amplitude

In both cases the amplitude of the oscillations decreases more or less rapidly.

(25) The sum of the disturbance is obtained by adding (24) and (25) y = y l +y 2 = 2a cos Ut s i n 57 x, (26) At any given instant t this is a sine curve of amplitude 2a cos (27r/A)Ut, and of wave-length A, and with nodes at x = o, a A, A, ..., that is, there is no displacement at these nodes whatever the value of t, and between them the displacement is always a sine curve, but of amplitude varying between +2a and - 2a.

Thus Mach found an amplitude 0 2 cm.

The 12-hour term is much less variable, especially as regards its phase angle; its amplitude shows distinct maxima near the equinoxes.

Each section then vibrates, and its amplitude goes through all its values in time given by 21rUT/A =2r, or T =A/U, and the frequency is U/A.

The maximum velocity of a particle in the wave-train is the amplitude of dy/dt.

(1); and for the intensity, represented by the square of the amplitude, 1 2 [fJsin f +?2 fC? ?

Methods of measuring the amplitude in sound waves in air have been devised and will be described later.

Further, the same harmonics with the same amplitude will always be present.

The amplitude of the fork was observed when the sound just ceased to be audible at 27.4 metres away, and the rate of energy emission from the resonator was calculated to be 42 .

This rate of loss for each amplitude was determined (i) when the fork was vibrating alone, and (2) when a resonator was placed with its mouth under the free ends of the fork.

When the plate vibrated the mirror was vibrated about the fixed edge, and the image of a reflected slit was broadened out into a band, the broadening giving the amplitude of vibration of the plate.

If th' maximum pressure change is determined, the amplitude is given by equation (20), viz.

For minimum audible sounds Wien found a somewhat smaller value of the amplitude than Rayleigh.

The 24-hour term is very variable both as regards its amplitude and its phase angle (and so [[Table Iv]].

The result was an amplitude of 1.27 X 107 cm.

The amplitude in the pipe was certainly much greater than in the issuing waves.

Let us suppose that two trains of sine waves of length A and amplitude a are travelling in opposite directions with velocity U.

Now the amplitude evidently corresponds to the loudness, and the length of period corresponds to the pitch or frequency.

The effects due to each of these rings are equal in amplitude and of phase ranging uniformly over half a complete period.

the resultant with amplitude I/-/2 that of (1).

§ 311) gives the pressure variations in the incident waves in terms of those in the resonator, and so the pressure variation and the amplitude of vibration in the waves to be measured were determined.

The first may be illustrated by Lord Rayleigh's experiments to determine the amplitude of vibration in waves only just audible (Sound, ii.

When electric oscillations are set up in an open or closed electric circuit having capacity and inductance, and left to themselves, they die away in amplitude, either because they dissipate their energy as heat in overcoming the resistance of the circuit, or because they radiate it by imparting wave motion to the surrounding ether.

301) Wien used a telephone plate, of which the amplitude could be determined from the value of the exciting current, and he found that the smallest amplitude audible was 6.3 X t010 cm.

Neither of them seemed to recognize anything as important except pitch and amplitude, and Reis thought the amplitude was to some extent obtained by the varying length of contact in the transmitting instrument.

The maximum particle velocity is 21rna (where n is the frequency and a the amplitude), or 27raU/X.

Another important result of the investigation was that the phase of vibration of the fork was not altered by bowing it, the amplitude alone changing.

In the other, the waves produce a measurable effect on a vibrating system of the same frequency, and the amplitude in the waves can be deduced.

When this is the case the amplitude of the potential difference of the surfaces of the tubular condenser becomes a maximum, and this is indicated by connecting a vacuum tube filled with neon to the surfaces of the condenser.

V i brat i ons thus excited are termed forced vibrations, and their amplitude is greater the more nearly the period of the applied force approaches that of the system when vibrating freely.

The component vibrations at P due to the successive zones are thus nearly equal in amplitude and opposite in phase (the phase of each corresponding to that of the infinitesimal circle midway between the boundaries), and the series which we have to sum is one in which the terms are alternately opposite in sign and, while at first nearly constant in numerical magnitude, gradually diminish to zero.

