Tremolo

“ All agitation is vibration. All force manifests itself in this way.
The painful brilliancy of the sun is produced by the rapid vibrations of the rays; the twinkle of the distant star, the waves of the ocean when ruffled by the winds; the shimmer of the moon on its crested surface; the brain in thinking; the mouth in talking; the beating of the heart; all, alike, obey the one grand and universal law of vibratory motion.
Qualities of Sound.—Sound is nothing but a succession of vibrations of greater or less magnitude. Pitch is produced by the number of vibrap. 157tions; intensity by their force ”

“ These vibrations of the string act on the bridge of the violin, which rests on the belly or sounding-board of the instrument. The surface of the sounding-board is thus set trembling, and these tremors, or vibrations, spread through the air in all directions around the instrument, somewhat in the manner that water-waves spread around the place where a stone has been dropped into a quiet pond. These tremors of the air, however, are not sound, but the cause of sound. Sound, as we have said, is a sensation ”

“ So, when, the pressure of the sound vibration is released, coincident with the cessation of its own inward vibration, the edges swing back and outward, unimpeded by a following blow of the second vibration.
“As a swing is accelerated by pushes that are all of equal strength, and yet flies higher each time, so does the glass act. With each continuing vibration of sound its edges go farther in, then farther out, than is normal. The strain becomes too great—the glass is shattered. ”

“ Bells, gongs, tuning-forks, are examples of solid bodies; drums and tambourines, of membranes; if we run a wet finger along the edge of a glass goblet, we throw the fluid which it contains into a regular vibration; and the various character which sounds possess according to the room in which they are uttered, shows that large masses of air have peculiar modes of vibration. Vibrations are generally accompanied by sound, and they may, therefore, be considered as acoustical phenomena, especially as the sound is one of the most decisive facts in indicating the mode of vibration. ”

“ All matter is vibration; that has been proven. A building of bricks, if shaken in the right manner, falls into its component parts; a bridge, crossed by soldiers in certain rhythmic time, is torn from its moorings. A tuning fork, receiving the sound vibrations from one of a similar size and shape begins to vibrate in turn. These are homely analogies, but applied to the less familiar sound vibrations, which make up our atomic world, they may help you to understand how the terrific forces I have discovered can disintegrate flesh. ”

“ Every one of these modes of vibration is dynamically possible by itself, and any number of them may coexist independently of each other.
By a proper adjustment of the initial amplitude and phase of each of these modes of vibration, so that their resultant shall represent the initial state of the string, we obtain a new representation of the whole motion of the string, in which it is seen to be the resultant of a series of simple harmonic vibrations whose periods are the fundamental period and its submultiples. ”

“ Sound will shatter glass if the vibration of the sound is equal to the vibration of the glass. Huge buildings could be destroyed by sound, if one could only create the properly vibrating sound. And here is the principle.
“Let us say—I do not pretend to be exact—that the mass of a glass vibrates four hundred times a second. Let a sound be made that vibrates four hundred times a second, near to the glass. Those vibrations of the sound—waves, so to speak—will accelerate the vibration of the glass. ”

“ But, if the rectangular shock be imparted to the pendulum when it is at the limit of its swing, then the compounding of the two impulses causes the suspended ball to describe, not a straight line, but an ellipse; and, if the shock be competent of itself to produce a vibration of the same amplitude as the first one, the ellipse becomes a circle.
Why do I dwell upon these things? Simply to make known to you the resemblance of these gross mechanical vibrations to the vibrations of light. I hold in my hand a plate of quartz cut from the crystal perpendicular to its axis. ”

“ The varied actions of the universe are all modes of motion; and the vibration of a ray claims strict brotherhood with the vibrations of our pendulum. Suppose aethereal waves striking upon atoms which oscillate in the same periods as the waves, the motion of the waves will be absorbed by the atoms; suppose we send our beam of white light through a sodium flame, the atoms of that flame will be chiefly affected by those undulations which are synchronous with their own periods of vibration. ”

“ 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. ”

“ Here is the dome of a bell, which I strike with a mallet or hammer, and thereby impart energy to it, and it sets the whole air of this room in motion, and every tympanum of every ear present is struck by the little bullets of air that are thrown into vibration, and the result is the effect called sound. ”

“ Sound is transmitted in longitudinal waves through air and other material substance as vibration. Heat is a motion of the ultimate particles or atoms of matter, and Light is a motion of the luminiferous ether transmitted in waves that are transverse. Electricity is also undoubtedly a mode of motion related in a peculiar way to the atoms of the conductor. ”

“ Let his audience imagine a large electric organ provided with an infinite number of stops, each stop giving rise to a particular ether note. Let the lowest stop produce one vibration a second. They should then get a gigantic wave of 186,000 miles long. Let the next stop give rise to two vibrations in a second, and let each succeeding stop produce higher and higher notes. Let them imagine an unseen hand pressing the different stops in rapid succession, producing higher and higher notes. ”

