Waves and ripples in water, air, and æther

by Sir J. A. Fleming

Fig. 10.

So much for the events revealed by the flash-light of an electric spark; but succeeding these there is a long train of interesting wave-making performance which can be watched with the eye, or the stages photographed with a hand camera. This wave production is best seen when a large stone is thrown into calm water in a lake or pond.

A story is recorded of the great artist Turner, that he once spent a morning throwing stones into a pond. A friend reproved him for his idleness. “No,” said the painter, “I have not been idle; I have learnt how to paint a ripple.” If the artist’s eye has to be carefully trained to notice all that there is to see when a stone is hurled into a pond, it is not strange that a careless observer cannot grasp at once what really happens to the water in this ordinary occurrence.

Fig. 11.—Ripples on a lake (Sierre), produced by throwing in a stone.

The photograph in [Fig. 11] will, however, show one stage in the event. As soon as the first wave-crest, the origin of which we have already explained, is formed, it begins to move outwards in a circular form, and as it moves it gives rise to a wave-train, that is, it multiplies itself into a series of concentric ripples, or waves, which move outwards, multiplying in number, but getting smaller as they move.

Thus if a large stone is thrown far out into a deep, still lake, after the first splash we shall see a circular wave spreading out from the place where the commotion was made in the water. As we look at this wave we shall see it growing in size and multiplying itself. At first there is but a single wave, then two, four, seven, ten, or more concentric ripples are seen, each circular wave expanding and getting feebler, but seeming to give birth to others as it moves. Moreover, a very careful examination will show us that the whole group of waves, or the wave-train, has an outward motion with a less speed than any individual wave. This observation will serve to initiate the conceptions of a wave-train and of a wave-group velocity. At first it is difficult to understand that a group of waves may move more slowly than the individual waves which compose it. If, however, we cast a stone into a pond, and look very carefully at what takes place, we shall see that the circular expanding band of ripples has an ill-defined but visible inner and outer edge, and that wavelets or ripples which compose it are being continually brought into existence on its inner edge, and dying away on its outer edge. Waves, so to speak, pass through the ripple band with a greater speed than that at which the whole band of waves moves forward. This rather difficult, but important, idea of the distinction between the velocity of a group of waves and that of an individual wave was first suggested by Sir George Stokes, who set a question in a Cambridge Examination on the subject in 1876, and subsequently it was elucidated by Professor Osborne Reynolds[6] and Lord Rayleigh.

It can be further explained as follows: Let us consider a wave-motion model such as that represented in [Fig. 7], in which a number of suspended heavy balls are connected to one another by elastic threads. Let one ball in the centre be drawn on one side and then released. It will swing to and fro, and will start a wave outwards in both directions. If the row of balls is sufficiently long, it will be seen that the ball by which the wave was started soon comes to rest, and that the wave-motion is confined to a certain group of balls on either side. As time goes on, the wave-motion in each group dies away on the side nearest the origin, and extends on the side furthest away. Hence the particular group of balls which are the seat of the visible wave-motion is continually being shifted along. The rate at which the centre of this active group of vibrating balls is displaced may be called the velocity of the wave-train. The velocity of the wave is, however, something greater, since the waves are all the time moving through the group. This wave-velocity is numerically estimated by taking the product of the wave-length and frequency of the motion.

At this stage it is necessary to explain that waves are not merely a mode of motion; they are a means of conveying energy. It is difficult to give in a compact form any simple definition of what is meant in modern scientific writings by the word Energy.

Briefly speaking, we may say that there are two fundamental agencies or things in Nature with which we are in contact, manifesting themselves in many different forms, but of which the total quantity is unchangeable by human operations. One of these is called Matter. This term is the collective name given to all the substance or stuff we can see or touch, and which can be weighed or has weight. All known solids, liquids, or gases, such things as ice, water, steam, iron, oil, or air, are called material substances, and they have in common the two qualities of occupying space or taking up room, and of having weight. Experiment has shown that there are some eighty different kinds of simple matter which cannot be transformed into each other, and these forms are called the Elements. Any other material substance is made up of mixtures or combinations of these elements. The elementary substances are therefore like the letters of the alphabet, which, taken in groups, make up words, these last corresponding to compound chemical bodies. Exact research has shown that no chemical changes taking place in a closed space can alter the total weight or amount of gravitating matter in it. If a chemist and numerous chemicals were enclosed in a great glass ball, and the ball balanced on a gigantic but very sensitive pair of scales, no operations which the chemist could conduct in the interior of his crystal laboratory would alter, by the ten-thousandth part of a grain, the total weight of it all. He might analyze or combine his chemicals, burn or mix them as he pleased, but as long as nothing entered or escaped from the ball, the total gravitating mass would remain precisely the same. This great fact is called the Law of Conservation of Matter, and it teaches us that although a scuttle of coal may seem to disappear when burnt, yet the weight of the ashes and of all the gaseous products of combustion are together equal to the weight of the original coal and the air required to burn it.