number of vibrations, and attach with a bristle fastened to one prong by a little wax. This will trace the vibrations, P, on the smoked paper L. The wave-forms of the marking, counted along either one side, indicate the number of vibrations. We count these wave-forms, and divide by the number of seconds the vibration lasted, and we have the number of vibrations per second corresponding to the tone of the fork. In this case we find "middle C" to vibrate 264 times in a second. In

Fig. 2.

the same way, we find D to vibrate 297; E, 330; F, 352; G, 396; A, 440; B, 495; and C, again, 528 times per second, just double of "middle C" below. In the same way each of the other tones doubles its vibrations going up, and halves them going down. Thus, from the first A of the bass of a seven-octave piano, to the last A of the treble, we have a range of from 27 vibrations, or pulses, per second to as many as 3,520. The number of vibrations is the same for the same note on any instrument.

We have thus proved, in a simple way, that a musical tone is produced by rapid, regular vibration, as shown by the marking—the air-waves, set up by the vibration, seeming to blend in the ear in a manner similar to that in which the vibrations of the string blend to the eye, which makes the tone seem continuous. In this experiment we notice that tones are high or low, according to the number of their vibrations—the higher the tone the greater the number of its vibrations per second. Again, we observe that we can make the same tone loud or soft, without making it higher or lower. We notice that loudness is obtained by striking with greater force, making the string or fork swing farther from side to side, but still swing the same number of times in a second. This force of the swing is given to the air, and carried to the ear, beating it with greater violence than before, but still only the same number of times a second. This width of swing, which makes the loudness of a sound, by a greater compression in the air-wave, is called the amplitude of vibration, and corresponds to the height of water-waves, where the amplitude is up and down. In water, the greater the force the higher are the waves. Now, let us turn to the sound-wave in the air, which we will study by the aid of Fig. 3. Here we take an ordinary A tuning-fork, having an elasticity of 440 vibrations per second, and set it a-vibrating. The prong of the fork, in moving from a to a', pushes the layer of air in front of it, which, in its endeavor to recover from this huddling, pushes against the next layer, which is thus in its turn compressed, the compression or push passing in this way, from layer to layer, through the air—the wider the swing of the prong the greater the compression in the air, and the louder the sound; meanwhile the prong moves back from a'

Fig. 3.

to a, causing a vacuum, which is instantly filled up by the return of the air which it had just pushed away. But the fork now swings back to a", causing the layer of air not only to return to its ordinary density at a, but causing it to expand, in order to fill up the vacuum from a a" thus producing a rarefaction, or stretch, in the air, which draws back on every other layer, causing a pulse of rarefaction to follow every pulse of compression; in other words, causing a stretch-gap to follow every push. A clear idea of this may be had by again using our illustration of a crowd: the place where some are just falling back on those behind them illustrates the wave of compression, while the gap between those falling back and those who have just recovered their balance illustrates the wave of rarefaction which follows it. An air-wave is made up of a compression and a rarefaction—a push and a stretch—the two being produced in one vibration of the prong, the compression by the motion from a to a', and the rarefaction by the reactive motion from a to a". On its way back to a, the prong lets up on the stretch, and goes on to a' with another push, and so on as long as it vibrates. These compressions and rarefactions, represented in the figure by its shadows and lights, correspond to the crests and hollows of water-waves.

In water we measure the length of waves (that is, the distance between them) from swell to swell. Sound-waves are measured from huddle to huddle. Now, how are we going to measure this? Let us take the case of water. If we knew that in 100 yards of water there were 100 equal waves, we would know that each wave was one yard in length—that is, that the wave-swells were thus far apart; or, if there were 50, each wave would stretch two yards. We would find the length of wave by dividing the distance covered by the number of waves stretched over it. The length of sound-waves is measured in the same way. We will measure the length, or distance apart, of the waves of our A-fork experiment. Sound travels, in round numbers, 1,100 feet in a second. Now, our A-fork, vibrating 440 times a second, sets 440 sound-waves in motion in a second, so that, at the end of a second, there would be 440 air-waves afloat, and the first one would have reached a distance of 1,100 feet away. Now, there being 440 equal air-waves in 1,100 feet, how far apart are they—in other words, how long is each wave? Dividing the 1,100 feet by the 440 waves, we get two and a half feet, or 30 inches, as the length of the air-waves of the first A-tone above "middle C"—the A-string of a violin. In the same way we find that the first A of the bass of our piano produces air-waves about forty feet in length, while the waves of the last A of the treble are not quite four inches long. We find the length of the air-waves of any musical note—that is, the distance apart of the pushes in the air—by dividing 1,100 feet, the distance which the waves would cover in a second, by the number of the note-vibrations per second, which represents the number of air-waves it would make in that time.