“ Sound. The Velocity of Sound in Water. THE Science of which the history is narrated in this Book has for its objects, the minute Vibrations of the parts of bodies such as those by which Sounds are produced, and the properties of Sounds. The Vibrations of bodies are the result of a certain tension of their structure which we term Elasticity. The Elasticity determines the rate of Vibration: the rate of Vibration determines the audible note: the Elasticity determines also the velocity with which the vibration travels through the substance. ”

“ If we could see the particles of the air in the concert-room, and fasten our attention upon any one of them, we should see it executing a most complicated motion under the combined action of these air-wave-producing instruments. We should be fascinated by the amazing dance of molecules to and fro and from side to side, as the medley of waves of compression or rarefaction embraced them and drove them hither and thither in their resistless grasp. ”

“ Metal springs fastened at one end, when forcibly bent, endeavour to return to rest by a series of vibrations, which give very pleasing tones, as in musical boxes. Various musical instruments have been constructed, consisting of metallic springs thrown into vibration by a current of air. ”

“ When a current is modified not by a musical vibration, but roughly so that it is either rubbed in passing through a narrow passage, or for a moment altogether stopped and then released, we get the two classes of sounds called Fricatives, or rubbed sounds, and Plosives, sounds with a kind of burst or explosion. ”

“ Every tremor gravitation excites in any planet is immediately transmitted to the farthest limits of the system, in oscillations corresponding in their periods with the causes that produce them, like sympathetic notes in music, or vibrations from the deep tones of an organ.... The human frame may be regarded as an elastic system, the different parts of which are capable of receiving the tremors of elastic media, and of vibrating in unison with their innumerable undulations. ”

“ As already stated, the limit of audible tremors is three to four thousand per second, but the smallest number of tremors that we can perceive as heat is between three and four millions of millions per second. The number of waves producing red light is estimated at four hundred and seventy-four millions of millions per second ”

“ Electric vibration is produced in a somewhat similar way. If two metallic spheres be strongly charged with opposite electrifications, the medium is electrically strained, and when this strain is suddenly removed by a discharge, waves are produced in the medium. ”

“ It did not matter in the least whether the vibration commenced with a right- or left-handed twist.
It may be stated here that similar electromotive variation is obtained by molecular disturbance produced by a tap.
I shall now describe the effect of mechanical stimulus of varying intensities and durations. The intensity may be varied by varying the amplitude of vibration. We shall also study the effect of a single stimulus, or the summated effect of rapidly succeeding stimuli. ”

“ VIBRATIONS OF THE AIR.—If a person stand beneath a railway girder-bridge with an open umbrella over his head, when a train is passing, the vibration of the air will be distinctly felt in the hand which grasps the umbrella, because the outspread surface collects and concentrates the waves into the focus of the handle. ”

“ These vibrations or undulations in air, water, and the theoretical ether, have therefore been called waves of water, waves of sound, and waves of light, just as if three clocks were made of three different metals, the mechanism would remain the same, though the material, or in this case the medium, be different in each.
Any increase in the number of vibrations of the air produces acute, whilst a decrease attends the grave sounds, and when the waves succeed each other not less than sixteen times in a second, the lowest sound is produced. ”

“ The box has two pipes connected with it, by means of which it can be filled with carbonic acid gas.
Provided with this apparatus, it is now possible to show you a series of experiments which will leave no doubt in your minds that the external agency which creates in us the sensation of sound is a wave-motion in the air we breathe. Let me, in the first place, show you that a sound-beam can be reflected. We adjust our sensitive flame and set the whistle in action, and create, as described, by the lens, a beam of sound. ”

“ 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
Fig. ”

“ By various contrivances we can compel the vibrations of the air to declare themselves we know the length and frequency of the sonorous waves, and we have also obtained great mastery over the various methods by which the air is thrown into vibration. We know the phenomena and laws of vibrating rods, of organ-pipes, strings, membranes, plates, and bells. ”

“ If, by the aid of properly-contrived machinery, we communicate merely to the hand fifty or sixty energetic vibrations in a second, a peculiar and powerful sensation is produced, resembling that of a prolonged electric shock, and at the same time the hand becomes clinched, and cannot be opened by an effort of the will. In this experiment the vibrations are communicated to the hand by direct contact with a solid piece of metal. Let us select a more refined case, and employ as the exciting cause twenty or twenty-five vibrations per second, not of metal, but of air. ”

“ When the waves of aether impinge upon molecules whose periods of vibration coincide with the recurrence of the undulations, the timed strokes of the waves augment the vibration of the molecules, as a heavy pendulum is set in motion by well-timed puffs of breath. Millions of millions of shocks are received every second from the calorific waves ”

“ The frequency of the vibration, and the quickness of succession of the sparks between the knobs, affect to a marked degree the appearance of the streams. When the frequency is very low, the air gives way in more or less the same manner, as by a steady difference of potential, and the streams consist of distinct threads, generally mingled with thin sparks, which probably correspond to the successive discharges occurring between the knobs. ”

“ For the theory of sounds deduced from the nature of an elastic fluid, and the tremors of the particles of sounding bodies, and afterwards verified, as it has been, by numerous experiments, becomes a guide to us in all inquiries into the vibrations of other elastic mediums, such as the æther, and into the effects, which such vibrations must impart to and receive from the small particles that are surrounded by the elastic medium. ”