Waves and ripples in water, air, and æther

by Sir J. A. Fleming

Fig. 5.

A very similar effect can be produced, and another illustration given of a wave-motion, as follows: Coil a piece of brass wire into an open spiral like a corkscrew, and affix to it a small fragment of sealing-wax ([see Fig. 5]). Hold this in the sun, and let the shadow of it fall upon paper. Then turn it round like a screw. We shall see that the shadow of the spiral is a wavy line, and that, as it is turned round, the humps appear to move along just as do the crests of sea waves, but that the shadow of the little bit of sealing-wax simply moves up and down.

Fig. 6.

Another wave-motion model may be made as follows: Procure a painter’s comb. This is a thin steel plate, cut into long narrow teeth. Provide also a slip of glass about 3 inches wide and 12 inches long. Paint one side of this glass with black enamel varnish, and when it is quite dry scratch a wavy line upon it ([see Fig. 6]). Place the glass slip close in front of the comb before the light, and, holding the comb still, move the glass slip to and fro, lengthways. The observer will see a row of dots of light lying in a wavy line, and these, as the glass moves, will rise and fall. If the movement is rapid enough, the appearance of a wave moving along will be seen.[4] In all these exhibitions of wave-motion the movement of the particles is due to a common cause, but the moving particles do not control each other’s motion. There is no connection or tie between them. Suppose, however, that we suspend a series of heavy balls like pendulums, and interconnect them by elastic threads ([see Fig. 7]), then we have an arrangement along which we can propagate a true wave. Draw the end ball to one side, and notice what takes place when it is released. The first ball, being displaced, pulls the second one through a less distance, and that the third one, and the third the fourth, and so on. This happens because the balls are tied together by elastic threads, which resist stretching. When the first ball is released, it is pulled back by the tension of the thread connecting it to its neighbours, and it begins to return to its old position. The ball possesses, however, a quality called inertia, and accordingly, when once set in motion, its motion persists until an opposing force brings it to rest. Hence the returning ball overshoots the mark, and passes to the opposite side of its original position of rest. Then, again, this displacement stretches the elastic threads connecting it to its fellows, and a controlling or retarding force is thus created, which brings it to rest, and forces it again to return on its steps. We see, therefore, that each ball must oscillate, or swing to and fro, and that its movement is gradually communicated to its neighbours. A wave-motion is thus started, and a true wave is propagated along the line of balls, in consequence of the presence of elasticity and inertia. The necessary conditions for the production of a true wave in a medium of any kind are therefore: (1) that the medium must elastically resist some sort of deformation; and (2) when it is deformed at any place, and returns to its original state, it must overshoot the mark or persist in movement, in consequence of inertia, or something equivalent to it.

Fig. 7.

Briefly speaking, any material or medium in or on which a true self-propagating wave-motion can be made must resist and persist. It must have an elastic resistance to some change or deformation, and it must have an inertia which causes it to persist in movement when once set in motion. These two qualities, or others equivalent to them, must invariably be present if we are to have a true wave produced in a medium.

These things may be best understood by considering, for example, the production of surface waves on water. Let us ask ourselves, in the first place, what alteration or change it is that a water-surface resists. The answer is, that, for one thing, it resists being made unlevel. A still water surface is everywhere a level surface. If we attempt to make it unlevel by pouring water on to it at one point, or by heaping it up, the water surface would resist this process. We can dig a hole in sand, or heap up sand to form a hillock, but we know full well we cannot do the same thing with water. If, for instance, some water is placed in a glass tube shaped like the letter ⋃, then it stands at the same level in both limbs. Again, if water is set in motion, being a heavy substance, it cannot be brought to rest instantly. Like every other body, it possesses inertia. Accordingly, if we do succeed by any means in making a depression in a water-surface for an instant, the water would immediately press in to fill up the hole; but more, it would, so to speak, overshoot the mark, and, in consequence of its inertia, it would create a momentary hump, or elevation, in the place on the surface where an instant ago there was a depression.

This elevation would again subside into a hollow, and the process would be continued until the water-motion was brought to rest by friction, or by the gradual dispersion of the original energy. The process by which a wave is started on the surface of water, as a consequence of these two qualities of resistance to being made unlevel and persistence in motion, is beautifully shown by the study of waves made by throwing stones into a pond. The events which give rise to the expanding wave are, however, over so quickly that they can only be studied by the aid of instantaneous photography. The most interesting work on this subject is that of Professor A. M. Worthington, who has photographed, by the exceedingly brief light of an electric spark, the various stages of the events which happen when a drop of water or a stone falls into water.[5] These photographs show us all that happens when the falling object touches the water, and the manner in which it gives rise to the wave or ripple which results. Some of Professor Worthington’s results for a drop of water falling into milk are reproduced in the appended diagrams. In the first place ([Fig. 8]) the drop is seen just entering the water. As it plunges down, it leaves behind it a cavity, or, as it may be called, a hole in the water ([see Fig. 9]).