One thing we notice in all sounds, and that is their character, or peculiarity. They may be as near alike as they can be made, but each different kind will have something about it which distinguishes it from every other, and it is by this means that we distinguish different instruments or voices. The cause of this is the peculiar shape in which the wave comes from different sources, a sort of individual stamp by which a sound carries the telltale mark of its maker. These different stamps or trimmings of air-waves may be illustrated in Fig. 4, and will

Fig. 4.

be explained presently. The heavings represent the compressions, and the hollows the rarefactions, in the air. Let A represent the wave-form of the purely ideal tone of the note A with no stamp or quality given to it. B might represent the wave-form given it by a piano; and C, that given to it by a violin. In each case the wave-length, or distance between swells, and therefore pitch of tone, and the amplitude, or size of swells, and therefore loudness of tone, are the same; the only difference is, that the last two tone-waves seem to be trimmed with feather-waves, so to speak, the trimming varying with the source of the wave. A simple noise being a sound-wave, has its wave-form or make-mark. The blending of many such would produce a tone in that likeness; hence, a musical note is a blending of like noises, and every noise is really the first wave, the key-note of a musical tone. Take the ringing of a door-bell. Here the ear hears not only a musical tone, a sound-blend, in the ring of the bell, but also the noise of the clapper's clang, clang, clang. The vibrations of the bell throw the air into musical waves, shown in Fig. 5, while a huge clang-wave will sweep

Fig. 5.

along among the ring-waves every time the clapper strikes. If these clang-waves were to come along fast enough to blend, and at regular intervals, they would produce a tone of their own. The clanging of the clapper would not be a noise, but a deep tone, perhaps making a chord with the ring-tone. But, as it is, the clang-waves come irregularly and slowly, and only a noise is the result. The clang-wave is not represented in the figure, but may be easily imagined. From this we see that different sets of air-waves can move along together, and, though they should conglomerate, the ear can single them out. And now we can explain the peculiar character of different sounds, represented by the different forms of waves in Fig. 4. If the string in Fig. 1 would really vibrate in a clean sweep as it appears to, it would make

Fig. 6.

a smooth wave-form, like A in Fig. 4; but, while it vibrates as a whole, in starting the vibration of the string the sudden jerk on it will run along the string in a sort of wabble-wave to its ends and back again, as long as the string vibrates.

These wabble-waves, in passing each other as they run back and forth on the string in opposite ways, will form stand-still crossing points at distances apart corresponding to the length of the wabble-waves; thus dividing the string into vibrating parts, as in Fig. 6.

These make their own little swift air-waves, while the whole string is making its large and comparatively slow ones, and thus produce what are called overtones—waves within waves. These form the feather-wave trimming spoken of, and shown in Fig. 4. These over-vibrations chord

PSM V13 D059 Overtones of C note.jpg

Fig. 7.

or harmonize with the vibrations of the whole string, and are drowned in it, forming a conglomerate air-wave. They are two, three, four, five, six, seven, eight, etc., times the vibration of the whole string, and it is according to which of these over-vibrations is the fullest, that the sound takes its peculiar quality. Sounds without overtones are dull; with too many, harsh and grating; and, with the first six in fair proportion, are rich and sweet. Fig. 7 represents in musical language the overtones of the note C of 132 vibrations; number 1 being the

PSM V13 D059 A sound note experiment.jpg

Fig. 8.

whole string, the other numbers denoting the overtones up to the eighth, the first six being those that give richness to the tone, and of these, one or another being the most prominent according to the source from which the note comes.

We have said that the over-tones are drowned in the tone—only stamping or trimming it, but they can be picked out. Let us see now how we can pick these overtones out of the conglomerate.

It is found that a column of air one-fourth the wave-length, of any note's air-waves, will resound to that note and to no other. Let us take our A-fork again with 440 vibrations per second, making a wave-length of 30 inches, and when vibrating hold it over a tall jar as in Fig. 8. The column of air may not be the right length. By pouring in water a point will be reached at which the jar will burst into the tone A with the fork. By pouring in more water it stops. A certain length only will resound A. Measuring the resounding column of air, from the water to the top of the jar, we find it to be 7½ inches, one-fourth the length of the A-wave. Now, by making a resounder of this size, with an ear-opening in the bottom, we shall have an instrument that will pick out A every time from a sea of sound. This resonator is shown in Fig. 9; and Fig. 10 shows another form of the same instrument. Resonators tuned to the different

Fig. 9.

notes are made, and by their aid any sound can be analyzed, and each overtone brought out like the throbbing of a single string.

In this way it has been found that the peculiar character, or stamp, of any sound depends on its overtones, and furthermore on exactly what ones, so that by reproducing them any sound can be imitated. Of all sounds those of the human voice are the sweetest. None others are so rich in harmonic overtones, and this brings us to Words.

The vocal mechanism is made in two pieces. One, a wonderful musical instrument with only one vibrator—the vocal chords, Fig. 11—which can tune itself at once to any note. The other, the mouth, as an echo-cave or resonator, no less wonderful in its power of forming itself to resound the harmonics of the vocal tones. This gives the

Fig 10. Fig. 11.

voice its power of imitating any sound within its reach. We will analyze the voice.