The amplitude is thus subject to fluctuations, which increase as the shadow is approached.

In mechanics, the amplitude of a wave is the maximum ordinate.

that which differentiates a note sounded on one instrument from the same note on another instrument, depends neither on amplitude nor on frequency or wave-length.

a (iI) We may find here the value of this when we have a train of waves in which the displacement is represented by a sine curve of amplitude a, viz.

Except at Karasjok, where the diurnal changes seem somewhat irregular, the relative amplitude of the 12-hour term is considerably greater in summer than in winter.

Accordingly, the amplitude of the resultant will be less than if all its components had the same phase, in the ratio +17r -17r or 2: 7.

At the central point there is still complete agreement of phase; but the amplitude is diminished in the ratio of a: a+d.

The effect of each of the elements of the grating is then the same; and, unless this vanishes on account of a particular adjustment of the ratio a: d, the resultant amplitude becomes comparatively very great.

We have now to consider the amplitude due to a single element, which we may conveniently regard as composed of a transparent part a bounded by two opaque parts of width id.

The hyperbolic or Gudermannian amplitude of the quantity x is ta n (sinh x).

If the two forks have the same frequency, it is easily seen that the figure will be an ellipse (including as limiting cases, depending on relative amplitude and phase, a circle and a straight line).

The energy of this fork with a given amplitude of vibration could be calculated from its dimensions and elasticity, and the amplitude was observed by measuring with a microscope the line into which the image of a starch grain on the prong was drawn by the vibration.

Further, the greater the dissipation of energy the less is the prominence of the amplitude of vibration for exact coincidence over the amplitude when the periods are not quite the same, though it is still the greatest for coincidence.

If on the other hand the number of zones be odd, the effects conspire; and the illumination (proportional to the square of the amplitude) is four times as great as if there were no obstruction at all.

The amplitude of the light at any point in the axis, when plane waves are incident perpendicularly upon an annular aperture, is, as above, cos k(at-r 1)-cos k(at-r 2) =2 sin kat sin k(r1-r2), r2, r i being the distances of the outer and inner boundaries from the point in question.

The phase of the resultant amplitude is the same as that due to the central secondary wave, and the discrepancies of phase among the components reduce the amplitude in the proportion l ` dri): 3?

The only effect of the ruling is to diminish the amplitude in the ratio a: a+d; and, except for the difference in illumination, the appearance of a line of light is the same as if the aperture were perfectly free.

The utility of the curve depends upon the fact that the elements of arc represent, in amplitude and phase, the component vibrations due to the corresponding portions of the primary wave-front.

The result, if considered alone, inevitably leads to an underestimate of the average amplitude of the regular diurnal variation.

The pitch of a musical sound depends on the number of cycles passed through by the fluctuations of the pressure per unit of time; the loudness depends on the amount or the amplitude of the fluctuation in each cycle; the quality depends on the form or the nature of the fluctuation in each cycle.

In elliptic integrals, the amplitude is the limit of integration when the integral is expressed in the form f 4) 1% I - N 2 sin e 4) d4.

In algebra, if a be a real positive quantity and w a root of unity, then a is the amplitude of the product aw.

An even greater effect (fourfold) can be attained by providing that the stoppage of the light from the alternate zones is replaced by a phase-reversal without loss of amplitude.

They are connected with the ocean by narrow straits, the salinity of the water contained in them differs in a marked degree from that of the ocean, and the tidal waves are of small amplitude.

The amplitude of the phase is 1ï¿½1 magnitude; and the absence of any stationary interval at minimum proves the eclipse to be partial, not annular.

Half the total excursion is called the amplitude.

4 QJ is the amplitude.

We may say here that the energy or the intensity of the sound of given wave-length is proportional to the square of the amplitude.

The maximum height of the curve HM =a is the amplitude.

at the distance of the listener, and thence from the energy in a wave, found above, to determine the amplitude.

