SUPERPOSITION OF VIBRATIONS.

257

may be caused to cross and interlace, and by the most wonderful self-analysis to untie their knotted scrolls. The adjacent figure, fig. 138, which is copied from the work

of the brothers Weber, will give some idea of the beauty of these effects. It represents the chasing produced by the intersection of direct and reflected water-waves in a circular vessel, the point of disturbance, marked by the smallest circle in the figure, being midway between the centre and the circumference.

This power of water to accept and transmit multitudinous impulses is shared by air, which concedes the right of space and motion to any number of sonorous waves. The same air is competent to accept and transmit the vibrations of a thousand instruments at the same time. When we try to visualise the motion of that air-to present to the eye of the mind the battling of the pulses direct and reverberated

S

-the imagination retires baffled from the attempt. Still, amid all the complexity, the law above enunciated holds good, every particle of air being auimated by a resultant motion, which is the algebraic sum of all the individual motions imparted to it. And the most wonderful thing of all is, that the human ear, though acted on only by a cylinder of that air, which does not exceed the thickness of a quill, can detect the components of the motion, and, aided by an act of attention, can even isolate from the aërial entanglement any particular sound.

I draw my bow across a tuning-fork, which for distinction's sake I will call A, and cause it to send a series of sonorous waves through the air. I now place a second fork, B, behind the first, and throw it also into vibration. From в waves issue which pass through the air already traversed by the waves from A. It is easy to see that the forks may so vibrate that the condensations of the one shall coincide with the condensations of the other, and the rarefactions of the one with the rarefactions of the other. If this be the case the two forks will assist each other. The condensations will, in fact, become more condensed, the rarefactions more rarefied, and as it is upon the difference of density between the condensations and rarefactions that loudness depends, the two vibrating forks, thus supporting each other, will produce a sound of greater intensity than that of either of them vibrating alone.

It is, however, also easy to see that the two forks may be so related to each other that one of them shall require a condensation at the place where the other requires a rarefaction; that one fork, for example, shall urge the airparticles forward, while the other urges them backward. If the opposing forces be equal, particles so solicited will move neither backwards nor forwards, and the aërial rest which corresponds to silence is the result. Thus, it is possible, by adding the sound of one fork to

that of another, to

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abolish the sounds of both. We have here a phenomenon which, above all others, characterises wave-motion. It was this phenomenon, as manifested in optics, that led to the undulatory theory of light, the most cogent proof of that theory being based upon the fact that, by adding light to light, we may produce darkness, just as we can produce silence by adding sound to sound.

During the vibration of a tuning-fork the distance between its two prongs is alternately increased and diminished. Let us call the motion which increases the distance the outward swing, and that which diminishes the distance the inward swing of the fork. And let us suppose that our two forks, A and B, reach the limits of their outward swing and their inward swing at the same moment. In this case the phases of their motion, to use the technical term, are the same. For the sake of simplicity we will confine our attention to the right-hand prongs, A and B, fig. 139, of the two forks, neglecting

B

A

FIG. 139.

C

the other two prongs; and now let us ask what must be the distance between the prongs ▲ and E, when the condensations and rarefactions of both, indicated respectively by the dark and light shading, coincide? A little reflection will make it clear, that if the distance from B to A be equal to the length of a whole sonorous wave, coincidence between the two systems of waves must follow. The same would evidently occur where the distance between A and B is two wave-lengths, three wave-lengths, four wave-lengths-in short, any num

ber of whole wave-lengths. In all such cases we should have coincidence of the two systems of waves, and consequently a reinforcement of the sound of the one fork by that of the other. Both the condensations and rarefactions between a and c are, in this case, more pronounced than they would be if either of the forks were suppressed.

But if the prong в be only half the length of a wave behind A, what must occur? Manifestly the rarefactions of one of the systems of waves will then coincide with the condensations of the other system, and we shall have interference; the air to the right of a being reduced to quiescence. This is shown in fig. 140, where the uniformity

of tint indicates an absence both of condensations and rarefactions. When в is two half wave-lengths behind A, B we have, as already explained, coincidence; when it is three half wave-lengths distant, we have again interference. Or, expressed generally, we have coincidence or interference according as the distance between the two prongs amounts to an even or an odd number of semi-undulations. Precisely the same is true of the waves of light. If through any cause one system of ethereal waves be any even number of semi-undulations behind another system, the two systems support each other when they coalesce, and we have more light. If the one system be any odd number of semi-undulations behind the other, they interfere with each other, and a destruction of light is the result of their coalescence.

Sir John Herschel first proposed to divide a stream of

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sound into two branches, of different lengths, causing the branches afterwards to reunite, and to interfere with each other. This idea has been recently followed out with success by M. Quincke; and it has been still further improved upon by M. König. The principle of these experiments will be at once evident from fig. 141. The tube of divides into two branches at f, the one branch being carried round n, and the other round m. The two branches are caused to reunite at g, and to end in a common canal, gp. The portion, b n, of the tube which slides over a b, can be drawn out as shown in the figure, and

FIG. 141.

m.

n

thus the sound-waves can be caused to pass over different distances in the two branches. Placing a vibrating tuningfork at o, and the ear at p, when the two branches are of the same length, the waves through both reach the ear together, and the sound of the fork is heard. Drawing a b out, a point is at length attained where the sound of the fork is extinguished. This occurs when the distance ab is one-fourth of a wave-length; or in other words, when the whole right-hand branch is half a wave-length longer than the left-hand one. Drawing b n still further out, the sound is again heard; and when twice the distance a b amounts to a whole wave-length, it reaches a maximum. Thus according as the difference of both branches amounts to