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24 VIBRATION-MODE AND WAVE-FORM. [I. |
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race from O to A, from A to B, and from B back to O, and that they reach the goal at the same moment. They may obviously do this in many different ways. For instance, they may keep abreast all through, or one may fall behind over the first half of the course and recover the lost ground in the second. Again, one may be in front over OAO, and the other over OBO, or each boy may pass, and be passed by, liis competitor repeatedly during the race. We may regard the movement of each boy as constituting one complete vibration, and thus convince ourselves that a vibratory motion of given extent and period may be performed in an indefinitely numerous variety of modes. Let us now compare the positions of a particle at the expiration of successive equal intervals of time, when cooperating in the transmission of waves of different forms.
In each of the three cases in Fig. 10 the front of a wave is shown in the positions it respectively occupies at the end of ten equal intervals of time during which its intersection with the level-line moves from O through the equidistant points 1, 2, 3, 4, &c. of the initial line.
A particle whose place of rest is O will necesÂsarily assume corresponding positions in the verÂtical line OA: thus the points where this line cuts the successive wave-fronts show the positions |
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