& 'm =21rnapU, for in the stationary wave system the pressure change and the amplitude are both double those in either train, so that the same relation holds.

The amplitude found by the other observers was of the same order.

The formation of beats may be illustrated by considering the disturbance at any point due to two trains of waves of equal amplitude a and of nearly equal frequencies n, n2.

If we measure the time from an instant at which the two are in the same phase the resultant disturbance is y=a sin i t+a sin 27rn2t =2a cos ir(n i - n 2)t sin ir(nl-t-n2)t, which may be regarded as a harmonic disturbance of frequency (ni+n2)/2 but with amplitude 2a cos 7r(n i - n 2)t slowly varying with the time.

Taking the squares of the amplitude to represent the intensity or loudness of the sound which would be heard by an ear at the point, this is 4a 2 cos t ir(ni - n2)t =2a 2 {1 -cos 27r(n l - n2)t}, a value which ranges between o and 4a 2 with frequency .n1 - n2.

If, instead of considering one point in a succession of instants, we consider a succession of points along the line of propagation at the same instant, we evidently have waves of amplitude varying from 2a down to o, and then up to 2a again in distance U/(ni - n2).

Formerly it was generally supposed that the Tartini tone was due to the beats themselves, that the mere variation in the amplitude was equivalent, as far as the ear is concerned, to a superposition on the two original tones of a smooth sine displacement of the same periodicity as that variation.

Let us suppose that with constant excess of pressure, p, in the wind-chest, the amplitude produced is proportional to the pressure, so that the two tones issuing may be represented by pa sin 27-nit and pb sin 21rn 2 t.

Moreover, a tendency to amplitude of language may be noticed here and there in some of the more concise narratives.

They were measured by the meridian-passages of the limiting stars, and varied in amplitude from 2° 42' to 30° 24'.

Lord Kelvin assumed as a superior limit of k, the ratio of amplitude to wave-length, the value io 2, which is a very safe limit.

It thus appears that if the amplitude of vibration could be as much as 1 o_2 of the wave-length, the aether would be an excessively rare medium with very slight elasticity; and yet it would be capable of transmitting the supply of solar energy on which all terrestrial activity depends.

In creased length necessitated an increase in the diameter of the main tube to limit the amplitude of the vibrations caused by being pushed through the water.

As the waves were propagated downwards through the soil the amplitude rapidly i ??.?

To illustrate the main features of the calculation, we may suppose that the surface is subject to a simple-harmonic cycle of temperature variation, so that the temperature at any time t is given by an equation of the form 0 - 0 0 = Asin 27rnt= A sin 27rt/T, (5) where 0 0 is the mean temperature of the surface, A the amplitude of the cycle, n the frequency, and T the period.

In this simple case the temperature cycle at a depth x is a precisely similar curve of the same period, but with the amplitude reduced in the proportion rn ', and the phase retarded by the fraction mx/27r of a cycle.

The dotted boundary curves have the equation 0 =omx, and show the rate of diminution of the amplitude of the temperature oscillation with depth in the metal.

4 is o 60 in., at which depth the amplitude of the variation is reduced to less than one five-hundredth part (e 2 7r) of that at the surface, so that for all practical purposes the oscillation may be neglected beyond one wave-length At half a wave-length the amplitude is only 3 rd of that at the surface.

The rate of diminution of amplitude expressed by the coefficient a in the index of the exponential is here greater than the coefficient b expressing the retardation of phase by a small term depending on the emissivity h.

Although by compounding corresponding portions of the diagrams given by instruments of this type, it is possible to determine the range and direction of the movement of which they are the resolved parts, their chief value is that they enable us to measure with ease the extent of any vibration, half of which is called its amplitude, and the time taken to make any complete back-and-forth movement, or its period.

Now if a be the amplitude expressed in millimetres, and t the period expressed in seconds, then the maximum velocity of an earth particle as it vibrates to and fro equals 27ra/t, whilst the maximum acceleration equals 4,r 2 0 2.

