WE have all stood many times by the seashore, watching the waves, crested with white foam, roll in and break upon the rocks or beach. Every one has more than once cast a stone upon still water in a lake or pond, and noticed the expanding rings of ripples; and some have voyaged over stormy seas, whereon great ships are tossed by mighty billows with no more seeming effort than the rocking of a cradle. In all these things we have been spectators of a wave-motion, as it is called, taking place upon a water surface. Perhaps it did not occur to us at the time that the sound of the splash or thunder of these breaking waves was conveyed to our ears as a wave-motion of another sort in the air we breathe, nay, even that the light by which we see these beautiful objects is also a wave-motion of a more recondite description, produced in a medium called the æther, which fills all space.
A progressive study of Nature has shown us that we are surrounded on all sides by wave-motions of various descriptions—waves in water, waves in air, and waves in æther—and that our most precious senses, our eyes and ears, are really wave-detectors of a very special form. The examination of these waves and their properties and powers has led us to see that waves in water, air, and æther, though differing greatly in detail, have much in common; and many things about them that are difficult to understand become more intelligible when we compare these various wave-motions together. In these lectures, therefore, I shall make use of your familiar experiences concerning sea and water waves to assist you to understand some of the properties of air waves to which we owe our sensations of sound and music; and, as far as possible, attempt an explanation of the nature of æther waves, created in the all-pervading æther, to which are due not only light and sight, but also many electrical effects, including such modern wonders as wireless telegraphy. In all departments of natural science we find ourselves confronted by the phenomena of wave-motion. In the study of earthquakes and tides, telegraphs and telephones, as well as terrestrial temperature, no less than in the examination of water waves and ripples, sound, music, or light and heat, we are bound to consider waves of some particular kind.
Fastening our attention for the moment on surface water waves, the first question we shall ask ourselves is—What is a wave? If we take our station on a high cliff looking down on the sea, on some clear day, when the wind is fresh, we see the waves on its surface like green rounded ridges racing forward, and it appears at first sight as if these elevations were themselves moving masses of water. If, however, we look instead at some patch of seaweed, or floating cork, or seagull, as each wave passes over it, we shall notice that this object is merely lifted up and let down again, or, at most, has a small movement to and fro. We are led, therefore, to infer that, even when agitated by waves, each particle of water never moves far from its position when at rest, and that the real movement of the water is something very different from its apparent motion. If we place on the surface of water a number of corks or pieces of paper, and then watch them as a wave passes over them, we shall notice that the corks or bits of paper rise and fall successively, that is, one after the other, and not all together. A little more careful scrutiny will show us that, in the case of sea waves in deep water, the motion of the floating object as the wave passes over it is a circular one, that is to say, it is first lifted up, then pushed forward, next let down, and, lastly, pulled back; and so it repeats a round-and-round motion, with the plane of the circle in the direction in which the wave is progressing. This may be illustrated by the diagram in [Fig. 1], where the circular dotted lines represent the paths described by corks floating on the sea-surface when waves are travelling over it.
Fig. 1.
Accordingly, we conclude that we have to distinguish clearly between the actual individual motion of each water particle and that general motion called the wave-motion. We may define the latter by saying that to produce a wave-motion, each separate particle of a medium, be it water, or air, or any other fluid, must execute a movement which is repeated again and again, and the several particles along any line must perform this same motion one after the other, that is, lagging behind each other, and not simultaneously. We might illustrate this performance by supposing a row of fifty boys to stand in a line in a play-ground, and each boy in turn to lift up his arm and let it down again, and to continue to perform this action. If all the boys lifted up their arms together, that would not produce a wave-motion; but if each boy did it one after the other in order, along the rank, it would constitute a wave-motion travelling along the line of boys. In more learned language, we may define a wave-motion by saying that a wave-motion exists in any medium when the separate portions of it along any line execute in order any kind of cyclical or repeated motion, the particles along this line performing the movement one after the other, and with a certain assigned delay between each adjacent particle as regards their stage in the movement.
It will be evident, therefore, that there can be many different kinds of waves, depending upon the sort of repeated motion the several parts perform.
Some of the numerous forms of wave-motion can be illustrated by mechanical models as follows:—
A board has fastened to it a series of wooden wheels, and on the edge of each wheel is fixed a white knob. The wheels are connected together by endless bands, so that on turning one wheel round they all revolve in the same direction. If the knobs are so arranged to begin with, that each one is a little in advance of its neighbour on the way round the wheel, then when the wheels are standing still the knobs will be arranged along a wavy line ([see Fig. 2]). On turning round the first wheel, each knob will move in a circle, but every knob will be lagging a little behind its neighbour on one side, and a little in advance of its neighbour on the other side. The result will be to produce a wave-motion, and, looking at the general effect of the moving knobs, we shall see that it resembles a hump moving along, just as in the case of a water wave.
