Waves and ripples in water, air, and æther

by Sir J. A. Fleming

Fig. 44.

We have here two principles involved, which it may be better to explain a little more in detail. An impression made upon the eye lasts for about the tenth part of a second. Hence, if a luminous point or bright object moves sufficiently rapidly, we cease to be able to follow its movement, and we receive on our eyes merely the effect of a luminous line of light. Every boy sees this when he whirls round a lighted squib or stick with a flaming end. In the next place, notice that two independent movements at right angles combine into what is called a resultant motion. Thus the vertical up-and-down motion of the spot of light in our experiment, combined with its uniform horizontal movement, results in the production of a wavy motion. For the sake of those who wish to repeat the experiment, a few little hints may be given. The revolving cubical mirror is a somewhat expensive piece of apparatus, but found in every well-appointed physical laboratory. A cheap substitute, however, may be made by firmly sticking on to the sides of a wooden box pieces of thin looking-glass. The box is then to be suspended by a string. If the string is twisted, the box may be set spinning like a joint of meat roasting before the fire. An ordinary magic lantern may be used to provide a parallel beam of light. In lecture demonstrations it is necessary to employ the electric arc lamp, and to make use of an arrangement of lenses to create the required powerful parallel beam of light. Then as regards the fork. We are employing here a rather elaborate contrivance called an electrically driven tuning-fork, but for home demonstration it is sufficient to make use of a single piece of stout steel clock-spring, or any other flexible and highly tempered piece of steel. This must be fixed to a block of wood as a support, and to its end must be fastened with care a small piece of lead, to which is attached a fragment of thin silvered glass of the kind called a galvanometer mirror, which may be procured of any scientific instrument maker. The position of this vibrating spring must be such that, if the spring vibrates alone, it will reflect the ray of light on to one face of the cubical mirror, and thence on to a white wall, and create a vertical bar of light, which becomes a spot of light when the spring is at rest. It is possible to purchase very small concave mirrors about half an inch in diameter, made of glass silvered at the back. If one of these can be procured, then there is no need to employ an optical lantern; with an ordinary table-lamp, or even a candle as a source of light, it is easy to focus a bright spot of light upon the screen, which effects the desired purpose of making evident the motion of the spring.

Before we dismiss the experiment, let me say one or two more words about it. You notice when it is proceeding that the luminous wavy line is a regular and symmetrical one. This shows us that the motion of the prong of the fork is similarly regular. This kind of backwards-and-forwards motion is called an harmonic motion, or a simple periodic motion. It is very similar to the kind of movement executed by the piston of a steam-engine as it oscillates to and fro. The exact nature of the wavy line of light you see upon the screen can be delineated by a line drawn as follows: On a sheet of paper describe a circle, and divide its circumference into twelve equal parts ([see Fig. 45]). Through the centre and through each of these points on the circumference draw parallel lines. Divide up a length of the line drawn through the centre into twelve equal parts, and number these divisions 1 to 12. Number also the points on the circumference of the circle. Through the twelve points on the horizontal line erect perpendiculars. Make a dot at the intersection of the perpendicular, or ordinate, as it is called, drawn through point 1 on the horizontal line, and the horizontal through point 1 on the circumference of the circle. Do this for all the twelve intersections, and then carefully draw a smooth curve through all these points. We obtain a wavy curve, which is called a sine curve, or simple harmonic curve, and is the same form of curve as that exhibited on the screen in the experiment with the tuning-fork and spot of light. The piece of the curve drawn as above is called one wave-length of the harmonic curve.

Fig. 45.—A simple harmonic curve.

In our case the tuning-fork is making one hundred complete vibrations (to and fro) per second. Hence the periodic time, or time occupied by one complete wave, is the hundredth part of a second. To realize what this small interval of time means, it is sufficient to remember that the hundredth part of a second is to one second as the duration of this lecture (one hour) is to four days and nights.

The prongs of a sounding tuning-fork or the surface of a gong or a bell, when struck, are therefore in rapid motion. We can then proceed to an experiment fitted to indicate the difference between those motions in sounding bodies which create musical tones, and those which create mere noises or vocal sounds.

I have on the table before me a bent brass tube provided with a mouthpiece at one end, and the other end of the tube is covered over with a very thin piece of sheet indiarubber tied on like the cover of a jam-pot. To the outer surface of this indiarubber is cemented a very small, light silvered-glass mirror. The same arrangements are made as in the case of the previous experiment, and the ray of light from a lantern is reflected from the little mirror on to the revolving cubical mirror, and thence on to the screen. Setting the cubical mirror in rotation, we have a line of bright light upon the screen. If, then, my assistant sings or speaks into the mouthpiece, the motion of the indiarubber sets in vibration the little attached mirror. This mirror is not attached to the centre of the membrane, but a little to one side. Hence you can easily understand that when the indiarubber is bulged in or out, the attached mirror is more or less tilted, and the spot of light is displaced up or down on the screen. In this manner the movements of the spot imitate those of the diaphragm. Hence the form of the bright line on the screen is an indication of the kind of movement the diaphragm is making. Let us then, in the first place, sing into the tube whilst the cubical mirror is uniformly rotated. If my assistant sounds a full pure note, you will see that the straight line of light instantly casts itself into a wavy form, which is not, however, quite of the same shape as in the case of the tuning-fork. Here the zigzag line resembles the outline of saw-teeth (see Frontispiece).

If he varies the loudness of his sound, you see the height of the teeth alter, being greater the louder his note. If he changes the tone, singing a bass or a treble note, you observe that, corresponding to a high or treble note, the waves are short, and corresponding to a deep or bass note, the waves are long. Accordingly, the shape of the line of light upon the screen gives us exact information as to the nature of the movement of the indiarubber diaphragm, viz. whether it is moving in and out, slowly or quickly, much or little.

Again, suppose, instead of singing into the tube, my assistant speaks a few words. If, for instance, he repeats in a loud tone the simple but familiar narrative of “Old Mother Hubbard,” you will see that, corresponding to each word of the sentence, the line of light upon the screen bends itself into a peculiar irregular form, and each particular word is as it were written in lines of fire upon the wall.