Sound

You will have little difficulty in seeing that we perform here, with air, substantially the same experiment as that of M. Melde with a vibrating string. When the string was too long to vibrate as a whole, it met the requirements of the tuning-fork to which it was attached by dividing into ventral segments. Now, in all cases, the length from a node to its next neighbor is half that of the sonorous wave: how many such half-waves then have we in our tube in the present instance? Sixteen (the figure shows only four of them). But the length of our glass tube vibrating thus longitudinally is also half that of the sonorous wave in glass. Hence, in the case before us, with the same rate of vibration, the length of the semi-wave in glass is sixteen times the length of the semi-wave in air. In other words, the velocity of sound in glass is sixteen times its velocity in air. Thus, by a single sweep of the wet rubber, we solve a most important problem. But, as M. Kundt has shown, we need not confine ourselves to air. Introducing any other gas into the tube, a single stroke of our wet cloth enables us to determine the relative velocity of sound in that gas and in glass. When hydrogen is introduced, the number of ventral segments is less than in air; when carbonic acid is introduced, the number is greater.

From the known velocity of sound in air, coupled with the length of one of these dust segments, we can immediately deduce the number of vibrations executed in a second by the tube itself. Clasping a glass tube at its centre and drawing my wetted cloth over one of its halves, I elicit this shrill note. The length of every dust segment, now within the tube, is 3 inches. Hence the length of the aërial sonorous wave corresponding to this note is 6 inches. But the velocity of sound in air of our present temperature is 1,120 feet per second; a distance which would embrace 2,240 of our sonorous waves. This number, therefore, expresses the number of vibrations per second executed by the glass tube now before us.

Instead of damping the centre of the tube, and making it a nodal point, we may employ any other of its subdivisions. Laying hold of it, for example, at a point midway between its centre and one of its ends, and rubbing it properly, it divides into three vibrating parts, separated by two nodes. We know that in this division the note elicited is the octave of that heard when a single node is formed at the middle of the tube; for the vibrations are twice as rapid. If therefore we divide the tube, having air within it, by two nodes instead of one, the number of ventral segments revealed by the lycopodium dust will be thirty-two instead of sixteen. The same remark applies, of course, to all other gases.

Filling a series of four tubes with air, carbonic acid, coal-gas, and hydrogen, and then rubbing each so as to produce two nodes, M. Kundt found the number of dust segments formed within the tube in the respective cases to be as follows:

Calling the velocity in air unity, the following fractions express the ratio of this velocity to those in the other gases:

Referring to a table introduced in our first chapter, we learn that Dulong by a totally different mode of experiment found the velocity in carbonic acid to be 0.86, and in hydrogen 3·8 times the velocity in air. The results of Dulong were deduced from the sounds of organ-pipes filled with the various gases; but here, by a process of the utmost simplicity, we arrive at a close approximation to his results. Dusting the interior surfaces of our tubes, filling them with the proper gases, and sealing their ends, they may be preserved for an indefinite time. By properly shaking one of them at any moment, its inner surface becomes thinly coated with the dust; and afterward a single stroke of the wet cloth produces the division from which the velocity of sound in the gas may be immediately inferred. Savart found that a spiral nodal line is formed round a tube or rod when it vibrates longitudinally, and Seebeck showed that this line was produced, not by longitudinal, but by secondary transverse vibrations. Now this spiral nodal line tends to complicate the division of the dust in our present experiments. It is, therefore, desirable to operate in a manner which shall altogether avoid the formation of this line; M. Kundt has accomplished this, by exciting the longitudinal vibrations in one tube, and producing the division into ventral segments in another, into which the first fits like a piston. Before you is a tube of glass, Fig. 110, seven feet long, and two inches internal diameter. One end of this tube is filled by the movable stopper b. The other end, K K, is also stopped by a cork, through the centre of which passes the narrower tube A a, which is firmly clasped at its middle by the cork, K K. The end of the interior tube, A a, is also closed with a projecting stopper, a, almost sufficient to fill the larger tube, but still fitting into it so loosely that the friction of a against the interior surface is too slight to interfere practically with its vibrations. The interior surface between a and b being lightly coated with the lycopodium dust, a wet cloth is passed briskly over A K; instantly the dust between a and b divides into a number of ventral segments. When the length of the column of air, a b, is equal to that of the glass tube, A a, the number of ventral segments is sixteen. When, as in the figure, a b is only one-half the length of A a, the number of ventral segments is eight.

