CHAPTER III

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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.

[Illustration: 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.

[Illustration: 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.

Notice how certain sounds, such as _b_ and _p_ and also _t_ are represented by very high notches or teeth in this line of light. These sounds are called _explosive consonants_, and if you examine the manner in which they are made by your mouth, you will notice that it consists in closing the mouth by the lips or tongue placed between the teeth, and then suddenly withdrawing the obstruction so as to allow the air from the lungs to rush forcibly out. Hence the air outside, and in this case the diaphragm, receives a sudden blow, which is represented by this tall tooth or notch in the luminous band. The experiment teaches us that whereas _musical tones_ are caused by certain very regular and uniform vibrations of the sounding body, _vocal sounds_ and _noises_ are caused by very irregular movements. Also that loud sounds are created by large motions, and feeble ones by small motions. Again, that the difference between tones in music is a difference in the rate of vibration of the sounding body. We may infer also that the difference between the quality of sounds is connected with the _form_ of the wave-motion made by them.

Having established these facts, we must, in the next place, proceed to notice a little more closely the nature of an _air wave_. It will be necessary to remind you of certain qualities possessed not only by the air we breathe, but by all gases as well. Here is a cylinder with a closely fitting piston, and a tap at the bottom of the tube. If I close the tap and try to force down the piston, I feel some resistance, which increases as the piston is pushed forward. If the pressure is removed, the piston flies back to its old position, as if there were a spring underneath it. The air in the tube is an elastic substance, and it resists compression. At constant temperature the volume into which the air is squeezed is inversely as the pressure applied.

The air, therefore, possesses _elasticity of bulk_, as it is called, and it resists being made to occupy a smaller volume. Again, the air possesses _inertia_, and when it is set in motion it continues to move like any other heavy body, after the moving force is withdrawn. We have, therefore, present in it the two essential qualities for the production of a wave-motion, as explained in the first lecture. The air _resists_ compression in virtue of elasticity, and when it is allowed to expand again back, it _persists_ in motion in virtue of inertia.

Let us consider next the process of production of a very simple sound, such as an explosion. Suppose a small quantity of gun-cotton to be detonated. It causes a sound, and therefore an air wave. The process by which this wave is made is as follows: The explosion of the gun-cotton suddenly creates a large quantity of gas, which administers to the air a very violent outward push or blow. In consequence of the inertia of the air, it cannot respond everywhere instantly to this force. Hence a certain spherical layer of air is compressed into a smaller volume. This layer, however, almost immediately expands again, and in so doing it compresses the next outer layer of air and rarefies itself. Then, again, the second layer in expanding compresses a third, and so on.

Accordingly, a state of compression is handed on from layer to layer, and each state of compression is followed by one of rarefaction. The individual air-particles are caused to move to and fro in the direction of the radii of the sphere of which the source of explosion is the centre. Hence we have what is called a spherical longitudinal wave produced.

Each air-particle swings backwards and forwards in the line of propagation of the wave. The actual motion of each air-particle is exceedingly small.

The speed with which this zone of compression travels outwards, is called the velocity of the sound wave, and the extent to which each air-particle moves backwards and forwards is called the amplitude of the wave.

Suppose, in the next place, that instead of a merely transitory sound like an explosion, we have a continuous musical sound, we have to inquire what then will be the description of air-movement executed. The experiments shown already will have convinced you that, in the case of a musical sound, each air-particle must repeat the same kind of motion again and again.

The precise nature of the displacement can be best illustrated by the use of two models. Before you is placed a frame to which are slung a series of golf-balls suspended by threads (see Fig. 4,