Page:Elementary Text-book of Physics (Anthony, 1897).djvu/170

156 as 1:2. It will be noticed that the resultant curve is no longer a simple sinusoid.

In the same way the resultant ware may be constructed for any number of wave systems having any relation of wave lengths, amplitudes, and phases. A very important case is that of two wave systems of the same period moving in opposite directions with the same velocity. In this case the two systems no longer maintain the same relative positions, and the resultant curve is not displaced along the axis, but continually changes form. In Fig. 49 let the full and dotted lines in I represent, at a given instant, the displacements due to the two waves respectively. The resultant is plainly the straight line $$ab$$, which indicates that at that instant there is no displacement of any particle. At an instant later by $$\tfrac{1}{8}$$ period, as shown in II, the wave represented by the full line has moved to the right $$\tfrac{1}{8}$$ wave length, while that represented by the dotted line has moved to the left the same distance. The heavy line indicates the corresponding displacements. In III, IV, V, etc., the conditions at instants $$\tfrac{1}{8}, \tfrac{3}{4}, \tfrac{1}{2},$$ etc., periods later are represented. A comparison of these figures will show that the particles at $$c$$ and $$d$$ are always at rest, that the particles between $$c$$ and $$d$$ all move in the same direction at the same time, and that particles on