But here you must perceive that the method of experiment is capable of great extension. Instead of the glass tube, A a, we may employ a rod of any other solid substance—of wood or metal, for example, and thus determine the relative velocity of sound in the solid and in air. In the place of the glass tube, for example, a rod of brass of equal length may be employed. Rubbing its external half by a resined cloth, it divides the column a b into the number of ventral segments proper to the metal’s rate of vibrations. In this way M. Kundt operated with brass, steel, glass, and copper, and his results prove the method to be capable of great accuracy. Calling, as before, the velocity of sound in air unity, the following numbers expressive of the ratio of the velocity of sound in brass to its velocity in air were obtained in three different series of experiments:

The coincidence is here extraordinary. To illustrate the possible accuracy of the method, the length of the individual dust segments was measured. In a series of twenty-seven experiments, this length was found to vary between 43 and 44 millimètres (each millimètre 1/25th of an inch), never rising so high as the latter and never falling so low as the former. The length of the metal rod, compared with that of one of the segments capable of this accurate measurement, gives us at once the velocity of sound in the metal, as compared with its velocity in air.

Three distinct experiments, performed in the same manner on steel, gave the following velocities, the velocity through air, as before, being regarded as unity:

Here the coincidence is quite as perfect as in the case of brass.

In glass, by this new mode of experiment, the velocity was found to be

15·25.49

Finally, in copper the velocity was found to be

11·96.

These results agree extremely well with those obtained by other methods. Wertheim, for example, found the velocity of sound in steel wire to be 15·108; M. Kundt finds it to be 15·34: Wertheim also found the velocity in copper to be 11·17; M. Kundt finds it to be 11·96. The differences are not greater than might be produced by differences in the materials employed by the two experimenters.

The length of the aërial column may or may not be an exact multiple of the wave-length, corresponding to the rod’s rate of vibration. If not, the dust segments usually take the form shown in Fig. 111. But if, by means of the stopper, b, the column of air be made an exact multiple of the wave-length, then the dust quits the vibrating segments altogether, and forms, as in Fig. 112, little isolated heaps at the nodes.

§ 19. Explanation of a Difficulty

And here a difficulty presents itself. The stopped end b of the tube Fig. 110 is, of course, a place of no vibration, where in all cases a nodal dust-heap is formed; but, whenever the column of air was an exact multiple of the wave-length, M. Kundt always found a dust-heap close to the end a of the vibrating rod also. Thus the point from which all the vibration emanated seemed itself to be a place of no vibration.

This difficulty was pointed out by M. Kundt, but he did not attempt its solution. We are now in a condition to explain it. In Lecture III. it was remarked that in strictness a node is not a place of no vibration; that it is a place of minimum vibration; and that, by the addition of the minute pulses which the node permits, vibrations of vast amplitude may be produced. The ends of M. Kundt’s tube are such points of minimum motion, the lengths of the vibrating segments being such that, by the coalescence of direct and reflected pulses, the air at a distance of half a ventral segment from the end of the tube vibrates much more vigorously than that at the end of the tube itself. This addition of impulses is more perfect when the aërial column is an exact multiple of the wave-length, and hence it is that, in this case, the vibrations become sufficiently intense to sweep the dust altogether away from the vibrating segments. The same point is illustrated by M. Melde’s tuning-forks, which, though they are the sources of all the motion, are themselves nodes.

