Popular Science Monthly/Volume 3/May 1873/Wave-Action in Nature
THE waves upon water are always objects of pleasing interest. From the ripples of the pond to the billows of the ocean, their beauty and their sublimity are sources of perennial inspiration to the poet and the painter. But there is an invisible realm of air-waves of a far subtler and more wonderful order. The water-waves belong to the sensuous eye and to art, but the aerial pulsations belong to the eye of the imagination and to science, the great revelator of the super-sensuous harmonies of the universe. Water-waves afford an agreeable spectacle, and have little further concern for us; but the waves of air take hold of our highest life, for the multitudinous sounds of Nature by which we are soothed and exhilarated, all the delights of music, the pleasures of speech, and the sweet experiences of social intercourse, are made possible only through their agency. Besides, air-waves form one link in the chain of agencies by which we pass from the material to the spiritual world. The first is the capacity by which matter may be thrown into vibration; second, the properties of air by which it can take up the impulses of vibration in the form of waves; third, those properties of the mechanism of hearing by which it can take up the motion of air-pulses; and, fourth, those properties of nerves by which they can take up the tympanic vibrations and translate them into feeling or consciousness. How the last step is effected we do not know, but many of the preliminary conditions to it are understood, and to some of these we ask the reader's attention.
All sound begins in those collisions and attritions among material things by which their parts are thrown into tremors. These are almost as various in quality as the properties of material substances. The sounds we hear are but indices to the vibrations of bodies from which they proceed, and the multitude of such terms as splash, roar, ring, thud, crack, whiz, squeak, crash, illustrate the marvellous diversity of characters which material vibrations may take. In the production of noise, the thrills of matter are transient and irregular, but, when prolonged and regular, they give rise to musical sounds. Vibration depends upon elasticity, and bodies which are capable of the protracted and measured pulsations of music must, of course, be highly elastic. We have said that bodies vibrate differently, and this depends upon the nature, form, and magnitude of the mass in motion. The vibrations of bells differ with their sizes and the metals and alloys which compose them; while wooden and metallic tubes, strained strings, and stretched membranes, illustrate the same thing. If a tense wire be plucked aside, it executes lateral vibrations which differ with its varying length, strain, and density. It may vibrate as a whole (1), Fig. 1, while, by relaxing the tension, or by touching or damping it at different points, it may be made to break up into different systems of vibration as shown in (2), (3), (4), Fig. 1. The points of rest in such cases are called nodes. Rods and tubes of wood or glass may be made to vibrate longitudinally by rubbing them lengthwise with the rosined fingers or a damp cloth. Fig. 2 represents a glass tube, six feet long and two inches in diameter, which, by being vigorously rubbed in this way, was set into such violent vibration that it went to pieces.
A String in Different Phases of Vibration.
If thin plates of glass or metal be clamped in the centre, and fine sand scattered over the surface, they may be set into vibration, and the sand will be tossed away from certain parts of the surface and collected in other parts, forming regular geometrical figures. The sand collects at the lines of rest, which are called nodal lines. Fig. 3 represents this experiment, the vibration being produced by a fiddle-bow, while the application of the fingers at different points determines the lines of rest and the geometrical figures. Fig. 4 represents a number of the beautiful patterns that were obtained by Chladni, who first drew attention to this interesting phenomenon.
Now, in order that all these multifarious and diversified tremblings of natural objects may be brought into relation with animate creatures a common medium of communication is necessary. The air around us is such a medium. It possesses the marvellous power of taking up
the numberless and ever-varying thrills of material objects, and conveying them through space with all their peculiarities. The sensitiveness of the air (if we may so speak) to the faintest tremors in material objects, and its power of transmitting their individual qualities, are most wonderful. It drinks up the infinitesimal motions of things, and diffuses them swiftly, simultaneously, and in countless myriads in all directions around.
That air is the medium of sound is proved by the fact that, when vibrations occur in space void of air, the silence is not broken. If a bell suspended by a string in a vacuum be struck, nothing is heard, although, if it is in contact with the jar, the vibrations are communicated to the outer air, and sounds produced. That air transmits the kind of motion that it receives is also proved by the fact that it will take up vibrations at one point and communicate them to a distant object that is capable of vibrating in the same way.