The schools of thought for which they stood have since contended for mastery in American politics: Hamilton's gradually strengthened by the necessities of stronger administration, as time gave widening amplitude and increasing weight to the specific powers - and so to Hamilton's great doctrine of the" implied powers "- of the general government of a growing country; Jefferson's rooted in colonial life, and buttressed by the hopes and convictions of democracy.

elements a, e are called the amplitude and epoch (or initial phase), respectively.

The numbers correspond to an amplitude of 10 centimetres and a period of two seconds.

which represents a vibration of continually increasing amplitude, Since the equation (12) is in practice generally only an approxi.

This may be described as a simple harmonic oscillation whose amplitude diminishes asymptotically to zero according to the law ehlr.

If the friction be comparatively slight the amplitude is greatest when the imposed period coincides with the free period, being then equal to f/kei, and therefore very great compnred with that due to a slowly varying force of the same average intensity.

The abnormal amplitude is greater, and is restricted to a narrower range of frequency, the smaller the friction.

The amplitudes of oscilla Ia tion of the various particles have definite ratios to one another, and the phases are in agreement, the absolute amplitude (depending on C) and the phase-constant () being alone arbitrary.

The amplitude becomes very great when o~1 approximates to a root of (6), i.e.

If the friction be small the amplitude becomes relatively very great if the imposed period approximate to a free period.

The amplitude of this part of his attire enables the Persian to sit without discomfort on his heels; chairs are only used by the rich, great or Europeanized.

This is a simple harmonic wave-line, whose mean distance from the axis is a, whose wave-length is lira, and whose amplitude is c. The internal pressure corresponding to this unduloid is as before p = T/a.

Thus the length of the continuous portion necessarily depends upon the character of the disturbances in respect of amplitude and wave-length.

The gradually increasing amplitude of the.

In front of this is a double series of stationary waves, the gravitation waves forming a series increasing in wave-length with their distance in front of the body, and the surface-tension waves or ripples diminishing in wave-length with their distance from the body, and both sets of waves rapidly diminishing in amplitude with their distance from the body.

Classical novae are seen to erupt once, and the amplitude of the outburst is the largest among CVs.

oscillation amplitude.

The system is not completely stable: one observes small amplitude oscillations around equilibrium.

The final probability of an event is then obtained by the sum of the squares of the two numbers describing the resultant probability amplitude.

quadrature amplitude modulation (QAM ).

receiver coil can be used to detect the amplitude of this magnetic field.

semiannual variation of the amplitude of ionospheric equatorial anomaly through fountain effect.

FM and amplitude modulated (AM) single sideband (SSB) voice radios are types of single-channel radios organic to the aviation brigade.

The amplitude of dynamic topography predicted by a layered mantle viscosity model is consistent with the observed upper bound of ~ 600m.

As to weather, expect increasingly turbulent storms of greater strength and amplitude.

The probe is optimized for amplitude and bandwidth, in order to present small scale surface undulations of a high spatial frequency to users.

waveform amplitude envelope provides useful perceptual information to listeners.

Holfmann, from observations on the amplitude of saturation currents, deduce q =4 as a mean value.

The amplitude of the signals can be varied in several ways, either by a shunt across the electromagnet, or by altering the tension of the controlling springs or by altering the air gap between electromagnets and armatures.

It was seen that the effect of the impact of the incident electric waves upon the vertical receiving wire was to create in it electrical oscillations, or in other words, high frequency alternating electric currents, such that whilst the potential variations were a maximum at the top or insulated end of the antenna the current at that point was zero and at the base the potential variation was zero and the current amplitude a maximum.

This has been achieved by employing a microphone transmitter at the sending end to vary the amplitude but not the wave-length of the emitted waves, and at the receiving end using an electrolytic receiver, which proves to be not merely a qualitative but also a quantitative instrument, to make these variations audible on a telephone.