An experiment of Helmholtz’s is here capable of instructive application. Upon the string of the sonometer described in our third lecture I place the iron stem of this tuning-fork, which executes 512 complete vibrations in a second. At present you hear no augmentation of the sound of the fork; the string remains quiescent. But on moving the fork along the string, at the number 33, a loud, swelling note issues from the string. At this particular tension the length 33 exactly synchronizes with the vibrations of the fork. By the intermediation of the string, therefore, the fork is enabled to transfer its motion to the sonometer, and through it to the air. The sound continues as long as the fork vibrates, but the least movement to the right or to the left from this point causes a sudden fall of the sound. Tightening the string, the note disappears; for it requires a greater length of this more highly tensioned string to respond to the fork. But, on moving the fork further away, at the number 36 the note again bursts forth. Tightening still more, 40 is found to be the point of maximum power. When the string is slackened, it must, of course, be shortened in order to make it respond to the fork. Moving the fork now toward the end of the string, at the number 25 the note is found as before. Again, shifting the fork to 35, nothing is heard; but, by the cautious turning of the key, the point of synchronism, if I may use the term, is moved further from the end of the string. It finally reaches the fork, and at that moment a clear, full note issues from the sonometer. In all cases, before the exact point is attained, and immediately in its vicinity, we hear “beats,” which, as we shall afterward understand, are due to the coalescence of the sound of the fork with that of the string, when they are nearly, but not quite, in unison with each other.

In these experiments, though the fork was the source of all the motion, the point on which it rested was a nodal point. It constituted the comparatively fixed extremity of the wire, whose vibrations synchronized with those of the fork. The case is exactly analogous to that of the hand holding the India-rubber tube, and to the tuning-fork in the experiments of M. Melde. It is also an effect precisely the same in kind as that observed by M. Kundt, where the part of the column of air in contact with the end of his vibrating rod proved to be a node instead of the middle of a ventral segment.

ADDENDUM REGARDING RESONANCE

The resonance of caves and of rocky inclosures is well known. Bunsen notices the thunder-like sound produced when one of the steam jets of Iceland breaks out near the mouth of a cavern. Most travellers in Switzerland have noticed the deafening sound produced by the fall of the Reuss at the Devil’s Bridge. The sound heard when a hollow shell is placed close to the ear is a case of resonance. Children think they hear in it the sound of the sea. The noise is really due to the reinforcement of the feeble sounds with which even the stillest air is pervaded, and also in part to the noise produced by the pressure of the shell against the ear itself. By using tubes of different lengths, the variation of the resonance with the length of the tube may be studied. The channel of the ear itself is also a resonant cavity. When a poker is held by two strings, and when the fingers of the hands holding the poker are thrust into the ears on striking the poker against a piece of wood, a sound is heard as deep and sonorous as that of a cathedral bell. When open, the channel of the ear resounds to notes whose periods of vibration are about 3,000 per second. This has been shown by Helmholtz, and Madame Seiler has found that dogs which howl to music are particularly sensitive to the same notes. We may expect from Mr. Francis Galton interesting results in connection with this subject.

SUMMARY OF CHAPTER V

When a stretched wire is suitably rubbed, in the direction of its length, it is thrown into longitudinal vibrations: the wire can either vibrate as a whole or divide itself into vibrating segments separated from each other by nodes.

The tones of such a wire follow the order of the numbers 1, 2, 3, 4, etc.

The transverse vibrations of a rod fixed at both ends do not follow the same order as the transverse vibrations of a stretched wire; for here the forces brought into play, as explained in Lecture IV., are different. But the longitudinal vibrations of a stretched wire do follow the same order as the longitudinal vibrations of a rod fixed at both ends, for here the forces brought into play are the same, being in both cases the elasticity of the material.

A rod fixed at one end vibrates longitudinally as a whole, or it divides into two, three, four, etc., vibrating parts, separated from each other by nodes. The order of the tones of such a rod is that of the odd numbers 1, 3, 5, 7, etc.

A rod free at both ends can also vibrate longitudinally. Its lowest note corresponds to a division of the rod into two vibrating parts by a node at its centre. The overtones of such a rod correspond to its division into three, four, five, etc., vibrating parts, separated from each other by two, three, four, etc., nodes. The order of the tones of such a rod is that of the numbers 1, 2, 3, 4, 5, etc.

We may also express the order by saying that while the tones of a rod fixed at both ends follow the order of the odd numbers 1, 3, 5, 7, etc., the tones of a rod free at both ends follow the order of the even numbers 2, 4, 6, 8, etc.