Let the vocal chords sing or vibrate any note, and by merely changing the hollow of the mouth the purely musical sound will turn into what are called the vowel-sounds of speech, the closest position of the mouth making it ee, the deepest oo. Why is this, since the musical note is the same in each? It is because the different positions of the mouth resound to different overtones. While some vowel is sung we hold different resonators to the ear until we find the overtones. They must be the cause of the vowelizing of the tone sung. To prove it we take a tuning-fork vibrating the note of that vowel's overtone as found by the resonator, and, holding it in front of the mouth, we shape the mouth until it resounds to the tuning-fork. Keeping the mouth in this position, we sound the vocal chords, and the result is the vowel, thus proving that that particular overtone is its stamp. And so each vowel-sound is found to be due only to different overtones of the tone sung, brought out by the resonance of the mouth. Mixing in some of the other overtones forms the distinguishing peculiarity of individual voices.

Vowel-sounds, then, are really an exquisite musical harmony, being nothing but "chords" of the tone with its different overtones, different "chords" making different vowels. The common musical scale is derived from a tone and its overtones, by making, on separate strings, full tones corresponding to the overtones of some fundamental string-tone. That which produces a "chord" in music, where the harmony is made by full tones, would produce a vowel if the main tone only were full, and the "chording" tones overtones. When, then, a vowel is sung, high or low, it is still the same vowel at a different pitch—that is, the same "chord" in another key. But "chords" are music, and music means air-waves, so that vowels are musical air-waves. But vowels alone, which are only musical tones, will not make speech. Yet, by breaking into the vowel-tone with certain expressive noises called consonants, we can give the vowel-tone such a turn as to make its motion a copy of a motion of sensation, which, reaching the mysterious mechanism of an ear, will be changed back into a sensation.

It seems strange that words should be nothing but music broken up by different expressive noises, but we all know how differently we are affected by different noises. And in music it is recognized that different keys produce different effects; certain keys better than others, exciting certain emotions. But what are certain keys but certain vibrations, and these vibrations but certain motions? And, again, what are emotions but derived motions, which again are but vibrations?

To illustrate, let us follow the transmutations of a sensation. Let a "consciousness" be excited. That means motion, and from that tense focus the emotion rushes through the nerves, losing, in intensity as it gains more room—that is, the more nerves there are that are set in vibration the slower the vibration becomes—music still and in the same key, but lower down the scale. Suppose the key of the emotion or sensation to be the one that moves the hand, then the hand will act. Suppose the key to be the one whose "chords" the vocal mechanism plays in, then that will take up the nerve-waves, which will thus be transformed into air-waves, but who can tell how many octaves below the pitch of the sensation-waves in the nerves? The waves have passed as through a lens, and been magnified like mites in a magic-lantern. Suppose the sensation to have made one speak the word "hope." We cannot explore the nerve-waves, but, projected in the air, they become a picture that we can study. First there is the rough breathing or tremor h, then the mouth tunes itself for the musical tone o. Suppose the o to be made in a man's voice at a pitch A, below middle C. The o-making overtone is its octave overtone or second, which in this case will be A above middle C, the pitch to which the mouth will resound. Besides this prominent overtone, o has some feeble third and fourth overtones, and for the personal peculiarity say a little fifth. What is

PSM V13 D062 Sound vibrations of increasing frequencies.jpg

Fig. 12.

this o, then? A tone-vibration of 220 per second, frilled with overtone vibrations of 440, 660, 880, and 1,100 per second. In the air, on its way to an ear, this o is a matter of air-waves 5 feet in length, filled in with waves of 30, 20, 15, and 10 inches in length, and—let us be thankful that we do not have to understand o before we can exclaim it. Following this, the mouth suddenly shuts up and pushes off the vowel-ripples with a noisy billowy p. Fig. 12 will give an idea of the "hope" waves going through the air, end-foremost, of course, as they were spoken. And so words follow each other in sets of waves like the above, with rests between the sets made by the pauses between words.

PSM V13 D062 The ear canal.jpg

Fig. 13.

Now, how far will these waves be loud enough to be heard—that is, how long will they keep strong enough to beat the drum-head of an ear? The farther they go the more they spread, and the weaker they become. A strong voice may be heard at an eighth of a mile, or about 700 feet. As sound travels 1,100 feet per second, it follows that, in less than a second after being spoken, the waves become too weak to make words. Let us be quick, then, to find what they are saying. Sun-waves, spreading from a focus, may be brought again to a focus by condensing them with a lens. So the sensation-waves, which spread from a focus, may be brought again to a focus by condensing them with an ear (Fig. 12). Here, across a little echo-cave, is hung a curtain, Ty. M., which is blown in and out as each air-wave beats against it; and, though the air-waves vary from 40 feet to 4 inches apart, they jump the distance quickly, and this curtain, taking an exact copy of each, in vibrations less than the thousandth part of an inch, sends them, through the tapping bones, Mall., Stp., to an inside curtain, F.o., where they are condensed again, and thrown through a liquid which fills the hollow inside of it. Here three thousand tuned nerves take up, each, its own acchording waves, and bear them to the brain; and thus the wild waves of an emotion passed from one "consciousness" to another in less than a second, proving that the "quickness of thought" is no metaphor. Through pipes, the sound of the voice may be heard nearly four miles, and conversation carried on at nearly a mile. Through the wire of the telephone, which has become literally the "thread of a conversation," sound, with all its qualities, is conveyed hundreds of miles, as we have already shown in a former article.