The velocity of impulses in the air which produce sound has been well established, and all kinds of shocks—the firing of a gun, notes of a musical instrument, or the voice, whether high or low, harsh or soft all move at the same rate. The velocity is not affected by changes in atmospheric pressure or moisture, or by rain or snow, but it is affected by wind and by temperature. The speed of sound is 1,090 feet per second at the freezing-point, and increases about one foot per second for each degree of ascent on the Fahrenheit scale. It, therefore, takes longer to hear in winter than in summer. In many parts of the country the change of temperature is so great that the velocity of sound will vary more than 100 feet a second in the different seasons. Sound moves in air with about the speed of a cannon-ball, and at a rate ten times greater than the swiftest motion of air in a hurricane. The sound produced in the open air tends to move in all directions with equal speed, but this tendency may be disturbed by various conditions. If the whole mass of air is moving in one direction, sound will travel faster with it than against it. In still air the sound of a musket-shot will be heard farthest in the direction of the impulse. Experiments have shown that a person speaking in the open air can be heard about equally well at a distance of 100 feet in front, 75 feet on each side, and 30 feet behind. When an obstacle checks a sound in one direction it can be heard farther in others, because, as a given amount of force produces a given amount of motion, if the motion is arrested in some directions, it is increased in others.
We have now seen that air is the common vehicle of sound, and that the sound-impulse moves in all directions at a high speed/ But what is it that actually moves? The particles of air are certainly not shot from the vibrating body to the ear, for then we should live in the midst of storms ten times more violent than tropical cyclones. The wonderful elastic properties of gases here come into play. The vibrations of bodies produce waves or pulses in the air. It is the same in effect as with water-waves. When we throw a stone into a quiet pool, the ripples chase each other in circles to the shore, but the water itself
Vibrations or a Clamped Plate.
Chladni's Figures of Vibrating Plates.
that to the third, and so on, while the last ball only of the row flies away. The balls being elastic, the first one struck is not pushed from its position, but is slightly compressed, and then expanding it compresses the second, which, again expanding, compresses the third; and so there is propagated a series of compressions and expansions through the row. In a similar way the action of a vibrating body upon the air is to produce a series of condensations and rarefactions which are sent successively forward through the atmosphere, and each condensation, with its associated rarefaction, constitutes a sonorous wave. This is illustrated in Fig. 6, where A B represents a tuning-fork in vibration. As the prong, a, strikes against the air, its particles are driven together or condensed in front of it, and, as the prong retreats, it leaves a partial vacuum behind. Each vibration thus generates
Propagation of Impulses through Balls.
a wave. The oscillations of the air-particles are communicated to the adjacent particles, and the impulse is sent forward. In Fig. 6, b c d represent the condensations, and b' c' d' the accompanying rarefactions in the propagation of impulses through the air.
If, now, we imagine these dark and light spaces prolonged in circles round the tuning-fork, we shall have an idea of the way sound moves in all directions. We are to conceive of air-waves as bubbles or spheres, which rapidly expand from the point of vibration, and chase each other outward with the speed of musket-balls.
We have said that the waves of sound take place in an invisible realm, yet it is in the power of science to bring them into view. This triumph of experiment is due to a German named Toepler. Prof. Rood has given an account of it in his admirable lecture on the "Mysteries of the Voice and Ear." It depends upon the principle that, "when light which is travelling through the atmosphere meets with a denser or rarer layer, it is usually turned a little out of its straight path—a very little—but enough, sometimes, to render the layer actually visible, if proper optical means are employed." But, how is a wave to be made visible, if it moves with the speed of a cannon-ball, "which goes so fast we cannot see it?" It is by getting a glimpse of it so quickly that it has no time to move, and appears as if at rest. Those who have seen a railway-train at high speed illuminated by a flash of lightning, will remember that it appeared as if standing still. So, if a cannon-ball were passing through a darkened room, and could be illuminated by an electric flash, it would seem to be at rest in mid-air. By suitable arrangements, and the use of the electric spark, Prof. Toepler caught the air-waves on the instant, and got a glimpse of their circular, and even their shaded aspect.
We have said that "the difference between noise and music is, that in noise the waves strike the ear irregularly, while in music they are regular, and so rapid as to blend together. Any sound which becomes continuous by rapid periodic strokes is said to be musical. "If a watch, for example, could be caused to tick with sufficient rapidity—say one hundred times a second—the ticks would lose their individuality, and blend to a musical tone. And, if the strokes of a pigeon's wings could be accomplished at the same rate, the progress of the bird through the air would be accompanied by music. In the hummingbird, the necessary rapidity is attained; and, when we pass on from birds to insects, where the vibrations are more rapid, we have a musical note as the ordinary accompaniment of the insect's flight."