At the points of maximum vibration the rod suffers no change of density; at the nodes, on the contrary, the changes of density reach a maximum. This may be proved by the action of the rod upon polarized light.

Columns of air of definite length resound to tuning-forks of definite rates of vibration.

The length of a tube filled with air, and closed at one end, which resounds to a fork is one-fourth of the length of the sonorous wave produced by the fork.

This resonance is due to the synchronism which exists between the vibrating period of the fork and that of the column of air.

By blowing across the mouth of a tube closed at one end, we produce a flutter of the air, and some pulse of this flutter may be raised by the resonance of the tube to a musical sound.

The sound is the same as that obtained when a tuning-fork, whose rate of vibration is that of the tube, is placed over the mouth of the tube.

When a tube closed at one end—a stopped organ-pipe, for example—sounds its lowest note, the column of air within it is undivided by a node. The overtones of such a column correspond to its division into parts, like those of a rod fixed at one end and vibrating longitudinally. The order of its tones is that of the odd numbers 1, 3, 5, 7, etc. That this must be the order follows from the manner in which the column is divided.

In organ-pipes the air is agitated by causing it to issue from a narrow slit, and to strike upon a cutting edge. Some pulse of the flutter thus produced is raised by the resonance of the pipe to a musical sound.

When, instead of the aërial flutter, a tuning-fork of the proper rate of vibration is placed at the embouchure of an organ-pipe, the pipe speaks in response to the fork. In practice, the organ-pipe virtually creates its own tuning-fork, by compelling the sheet of air at its embouchure to vibrate in periods synchronous with its own.

An open organ-pipe yields a note an octave higher than that of a closed pipe of the same length. This relation is a necessary consequence of the respective modes of vibration.

When, for example, a stopped organ-pipe sounds its deepest note, the column of air, as already explained, is undivided. When an open pipe sounds its deepest note, the column is divided by a node at its centre. The open pipe in this case virtually consists of two stopped pipes with a common base. Hence it is plain that the fundamental note of an open pipe must be the same as that of a stopped pipe of half its length.

The length of a stopped pipe is one-fourth that of the sonorous wave which it produces, while the length of an open pipe is one-half that of its sonorous wave.

The order of the tones of an open pipe is that of the even numbers 2, 4, 6, 8, etc., or of the natural numbers 1, 2, 3, 4, etc.

In both stopped and open pipes the number of vibrations executed in a given time is inversely proportional to the length of the pipe.

The places of maximum vibration in organ-pipes are places of minimum changes of density; while at the places of minimum vibration the changes of density reach a maximum.

The velocities of sound in gases, liquids, and solids may be inferred from the tones which equal lengths of them produce; or they may be inferred from the lengths of these substances which yield equal tones.

Reeds, or vibrating tongues, are often associated with vibrating columns of air. They consist of flexible laminæ, which vibrate to and fro in a rectangular orifice, thus rendering intermittent the air-current passing through the orifice.

The action of the reed is the same as that of the siren.

The flexible wooden reeds sometimes associated with organ-pipes are compelled to vibrate in unison with the column of air in the pipe; other reeds are too stiff to be thus controlled by the vibrating air. In this latter case the column of air is taken of such a length that its vibrations synchronize with those of the reed.

By associating suitable pipes with reeds we impart to their tones the qualities of the human voice.

The vocal organ in man is a reed instrument, the vibrating reed in this case being elastic bands placed at the top of the trachea, and capable of various degrees of tension.

The rate of vibration of these vocal chords is practically uninfluenced by the resonance of the mouth; but the mouth, by changing its shape, can be caused to resound to the fundamental tone, or to any of the overtones of the vocal chords.

By the strengthening of particular tones through the resonance of the mouth, the clang-tint of the voice is altered.

The different vowel-sounds are produced by different admixtures of the fundamental tone and the overtones of the vocal chords.

When the solid substance of a tube stopped at one, or at both ends, is caused to vibrate longitudinally, the air within it is also thrown into vibration.

