Waves and ripples in water, air, and æther

by Sir J. A. Fleming

This last experiment shows, in a very remarkable manner, the way in which the force required to drag the boat falls off as the critical speed of 9 miles an hour is reached.

Here, then, we have the outlines of the proof first given by Mr. Scott Russell, that the tractive force undergoes a sudden diminution when the speed of the boat in a canal approximates to or just exceeds that of the long wave in that particular depth of water. If passenger traffic on canals had not been destroyed by the advent of railways, we should, no doubt, have seen extensive applications of the principle discovered so curiously by the aid of an alarmed horse, and so skilfully investigated by a celebrated engineer.

The whole theory of the trail of waves made by a canal-boat is only comprehensible if it is clearly seen that a water-surface wave has a certain velocity determined by its wave-length. If the wave-speed is small, the waves are short. As the speed increases the waves get longer. Or the matter may be put in another way. We may say that just as a pendulum has a certain rate of vibration depending on its length, so a water wave has a certain frequency, and therefore, a certain speed of propagation dependent upon the wave-length, or shortest distance from one wave-crest to the next. When a boat moves along a canal the waves it makes move with it, and the first wave of all moves with the speed of the boat. Hence the wave-length must accommodate itself to that speed. As the speed of the boat increases towards that of the free “long wave,” the wave-length gets greater and greater, and when the boat-speed is equal to that acquired by a heavy body, say a stone in falling through half the depth of the canal, then there is only one wave, and the boat rides up on that one. The next wave is practically so far behind that it is non-existent, and the boat ceases to be followed by any trail of waves, or “wash.”

CHAPTER III.

WAVES AND RIPPLES IN THE AIR.

LEAVING the consideration of waves and ripples on a water-surface, we pass on to discuss the subject of waves and ripples in the air. Nearly every one is aware, in a general way, that sound is due to a disturbance created in the atmosphere. Few, however, are fully acquainted with the nature of the movements in the air which excite our sense of hearing, and to which we owe, not only the pleasures of conversation and the enjoyment of all the sounds in nature, but those delights of music which are amongst the purest forms of pleasure we possess.

In the first place, it is necessary to demonstrate the fact that in a place where there is no air there can be no sound. Before you on the table is a brass plate covered with a glass dome. Under the dome is a piece of clockwork, which, when set in action, strikes a gong. This clockwork is suspended by silk strings from a frame to keep it out of contact with the plate. The plate is in connection, by a pipe, with an air-pump downstairs, and from the space under the dome we can at pleasure remove the air. Before so doing, however, the clockwork shall be set in motion, so that you will then see the hammer striking the gong, and you also hear the sound. If now we exhaust the air, the sound rapidly dies away, and when a fairly perfect vacuum has been made, whilst you see the hammer continuing to pound the bell, you notice that no sound at all reaches your ears. Turning a tap, I let in the air, and once more the ring of the bell peals forth. The experiment shows conclusively that sound is conveyed to us through the air, and that if we isolate a sounding body by removing the air around it, all transmission of sound is stopped. Even rarefying the air greatly weakens the sound, for it is noticed that an exploding pistol or cracker does not create the same intensity of sensation in the ear at the top of a very high mountain as it does in the valley below.

We have then to show, in the next place, that a substance which is emitting sound is in a rapid state of vibration, or to-and-fro movement. Taking a tuning-fork in my hand, I strike its prongs against the table, and you hear it faintly sounding. Your unassisted vision will not, however, enable you to see that the prongs are in rapid motion. If, however, I hold it against a pith-ball suspended by a silk fibre, you see by the violent bouncing of the ball that the prongs must be in energetic vibration.

Another experiment of the same kind, which you can yourselves repeat, is to elicit a sound from a small table-gong by striking it with the hammer. Then hold near the surface of the metal a small ball of wood or cork, to which a suspending thread has been tied. The ball will keep jumping from the gong-surface in a manner which will convince you that the latter is in a state of violent agitation. The mode and extent of this movement in a sound-emitting body must next be more thoroughly examined. Let me explain the means by which I shall make this analysis. On the prong of a tuning-fork, T ([see Fig. 44]), is fixed a small mirror, M, and a ray of light is reflected from an electric lantern on to this mirror. The ray is then reflected back again on to a sort of cubical box, C, the sides of which are covered with looking-glass, and finally it falls upon the screen. The mirrors are so arranged that if the cubical mirror is at rest and the fork also, a bright spot of light is seen upon the screen. If the fork is set in vibration, then the spot of light moves up and down so rapidly that it forms a vertical bar or line of light upon the screen. The cubical mirror is carried upon an axis, and can be set in rotation. If the fork is at rest and the cubical mirror revolves, then the spot of light marches horizontally across the screen, and when the motion of the mirror is sufficiently rapid it forms a horizontal and brilliant band of light. If, then, these two motions are performed at the same time, the tuning-fork being set in vibration and the cubical mirror in rotation, we find that the spot of light on the screen executes a wavy motion, and we see in consequence a sinuous bright line upon the wall.