Amplitude

“ For quantitative measurement it is necessary to have the intensity of stimulus maintained uniform, or increased or decreased in a definite manner. Instead of a tap, the stimulus of torsional vibration is more satisfactory. By maintaining the amplitude of vibration constant, or increasing or decreasing the amplitude, we can either keep the stimulus constant, or increase or decrease it in a quantitative manner. I shall first describe some of the typical results which may be obtained with the simple "straight wire form" of the apparatus. Worked with care it gives consistent and good results. ”

“ Amplitude.—The largest displacement of the drop, i.e. the distance from the dotted line to C or to T, is called the amplitude of the wave. The time taken for a drop to complete one whole oscillation, i.e. the time taken for a wave to travel one whole wave-length forward, is called the period of the wave. The number of oscillations in one second, i.e. the number of wave-lengths travelled in one second, is called the frequency.
FIG. 11.
Although there is no visible displacement in the waves of light and heat, yet we may represent them in much the same way. Thus if AB, Fig. ”

“ 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. ”

“ Since the distance travelled by a particle in a single period of the wave will be equal to four times the amplitude, the velocity at any point in the wave must be proportional to the amplitude and therefore the kinetic energy is proportional to the square of the amplitude. ”

“ Amplitude is designated as true, magnetic, compass, or grid as the reference direction is true, magnetic, compass, or grid east or west, respectively. 2. The maximum value of the displacement of a wave, or other periodic phenomenon, from the zero position. 3. One-half the range of a constituent tide. By analogy, it may be applied also to the maximum speed of a constituent current.
amplitude compass. . A compass intended primarily for measuring amplitude. It is graduated from 0° at east and west to 90° at north and south. Seldom used on modern vessels. ”

“ When such movements of certain frequency and amplitude strike our organs of vision, the sensation of light is produced. When others of greater amplitude and smaller frequency45 strike the terminal outspread of our common sensory nerves, the sensation of heat results. The difference between the frequency and amplitude of the heat waves and the light waves is but small, or, strictly speaking, there is no actual line of separation lying between them; they run directly into each other. ”

“ Amplitudes A celestial body’s amplitude angle is the complement of its azimuth angle. At the moment that a body rises or sets, the amplitude angle is the arc of the horizon between the body and the East/West point of the horizon where the observer’s prime vertical intersects the horizon (at 90°) , which is also the point where the plane of the equator intersects the horizon (at an angle numerically equal to the observer’s co-latitude) . ”

“ We may then conveniently discard the idea of phase, and regard the amplitudes as at random positive or negative. If all the signs are the same, the intensity is n2; if, on the other hand, there are as many positive as negative, the result is zero. But, although the intensity may range from 0 to n2, the smaller values are much more probable than the greater. ”

“ First, its intensity, or loudness, which is governed by the height, depth, amplitude—for these amount to the same thing—of the waves produced in the medium. Second, the timbre, or quality, which is regulated by the shape, or outline, of these waves. Third the pitch, high or low, which is controlled by the distance from crest to crest of the sound-waves—or, as we say, from node to node of the vibrations. ”

“ However delicately etheric the substance its movement commences by the vibration of its particles, and a vibration is a wave having a certain length, amplitude, and periodicity, that is to say, something which can exist only in terms of space and time; and as soon as we are dealing with anything capable of the conception of measurement we may be quite certain that we are not dealing with Spirit but only with one of its vehicles. ”

“ But if the amplitude of that circular vibration which agrees in sense with the rotation will continually increase, and the particle will work its way in an ever-widening spiral path towards the eccentric position of secular stability. ”

“ Atoms and molecules may vibrate to and fro, or may execute various oscillations about each other, with a moderate velocity, or perform their motions with a rapidity beyond conception; and be the intensity of the vibrations ever so great or ever so small, these same vibrations determine the amplitude of the ethereal waves—those waves of greatest length giving rise to all the phenomena of radiant heat, while shorter ones constitute light in all its luminous and chromatic effects ”

“ An observer in the plane of the motion can easily hear a change in the pitch as the pitch-pipe moves to and from him.
Musical Quality or Timbre.—Though a musical note has definite pitch or frequency, notes of the same pitch emitted by different instruments have quite different quality or timbre. The three characteristics of a longitudinal periodic disturbance are its amplitude, the length after which it repeats itself, and its form, which may be represented by the shape of the displacement curve. ”

“ If we make the string of a piano sound by plucking it in the middle, then, as the science of physics teaches us, not only does the whole string vibrate, but each half vibrates as well in a smaller degree, and in general each third part, each fourth, &c., in ever decreasing amplitudes. ”

“ For the ratio of amplitudes and frequencies, Einstein gives the following equation:
Due to relation (2) we can write it in the form
or also
If equation (7) is considered, then it becomes
However, for the reflected ray it is
according to formula (28) on p. ”

“ I have found out that by uttering the true inner name of anything I can set in motion harmonics--harmonics, note well, half the wave length and twice the frequency!--that are delicate and swift enough to insert themselves between the whirling molecules of any reasonable object--any object, I mean, not too closely or coherently packed. By then swelling or lowering my voice I can alter the scale, size or shape of that object almost indefinitely, its parts nevertheless retaining their normal relative proportions. ”