By covering the interior surface of the tube with a light powder, the manner in which the aërial column divides itself may be rendered apparent. From the division of the column the velocity of sound in the substance of the tube, compared with its velocity in air, may be inferred.

Other gases may be employed instead of air, and the velocity of sound in these gases, compared with its velocity in the substance of the tube, may be determined.

The end of a rod vibrating longitudinally may be caused to agitate a column of air contained in a tube, compelling the air to divide itself into ventral segments. These segments may be rendered visible by light powders, and from them the velocity of sound in the substance of the vibrating rod, compared with its velocity in air, may be inferred.

In this way the relative velocities of sound in all solid substances capable of being formed into rods, and of vibrating longitudinally, may be determined.

CHAPTER VI

Singing Flames—Influence of the Tube surrounding the Flame—Influence of Size of Flame—Harmonic Notes of Flames—Effect of Unisonant Notes on Singing Flames—-Action of Sound on Naked Flames—Experiments with Fish-Tail and Bat’s-Wing Burners—Experiments on Tall Flames—Extraordinary Delicacy of Flames as Acoustic Reagents—The Vowel-Flame—Action of Conversational Tones upon Flames—Action of Musical Sounds on Smoke-Jets—Constitution of Water-Jets—Plateau’s Theory of the Resolution of a Liquid Vein into Drops—Action of Musical Sounds on Water-Jets—A Liquid Vein may compete in Point of Delicacy with the Ear

§ 1. Rhythm of Friction: Musical Flow of a Liquid through a Small Aperture

FRICTION is always rhythmic. When a resined bow is passed across a string, the tension of the string secures the perfect rhythm of the friction. When the wetted finger is moved round the edge of a glass, the breaking up of the friction into rhythmic pulses expresses itself in music. Savart’s beautiful experiments on the flow of liquids through small orifices bear immediately upon this question. We have here the means of verifying his results. The tube A B, Fig. 113, is filled with water, its extremity, B, being closed by a plate of brass, which is pierced by a circular orifice of a diameter equal to the thickness of the plate. Removing a little peg which stops the orifice, the water issues from it, and as it sinks in the tube a musical note of great sweetness issues from the liquid column. This note is due to the intermittent flow of the liquid through the orifice, by which the whole column above it is thrown into vibration. The tendency to this effect shows itself when tea is poured from a teapot, in the circular ripples that cover the falling liquid. The same intermittence is observed in the black, dense smoke which rolls in rhythmic rings from the funnel of a steamer. The unpleasant noise of unoiled machinery is also a declaration of the fact that the friction is not uniform, but is due to the alternate “bite” and release of the rubbing surfaces.

Where gases are concerned, friction is of the same intermittent character. A rifle-bullet sings in its passage through the air; while to the rubbing of the wind against the boles and branches of the trees are to be ascribed the “waterfall tones” of an agitated pine-wood. Pass a steadily-burning candle rapidly through the air; an indented band of light, declaring intermittence, is often the consequence, while the almost musical sound which accompanies the appearance of this band is the audible expression of the rhythm. On the other hand, if you blow gently against a candle-flame, the fluttering noise announces a rhythmic action. We have already learned what can be done when a pipe is associated with such a flutter; we have learned that the pipe selects a special pulse from the flutter, and raises it by resonance to a musical sound. In a similar manner the noise of a flame may be turned to account. The blow-pipe flame of our laboratory, for example, when inclosed within an appropriate tube, has its flutter raised to a roar. The special pulse first selected soon reacts upon the flame so as to abolish in a great degree the other pulses, compelling the flame to vibrate in periods answering to the selected one. And this reaction can become so powerful—the timed shock of the reflected pulses may accumulate to such an extent—as to beat the flame, even when very large, into extinction.

