The tutorial physics. Volume 1, A textbook of sound / by Edmund Catchpool.

  • Catchpool, Edmund
Date:
[between 1890 and 1899]
Catalogue details

Licence: Public Domain Mark

Credit: The tutorial physics. Volume 1, A textbook of sound / by Edmund Catchpool. Source: Wellcome Collection.

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    6. Phase.—The phase of a harmonically vibrating poipt usually means the fraction of a whole period of its vibration which has elapsed since it last passed its mean position in the direction which we are counting as positive^ Some writers, however, count the time which has elapsed since it started from the positive end of its vibration. Upwards and to the right are usually counted the positive directions for vertical and horizontal vibrations respectively. If two points, both vibrating harmonically in the same period, are in the same phase at one instant, they are, of course, always in the same phase, and if they are not, the difference of phase between them may be conveniently defined by stating the difference between the times at which they cross their mean positions in the positive direction as a fraction of the whole period of either ; it may also be stated as the corresponding angle of revolution of the uniformly revolving point, either in degrees or in radian measure. Thus, in Fig. 5, if we suppose / and g to be positions at the same instant of two points vibrating harmonically in the same period, and that they are moving in the same direction, their phase-difference 1 7r may be called — or J 16 — or 22£°, as we prefer. When the two vibrations are of different periods, their phases change at different rates, and there is no constant phase-difference between them, and there will be instants at which the two vibrations are in the same phase. The u phase-difference ” is, in this case, usually taken to mean the difference between the times at which the points cross their mean positions in the positive direction, expressed as a fraction of the greatest common measure of their periods, but other notations are also used. 7. Composition of Harmonic Vibrations.—A point may execute two or more harmonic vibrations at the same time. This does not mean, as it appears to, that a point A can be moving, at any one instant, with respect to a given point of reference such as the earth, with more than one velocity or in more than one direction. A conventional meaning is attached to the phrase. Harmonic motion, like all motion, is, of course, relative; thus the piston of the engine of a
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