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V. § 51.] FORMATION OF NODES. 103 |
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equal velocities. The moment chosen is that at which crest coincides with crest and trough with trough. The joint effect thus produced does not appear in the figure, our object at present being merely to determine the number and positions of the resulting nodes. For the sake of clearness, one set of waves is represented slightly below the other, though in fact the two are strictly coincident.
Let the waves
abdf...z be moving from left to right, the waves ztsq...a from right to left. The crest klm meets the trough pn'm at m. After these have crossed each other, the trough ghk and the crest rq'p will also meet at m, since km and pm are equal distances. Similarly the crest efg and the trough ts'r will meet at m. Accordingly the point m is a node, and, by exactly the same reasoning, so are a, c, e, g, k, p, r, t, &c. The distances between pairs of consecutive nodes are all equal, each being a single pulse-length, i.e. half a wave-length, of either series.Two pulse-lengths, as gk and km, give three nodes g, k, and m; three pulse-lengths four nodes, and so on. There is thus always one node more than the number of pulses. On the other hand, the fixed ends |
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