§ 2. Musical Flames

Nor is it necessary to produce this flutter by any extraneous means. When a gas-flame is simply inclosed within a tube, the passage of the air over it is usually sufficient to produce the necessary rhythmic action, so as to cause the flame to burst spontaneously into song. This flame-music may be rendered exceedingly intense. Over a flame issuing from a ring burner with twenty-eight orifices, I place a tin tube 5 feet long and 2-1/2 inches in diameter. The flame flutters at first, but it soon chastens its impulses into perfect periodicity, and a deep and clear musical tone is the result. By lowering the gas the note now sounded is caused to cease, but, after a momentary interval of silence, another note, which is the octave of the last, is yielded by the flame. The first note was the fundamental note of the surrounding tube; this second note is its first harmonic. Here, as in the case of open organ-pipes, we have the aërial column dividing itself into vibrating segments, separated from each other by nodes.

Fig. 114. A still more striking effect is obtained with this larger tube, a b, Fig. 114, 15 feet long and 4 inches wide, which was made for a totally different purpose. It is supported by a steady stand, s s′, and into it is lifted the tall burner, shown enlarged at B. You hear the incipient flutter: you now hear the more powerful sound. As the flame is lifted higher the action becomes more violent, until finally a storm of music issues from the tube. And now all has suddenly ceased; the reaction of its own pulses upon the flame has beaten it into extinction. I relight the flame and make it very small. When raised within the tube, the flame again sings, but it is one of the harmonics of the tube that you now hear. On turning the gas fully on, the note ceases—all is silent for a moment; but the storm is brewing, and soon it bursts forth, as at first in a kind of hurricane of sound. By lowering the flame the fundamental note is abolished, and now you hear the first harmonic of the tube. Making the flame still smaller, the first harmonic disappears, and the second is heard. Your ears being disciplined to the apprehension of these sounds, I turn the gas once more fully on. Mingling with the deepest note you notice the harmonics, as if struggling to be heard amid the general uproar of the flame. With a large Bunsen’s rose burner, the sound of this tube becomes powerful enough to shake the floor and seats, and the large audience that occupies the seats of this room, while the extinction of the flame, by the reaction of the Fig. 115. sonorous pulses, announces itself by an explosion almost as loud as a pistol-shot. It must occur to you that a chimney is a tube of this kind upon a large scale, and that the roar of a flame in a chimney is simply a rough attempt at music.

Let us now pass on to shorter tubes and smaller flames. Placing tubes of different lengths over eight small flames, each of them starts into song, and you notice that as the tubes lengthen the tones deepen. The lengths of these tubes are so chosen that they yield in succession the eight notes of the gamut. Round some of them you observe a paper slider, s, Fig. 115, by which the tube can be lengthened or shortened. If while the flame is sounding the slider be raised, the pitch instantly falls; if lowered, the pitch rises. These experiments prove the flame to be governed by the tube. By the reaction of the pulses, reflected back upon the flame, its flutter is rendered perfectly periodic, the length of that period being determined, as in the case of organ-pipes, by the length of the tube.

The fixed stars, especially those near the horizon, shine with an unsteady light, sometimes changing color as they twinkle. I have often watched at night, upon the plateaux of the Alps, the alternate flash of ruby and emerald in the lower and larger stars. If you place a piece of looking-glass so that you can see in it the image of such a star, on tilting the glass quickly to and Fig. 116. fro, the line of light obtained will not be continuous, but will form a string of colored beads of extreme beauty. The same effect is obtained when an opera-glass is pointed to the star and shaken. This experiment shows that in the act of twinkling the light of the star is quenched at intervals; the dark spaces between the bright beads corresponding to the periods of extinction. Now, our singing flame is a twinkling flame. When it begins to sing you observe a certain quivering motion which may be analyzed with a looking-glass, or an opera-glass, as in the case of the star.50 I can now see the image of this flame in a small looking-glass. On tilting the glass, so as to cause the image to form a circle of light, the luminous band is not seen to be continuous, as it would be if the flame were perfectly steady; it is resolved into a beautiful chain of flames, Fig. 116.