Now 2 area 17r=2Xr; so that, in order to reconcile the amplitude of the primary wave (taken as unity) with the half effect of the first zone, the amplitude, at distance r, of the secondary wave emitted from the element of area dS must be taken to be dS/Xr (1) By this expression, in conjunction with the quarter-period acceleration of phase, the law of the secondary wave is determined.

That the amplitude of the secondary wave should vary as r1 was to be expected from considerations respecting energy; but the occurrence of the factor A1, and the acceleration of phase, have sometimes been regarded as mysterious.

The fact that the other components have phases differing from this by amounts ranging between tam 2 r/(a+d) causes the resultant amplitude to be less than for the central image (where there is complete phase agreement).

Hence, in accordance with the rule for compounding vector quantities, the resultant vibration at B, due to any finite part of the primary wave, is represented in amplitude and phase by the chord joining the extremities of the corresponding arc (U2-0.1).

AMPLITUDE (from Lat.

The amplitude of the phase is 1Ã¯¿½1 magnitude; and the absence of any stationary interval at minimum proves the eclipse to be partial, not annular.

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.

The velocity perpendicular to the axis of any point on the curve at a fixed distance x from 0 is dy_ (I ]) at A A The acceleration perpendicular to the axis is d2y = 2 2 dt 2 - A 2 sin A (x - Ut) The maximum pressure excess is the amplitude of ("6= Eu /U _ (E/U)dy/dt.

But it is very difficult to suppose that the same sensation would be aroused by a truly periodic displacement represented by a smooth curve, and a displacement in which the period is only in the amplitude of the to-and-fro motion, and which is represented by a jagged curve.

23-28, and 40-45), there is in other cases considerable amplitude of description (see esp. v.

They were measured by the meridian-passages of the limiting stars, and varied in amplitude from 2Ã‚° 42' to 30Ã‚° 24'.

At normal incidence the intensity of the reflected light, measured by the square of the amplitude, is { (µ -1) /(µ+ I) } 2 in both cases; but whereas in the former the intensity increases uniformly with i to the value unity for i =90Ã‚°, in the latter the intensity at first decreases as i increases, until it attains the value zero when i -Fr = 90Ã‚°, or tan i =,u - the polarizing angle of Brewster - and then increases until it becomes unity at grazing incidence.

This causes the semiannual variation of the amplitude of ionospheric equatorial anomaly through fountain effect.

In an amplitude plot, you see the actual amplitude of sine components.

The waveform amplitude envelope provides useful perceptual information to listeners.

Guitar Hero is a rhthym game from Harmonix, the makers of Frequency and Amplitude.

Just when you were getting tired of moving your feet to the music, Harmonix, the company behind the fantastic Frequency and Amplitude, brings you Guitar Hero, a rhythm game that features, you guessed it, playing a guitar.

Games such as Frequency and Amplitude, for example, allow you to play along to popular rock songs while gliding along multi-colored tracks.

An EEG returns normal results when brain waves have normal frequency and amplitude and other characteristics are typical.

If, however, the primary wave be spherical, and of radius a at the wave-front of resolution, then we kno* that at a distance r further on the amplitude of the primary wave will be diminished in the ratio a:(r+a).

When a system vibrating in a free period of its own encounters, say through the medium of an enveloping aether, a second system having a different free period, and sets it in vibration, the amplitude of the second vibration is inconsiderable, except when the periods approach equality.

In "frilling" or "frilled structure" the folds have still smaller amplitude, and in many highly corrugated rocks minute folds are observable with the microscope that do not appear to the unaided eye.

He had the style of his subjects; the amplitude, the weightiness, the laboriousness, the sense, the high flight, the grandeur, proper to a man dealing with imperial themes, with the fortunes of great societies, with the sacredness of law, the freedom of nations, the justice of rulers.

Sieger has traced a series of isobasic lines, or lines of equal rate of elevation, for portions of Sweden and Finland; these indicate that the movement is now almost nil along the axial lines of the Baltic and the Gulf of Finland, but increases in amplitude northwards to the Gulf of Bothnia and in the direction of the main ridge of the massif of southern Sweden.

