If now one of the particles be deflected from its natural position—suppose it is moved to the position M—then we should have one particle at M out of its place, and all the others in their places.
But this does not happen. If the particle is pulled to M, the particles near it follow after it, and are also disturbed from their places, though not so much as the particle at M.
We should have a set of particles forming a shape like L M N, only much longer; in fact, the particles all along the cord would be raised.
If the cord is struck suddenly we do have a set arranging themselves like L M N, but only for a limited distance along the cord.
And here we notice a curious thing.
If a set of particles is forced to go like L M N, removed from their position of repose, then at once a set of particles goes like N O N′.
A displacement is accompanied by another displacement which is the opposite of it. And this displacement and opposite displacement travels along the elastic cord.
But the point of view which is the most natural one to regard it from is a little different from this. Let us consider a single point, P. When this is disturbed it moves above its original position to M, and below to the other end of the dotted line. Its complete movement is from one of these extremes to the other. And if we take the complete disturbance as exhibited in all its phases by different points, we ought to look at the portion of the diagram M N O. For here at N we have a point not displaced at all; at M, one displaced to its full extent upwards; at O, one displaced to its full extent downwards. And intermediate particles have intermediate displacements.
Now when a complex displacement of this kind is put into a cord, its image at once springs up. The displacement represented by M N O at once calls up the displacement represented by O N′ M′, and this condition of displacement and image displacement continues repeating itself till the cord comes to rest.
If the diagram be closely looked at, it will be seen that it exhibits the image relationship twice over. For the movement of the particle P from P to M has its image in the motion of another particle from its place of repose to the position O. The disturbance itself, M N O, consists of displacements and image displacements; and this disturbance, with its image O N′ M′, makes the wave from crest to crest.