§ 3. Experimental Analysis of Musical Flame

With a larger, brighter, and less rapidly-vibrating flame, you may all see this intermittent action. Over this gas-flame, f, Fig. 117, is placed a glass tube, A B, 6 feet long and 2 inches in diameter. The back of the tube is blackened, so as to prevent the light of the flame from falling directly upon the screen, which it is now desirable to have as dark as possible. In front of the tube is placed a concave mirror, M, which forms upon the screen an enlarged image of the flame. I turn the mirror with my hand and cause the image to pass over the screen. Were the flame silent and steady, we should obtain a continuous band of light; but it quivers, and emits at the same time a deep and powerful note. On twirling the mirror, therefore, we obtain, instead of a continuous band, a luminous chain of images. By fast turning, these images are drawn more widely apart; by slow turning, they are caused to close up, the chain of flames passing through the most beautiful variations. Clasping the lower end, B, of the tube with my hand, I so impede the air as to stop the flame’s vibration; a continuous band is the consequence. Observe the suddenness with which this band breaks up into a rippling line of images the moment my hand is removed and the current of air is permitted to pass over the flame.

§ 4. Rate of Vibration of Flame: Toepler’s Experiment

When a small vibrating coal-gas flame is carefully examined by the rotating mirror, the beaded line is a series of yellow-tipped flames, each resting upon a base of the richest blue. In some cases I have been unable to observe any union of one flame with another; the spaces between the flames being absolutely dark to the eye. But if dark, the flame must have been totally extinguished at intervals, a residue of heat, however, remaining sufficient to reignite the gas. This is at least possible, for gas may be ignited by non-luminous air.51 By means of the siren, we can readily determine the number of times this flame extinguishes and relights itself in a second. As the note of the instrument approaches that of the flame, unison is preceded by these well-known beats, which become gradually less rapid, and now the two notes melt into perfect unison. Maintaining the siren at this pitch for a minute, at the end of that time I find recorded upon our dials 1,700 revolutions. But the disk being perforated by 16 holes, it follows that every revolution corresponds to 16 pulses. Multiplying 1,700 by 16, we find the number of pulses in a minute to be 27,200. This number of times did our little flame extinguish and rekindle itself during the continuance of the experiment; that is to say, it was put out and relighted 453 times in a second.

A flash of light, though instantaneous, makes an impression upon the retina which endures for the tenth of a second or more. A flying rifle-bullet, illuminated by a single flash of lightning, would seem to stand still in the air for the tenth of a second. A black disk with radial white strips, when rapidly rotated, causes the white and black to blend to an impure gray; while a spark of electricity, or a flash of lightning, reduces the disk to apparent stillness, the white radial strips being for a time plainly seen. Now, the singing flame is a flashing flame, and M. Toepler has shown that by causing a striped disk to rotate at the proper speed in the presence of such a flame it is brought to apparent stillness, the white stripes being rendered plainly visible. The experiment is both easy and interesting.

§ 5. Harmonic Sounds of Flame

A singing flame yields so freely to the pulses falling upon it that it is almost wholly governed by the surrounding tube; almost, but not altogether. The pitch of the note depends in some measure upon the size of the flame. This is readily proved, by causing two flames to emit the same note, and then slightly altering the size of either of them. The unison is instantly disturbed by beats. By altering the size of a flame we can also, as already illustrated, draw forth the harmonic overtones of the tube which surrounds it. This experiment is best performed with hydrogen, its combustion being much more vigorous than that of ordinary gas. When a glass tube 7 feet long is placed over a large hydrogen-flame, the fundamental note of the tube is obtained, corresponding to a division of the column of air within it by a single node at the centre. Placing a second tube, 3 feet 6 inches long, over the same flame, no musical sound whatever is obtained; the large flame, in fact, is not able to accommodate itself to the vibrating period of the shorter tube. But, on lessening the flame, it soon bursts into vigorous song, its note being the octave of that yielded by the longer tube. I now remove the shorter tube, and once more cover the flame with the longer one. It no longer sounds its fundamental notes, but the precise note of the shorter tube. To accommodate itself to the vibrating period of the diminished flame, the longer column of air divides itself like an open organ-pipe when it yields its first harmonic. By varying the size of the flame, it is possible, with the tube now before you, to obtain a series of notes whose rates of vibration are in the ratio of the numbers 1:2:3:4:5; that is to say, the fundamental tone and its first four harmonics.