Beneath these layers are masses of salter water, through which a thermal wave of small amplitude is slowly propagated to the bottom by conduction.

This was supplied by Fresnel, who, starting from a mechanical hypothesis, showed by ingenious but not strictly dynamical reasoning that if the incident stream have unit amplitude, that of the reflected stream will be - sin (i - r) /sin (i -{- r) or tan (i - r) /tan (i -{- r), according as the incident light is polarized in or perpendicularly to the plane of incidence i, r, being the angles of incidence and refraction connected by the formula sin i =,u sin r.

At normal incidence the intensity of the reflected light, measured by the square of the amplitude, is { (µ -1) /(µ+ I) } 2 in both cases; but whereas in the former the intensity increases uniformly with i to the value unity for i =90°, in the latter the intensity at first decreases as i increases, until it attains the value zero when i -Fr = 90°, or tan i =,u - the polarizing angle of Brewster - and then increases until it becomes unity at grazing incidence.

The intensities of the incident, reflected and refracted streams are then measured in the same way, and we have merely to express that the square of the amplitude of the incident vibrations is equal to the sum of the squares of the amplitudes of the reflected and refracted vibrations.

amplitude of the primary oscillation has fallen to zero.

amplitude of the waveform for detailed editing.

amplitude of vibration of the system at resonance is observed to be 14 mm.

amplitude of the fluctuations, and the fact that the vacuum energy now, is incredibly near zero.

E is the normalized structure amplitude, SIGE is its standard deviation.

amplitude modulated by the sound.

The default value is 1/3 the value of the largest observed structure amplitude, Fo, which is printed on each run.

amplitude modulation ).

amplitude oscillations around equilibrium.

amplitude envelope.

amplitude loading at room temperature in laboratory air.

Solution method: The automatic amplitude generator GRACE is used to get the necessary helicity amplitudes for all the four-fermion processes.

The displacement amplitude at the resonance frequency with increasing applied voltage does not increase linearly.

By redefining the zero of time the voltage amplitude can always be made real.

The wave amplitude varies from zero (nodes) to a maximum, half way between the nodes.

This modulation technique is called quadrature amplitude modulation (QAM ).

Hodes [52] found a decrement of the compound muscle action potential amplitude on repetitive stimulation in patients with previous paralytic polio.

At the higher-frequency end, a sharp drop-off in amplitude was found when going from a 15- to 8-year forcing period.

amplitude envelope of speech signal (rectified and smoothed at 25Hz ).

The third component contains the same amplitude and rate, but is now a real exponential.

Envelope amplitude modulation occurs in cochlear filtered speech because of unresolved harmonics.

integral squared amplitude power) is the actual integral under the curve defined by the square of the raw data.

In contrast to other optical methods of the detection of Shear force interactions the fiber interferometer enables to measure the tip amplitude oscillation.

All these data have been taken as sets of different intermediate frequency (IF) amplitude modulation of the RF carriers.

Use the complex amplitude to calculate a quantity proportional to the measured irradiance.

The light scattering irradiance for spheres is calculated using the equation, 1.0 where is the scattering amplitude function given by [2] .

This includes probe linearity to pulse modulated and amplitude modulated signals, spherical isotropy, and spatial resolution.

Specimens were tested under constant amplitude loading at room temperature in laboratory air.

logarithm of the amplitude of the strongest wave during an earthquake.

lysed by sonication, 10 s on, 2 s off at 40% amplitude for 8 min.

The laser beam is being amplitude modulated by the signal generator.

Some radios may have a setting marked AM (amplitude modulation ).

A receiver coil can be used to detect the amplitude of this magnetic field.

The frequency of the oscillation or movement and the amplitude of the oscillation also vary.

The type of nystagmus can accurately be determined by eye movement recordings, which map direction, frequency, null point, and amplitude of the nystagmus.

such as ad-ib where i=1/ - i, the "argument" (or "amplitude") is the angle 0 given by tan 0 = b/a.

In consequence, the change in the amplitude of the fluctuation through the seven-year period is not so well marked as before 190o.

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