“ It is to be noticed, in this as in all analogous cases, that the wave-velocity appears as the square root of the ratio of two quantities, one of which represents (in a generalized sense) the elasticity of the medians, and the other its inertia.
The expressions for the kinetic and potential energies of any portion of the string are
where the integrations extend over the portion considered. The relation (4) shows that in a single progressive wave the total energy is half kinetic and half potential. ”

“ A musical string is of a uniform thickness, and is stretched between two points, by a force much greater than its weight. The stretching force which is applied is generally conceived as measured by the weight which would occasion an equal tension. The sound which a string gives, thus stretched, or in this mode of vibration, is called its fundamental sound. The tone of a string becomes more acute as we increase its tension, or diminish its length, and the weight of a given portion. ”

“ 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. ”

“ Analytical Power of the Ear.—When we listen to a compound tone, we have the power of picking out these partials from the general mass of sound. It is known that the frequencies of the partials as compared with that of the fundamental tone are simple multiples of the frequency of the fundamental, and also that physically the waves of the partials so blend with each other as to produce waves of very complicated forms. ”

“ The density and elasticity of the air, varying with every alternation of temperature, lead to the consideration of barometrical changes, the measurement of heights, and capillary attraction; and the doctrine of sound, including the theory of music, is to be referred to the small undulations of the aërial medium. A knowledge of the action of matter upon light is requisite for tracing the curved path of its rays through the atmosphere, by which the true places of distant objects are determined, whether in the heavens or on the earth. ”

“ In the limiting cases, that is, when we regard the velocity of the missing wave in the elastic theory as zero, and in the electric theory as infinite, we shall find a remarkable correspondence between the two theories, the motions of monochromatic light within isotropic or aeolotropic media of any degree of transparency or opacity, and at the boundary between two such media, being represented by equations absolutely identical, except that the symbols which denote displacement in one theory denote force in the other, and vice versâ. ”

“ By the side of magnitudes perceived by sight there are magnitudes perceived by the hearing,—I mean the velocities of sonorous vibrations; and these vibrations being magnitudes may also form aggregates of parts connected by mathematical laws. In the first place, as you are aware, a musical sound is composed of continuous vibrations of equal velocity, and this equality already places between them a mathematical relationship ”

“ Our actual knowledge of the subject is at present limited to mathematics. The velocity of the impulses has been noted and the number of the vibrations has been counted. We know those of sound to be comparatively slow, there being but 4,000 vibrations to the inch in the highest treble note of the piano. Above this on the ascending scale comes a long series of vibrations of which we know little or nothing; and it is not until we reach 36,000 vibrations to the inch that we come again within the range of human sensory consciousness. ”

“ Let the fifteenth motion be that of transmission or of passage, by which the powers of bodies are more or less impeded or advanced by the medium, according to the nature of the bodies and their effective powers, and also according to that of the medium. For one medium is adapted to light, another to sound, another to heat and cold, another to magnetic action, and so on with regard to the other actions. ”

“ If you divide the string, for example, into five equal parts, and touch any of the four points of division you choose, you check and finally prevent the continuance of any motion at the point touched, though at the same time it would appear that the touching (which, to make the experiment answer, must be very light) is not enough to hinder the shaking, or, as the learned people call it, the vibration, given at one end, from being communicated past the point of touch. ”

“ He obtained a formula showing that the rapidity of vibration of a string varies directly as the weight stretching it and inversely as its own length and weight. For the first time he determined the differential equation of the path of a ray of light when traversing a heterogeneous medium. ”

“ If the distances of the pulses or their lengths are greater in one medium than in another, let us suppose that the correspondent parts describe spaces, in going and returning, each time proportional to the breadths of the pulses; then will their contractions and dilatations be equal: and therefore if the mediums are homogeneous, the motive elastic forces, which agitate them with a reciprocal motion, will be equal also. Now the matter to be moved by these forces is as the breadth of the pulses; and the space through which they move every time they go and return is in the same ratio. ”

“ When a wave of sound travelling through one medium meets a second medium of a different kind, the vibrations of its own particles are communicated to the particles of the new medium, so that a wave is excited in the latter, and is propagated through it with a velocity dependent on the density and elasticity of the second medium, and therefore differing in general from the previous velocity. ”

“ When light is analysed by a prism or grating into a spectrum, the course of each ray is deflected—refracted or diffracted—by an amount corresponding to its frequency of vibration or wave-length.
Motion of the medium, so long as it is steady, affects neither frequency nor wave-length, and accordingly is without influence on the result. ”

“ The magnitude of a sound is known not by actual quantity but by degree of impact, by intensity- and this in no indirect knowledge; the ear appreciates a certain degree of force, exactly as the palate perceives by no indirect knowledge, a certain degree of sweetness. But the true magnitude of a sound is its extension ”

“ When these dissipative forces are disregarded, it is found that an elastic solid body is capable of vibrating in such a way that the motion of any particle is simple harmonic motion, all the particles completing their oscillations in the same period and being at any instant in the same phase, and the displacement of any selected one in any particular direction bearing a definite ratio to the displacement of an assigned one in an assigned direction. ”