(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.
The 12-hour term is much less variable, especially as regards its phase angle; its amplitude shows distinct maxima near the equinoxes.
(1); and for the intensity, represented by the square of the amplitude, 1 2 [fJsin f +?2 fC? ?
The maximum velocity of a particle in the wave-train is the amplitude of dy/dt.
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.
If th' maximum pressure change is determined, the amplitude is given by equation (20), viz.
Now the amplitude evidently corresponds to the loudness, and the length of period corresponds to the pitch or frequency.
The amplitude in the pipe was certainly much greater than in the issuing waves.
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 result was an amplitude of 1.27 X 107 cm.
The resultant with amplitude I/-/2 that of (1).
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 effects due to each of these rings are equal in amplitude and of phase ranging uniformly over half a complete period.
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 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?
At the central point there is still complete agreement of phase; but the amplitude is diminished in the ratio of a: a+d.
The amplitude is thus subject to fluctuations, which increase as the shadow is approached.
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).
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.
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.
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.
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.
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.
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).
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.
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.
The maximum particle velocity is 21rna (where n is the frequency and a the amplitude), or 27raU/X.