Sounds vary in pitch, and the pitch depends upon the rate of vibration. The greater the number of vibrations in a second, the shorter and quicker are the waves, and the higher the tone. It has been determined, in various ways, exactly how many vibrations there are in
Constitution of Air-Waves
each musical note. Savart employed a toothed wheel, which could be set in motion at any desired rate of speed, and which had attached a small recording apparatus that gave the number of revolutions in a second. Fig. 7 represents the mechanism, and the mode of using it. While the wheel is in revolution, a thin visiting-card, or a piece of pasteboard, is held against its toothed edge. The card is bent a little by each tooth, as it goes by, and springs back to its first position as soon as it is released. When the wheel is turned slowly, there is heard only a succession of taps, distinctly separable one from another; but, as the rapidity of the rotations increases, the number of strokes increases also, and they soon unite to form a musical sound, while, exactly as the motion is accelerated, the sound rises in pitch. In this way it is possible to count the number of vibrations in producing every note in the musical scale.
The usual range of hearing lies between 16 vibrations in a second and about 38,000 vibrations per second. Starting with 16 vibrations per second, as the number is increased we have a series of rising musical notes, until the number is doubled, and an octave is produced with 32 vibrations per second. Increasing them from this point, the notes rise in pitch until they are again doubled, and we have the second octave with 64 vibrations per second. By thus ascending through 11 octaves, the number of vibrations reached would be 32,768 per second; but all the notes comprised within these limits cannot be employed in music. Tyndall states that the practical range of musical
Savart's Apparatus For Numbering Vibrations.
sounds is comprised between 40 and 4,000 vibrations per second, which amounts, in round numbers, to seven octaves. Helmholtz says that the deepest tone of orchestra instruments is the E of the double bass with 41 ¼ vibrations. The new pianos and organs generally go down to 33 vibrations. In height, the piano-forte reaches to 3,520 vibrations, or sometimes to 4,224; while the highest note of the orchestra is that of the piccolo flute, with 4,752 vibrations per second. The limits of hearing vary in different persons. The squeak of the bat, the sound of the cricket, and even the chirrup of the sparrow, cannot be heard by some persons. The limit of sensibility often varies by as much as two octaves.
Waves of water, as everybody knows, vary greatly in magnitude; the riplets of the pool may be not more than an inch in length, while the sea-waves may measure a hundred feet from crest to crest. Sound-waves also vary greatly in magnitude, though to each rate of vibration there corresponds a definite length of wave. Knowing the rate of vibration per second, and the velocity of sound per second, lengths of waves are easily calculated. Take, for example, a tuning-fork that sounds the lowest note of the common D-flute, and it gives 288 vibrations per second. If, now, it be struck in still air, at the freezing-point, the foremost wave will reach a distance of 1,090 feet, at the end of a second, while the chain of waves which connects it with the vibrating fork will be 288 in number: each wave-link will therefore be about 3 feet 9 inches long. With few vibrations and deep tones, waves are long, while, with rapid vibrations and shrill tones, waves are correspondingly short. Within the limits of hearing, sound-waves vary in length, from 70 feet to a half an inch. "The waves generated by a man's organs of voice in common conversation are from 8 to 1 2 feet; those of a woman are from 2 to 4 feet in length. Hence, a woman's ordinary pitch, in the lower sounds of conversation, is more than an octave above a man's; in the higher sounds it is two octaves."
But, because the numbers of their oscillations are exactly determined, we must not suppose that the motions are so simple, for, as Prof. Rood remarks, smooth and clean-cut waves but seldom reach the ear. There are compound vibrations which give complexity to wave-figures. The large waves at sea are often covered by smaller waves, so that the water-particles obey double impulses, and swing in double oscillations. It was illustrated, in Fig. 1, that a string may vibrate as a whole, or in various subdivisions. When a string or any other body vibrates as a whole, it produces its lowest note, which is called the fundamental note. But the fundamental note is never perfectly pure. It is not possible to sound the string as a whole, without at the same time causing the vibrations of its parts. But, as these shorter vibrations are quicker, they yield notes of a higher pitch, which mingle with the fundamental note, and alter its quality. These accompanying higher notes may be in harmony with the fundamental note (when they are called harmonics), or they may not harmonize with it. The sounds emitted by the parts of a vibrating body are called overtones, and it is possible for a string to furnish as many as 20 or 30 of these. The mingling of the overtones with the fundamental one determines the timbre of sound. It is this which gives their peculiar character to different musical instruments, and enables us to distinguish them. A clarinet and a violin may give the same fundamental note, but their overtones are so different that the instruments are never confounded.
Sound-waves are not only transmitted by the air, but also by liquids and solids. That water will convey musical sounds is shown by the following experiment: Fig. 8 represents a tube a yard long, set upon the wooden tray A B, with a funnel at the top, and filled with water. A tuning-fork is attached to a little wooden foot, set into vibration, and the foot is then dipped into the water without touching the sides of the funnel. The vibrations are transmitted by the liquid to the tray below, which is thrown into tremors, and a swelling musical sound is the result.