These sounding flames, though probably never before raised to the intensity in which they have been exhibited here to-day, are of old standing. In 1777, the sounds of a hydrogen-flame were heard by Dr. Higgins. In 1802, they were investigated to some extent by Chladni, who also refers to an incorrect account of them given by De Luc. Chladni showed that the tones are those of the open tube which surrounds the flame, and he succeeded in obtaining the first two harmonics. In 1802, G. De la Rive experimented on this subject. Placing a little water in the bulb of a thermometer, and heating it, he showed that musical tones of force and sweetness could be produced by the periodic condensation of the vapor in the stem of the thermometer. He accordingly referred the sounds of flames to the alternate expansion and condensation of the aqueous vapor produced by the combustion. We can readily imitate his experiments. Holding, with its stem oblique, a thermometer-bulb containing water in the flame of a spirit-lamp the sounds are heard soon after the water begins to boil. In 1818, however, Faraday showed that the tones are produced when the tube surrounding the flame is placed in air of a temperature higher than 100° C., condensation being then impossible. He also showed that the tones could be obtained from flames of carbonic oxide, where aqueous vapor is entirely out of the question.

§ 6. Action of Extraneous Sounds on Flame: Experiments of Schaffgotsch and Tyndall

After these experiments, the first novel acoustic observation on flames was made in Berlin by the late Count Schaffgotsch, who showed that when an ordinary gas-flame was surmounted by a short tube, a strong falsetto voice pitched to the note of the tube, or to its higher octave, caused the flame to quiver. In some cases when the note of the tube was high, the flame could even be extinguished by the voice.

In the spring of 1857, this experiment came to my notice. No directions were given in the short account of the observation published in “Poggendorff’s Annalen”; but, in endeavoring to ascertain the conditions of success, a number of singular effects forced themselves upon my attention. Meanwhile, Count Schaffgotsch also followed up the subject. To a great extent we travelled over the same ground, neither of us knowing how the other was engaged; but, so far as the experiments then executed are common to us both, to Count Schaffgotsch belongs the priority.

Let me here repeat his first observation. Within this tube, 11 inches long, burns a small gas-flame, bright and silent. The note of the tube has been ascertained, and now, standing at some distance from the flame, I sound that note; the flame quivers. To obtain the extinction of the flame it is necessary to employ a burner with a very narrow aperture, from which the gas issues under considerable pressure. On gently sounding the note of the tube surrounding such a flame, it quivers; but on throwing more power into the voice the flame is extinguished.

The cause of the quivering of the flame will be best revealed by an experiment with the siren. As the note of the siren approaches that of the flame you hear beats, and at the same time you observe a dancing of the flame synchronous with the beats. The jumps succeed each other more slowly as unison is approached. They cease when the unison is perfect, and they begin again as soon as the siren is urged beyond unison, becoming more rapid as the discordance is increased. The cause of the quiver observed by M. Schaffgotsch was revealed to me. The flame jumped because the note of the tube surrounding it was nearly, but not quite, in unison with the voice of the experimenter.

That the jumping of the flame proceeds in exact accordance with the beats is well shown by a tuning-fork, which yields the same note as the flame. Loading such a fork with a bit of wax, so as to throw it slightly out of unison, and bringing it, when agitated, near the tube in which the flame is singing, the beats and the leaps of the flame occur at the same intervals. When the fork is placed over a resonant jar, all of you can hear the beats, and see at the same time the dancing of the flame. By changing the load upon the tuning-fork, or by slightly altering the size of the flame, the rate at which the beats succeed each other may be altered; but in all cases the jumps address the eye at the moments when the beats address the ear.

While executing these experiments I noticed that, on raising my voice to the proper pitch, a flame which had been burning silently in its tube began to sing. The same observation had, without my knowledge, been made a short time previously by Count Schaffgotsch. A tube, 12 inches long, is placed over this flame, which occupies a position about an inch and a half from the lower end of the tube. When the proper note is sounded the flame trembles, but it does not sing. When the tube is lowered until the flame is three inches from its end, the song is spontaneous. Between these two positions there is a third, at which, if the flame be placed, it will burn silently; but if it be excited by the voice it will sing, and continue to sing.