Vibrations conveyed through Water.
The following beautiful experiment, described by Prof. Tyndall, shows how music may be transmitted by an ordinary wooden rod. In a room two floors beneath his lecture-room, there was a piano upon which an artist was playing, but the audience could not hear it. A rod of deal, with its lower end resting upon the sounding-board of the piano, extended upward through the two floors, its upper end being exposed before the lecture-table. But still no sound was heard. A violin was then placed upon the end of the rod, which was thrown into resonance by the ascending thrills, and instantly the music of the piano was given out in the lecture-room. A guitar and a harp were substituted for the violin, and with the same result. The vibrations of the piano-strings were communicated to the sounding-board, they traversed the long rod, were reproduced by the resonant bodies above, the air was carved into waves, and the whole musical composition was delivered to the listening audience.
The instrument of hearing in man consists of an external orifice about an inch and a half deep in adults, which is closed at the bottom by the circular tympanic membrane. This membrane, though moderately strong, is quite thin, and almost transparent. It is made up of fine fibres, some radiating from the central part to the circumference, and others arranged in concentric rings. It is kept gently on the stretch by two small muscles, one of which draws it tighter, and the other loosens it, by acting upon a chain of small bones. We shall not undertake to describe the curious and complicated anatomy of the inner ear—the drum, containing air, the curious chain-work of minute vibrating bones, the labyrinth filled with water containing little crystalline particles and fine elastic bristles, and where the delicate fibres of the auditory nerve commence. "There is also," says Tyndall, "in the labyrinth a wonderful organ discovered by the Marchese Corti, which is, to all appearance, a musical instrument, with its chords so stretched as to accept vibrations of different periods, and transmit them to the nerve-filaments which traverse the organ. Within the ears of men, and without their knowledge or contrivance, this lute of 3,000 strings (as Kölliker estimates) has existed for ages, accepting the music of the outer world, and rendering it fit for reception by the brain. Each musical tremor which falls upon this organ selects from its tensioned fibres the one appropriate to its own pitch, and throws that fibre into unisonant vibration. And thus, no matter how complicated the motion of the external air may be, those microscopic strings can analyze it, and reveal the constituents of which it is composed." By this wonderful apparatus are all the tremulous movements of the outer world translated to the world within. How the auditory nerve transmits its impressions is not a matter of demonstration, but the probability is great that it transmits them as it receives them as impulses of motion waves of force that are conveyed to the brain and expended in the production of those physical motions which are the material conditions and accompaniments of consciousness. That the organ of feeling and thought is itself a sphere of vibrations and wave-actions traversing in all directions the millions of microscopic fibres which pervade the encephalon, will be thought absurd by many: but we know that wave-action is a part of the method of Nature; that it produces the most wonderful effects in all the common forms of matter; that the brain is a material instrument in the closest physical relation with the outward order; and that material changes of some kind within it are the concomitants of its exalted functions. That there should be unity in the whole scheme does not appear irrational.
Be this as it may, the marvels of what is known are inexhaustible. Could we see what takes place in a room when a tuning-fork is in vibration, giving out a single note, we should behold all the particles of the air agitated in tremulous sympathy, and filling the space with swiftly-expanding spheres of spectral beauty. Or, were the effect produced by several instruments concurrently played, we should see the forms in countless variety carving the air into ever-changing figures of geometrical harmony, and creating the perfect music of geometrical form. Such a revelation is impossible, from the swiftness of movement, which would foil the eye; but it would be also impossible, because the complications of movement would confuse it. But, where the optical sense fails, the auditory sense succeeds. The membrane of the ear receives the torrent of motion, and transmits it with all its harmonies. In an orchestra, where scores of instruments are playing through the whole compass of the scale, the air is cut into waves by every complexity of vibration—grave tones mingle with shrill, soft with harsh, fundamentals are merged in overtones, and the storm of impulses is shot with the speed of rifle-bullets against the tympanum; and yet there is no confusion. In all their infinite diversity of qualities the waves are legible to the little membrane. It vibrates to the lowest and to the highest, to each and all, and telegraphs the whole performance with incomprehensible exactness to its cerebral destination and an exquisite work of art is produced in the sphere of pleasurable feeling and critical intelligence.
Our glance at this fascinating subject has been very imperfect, but, if any care to pursue it, we recommend them to the admirable book of Prof. Tyndall, "On Sound," to which we are indebted for the foregoing illustrations, and for many of the facts stated.