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 the one fork shall urge the air-particles forward, while the other urges them backward. If the opposing forces be equal, particles so solicited will move neither backward nor forward, the aërial rest which corresponds to silence being the result. Thus it is possible, by adding the sound of one fork to that of another, to abolish the sounds of both. We have here a phenomenon which, above all others, characterizes 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.
Fig. 150.
During the vibration of a tuning-fork the distance between the 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, Fig. 150, 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, of the two forks, neglecting the other two prongs; and now let us ask what must be the distance between the prongs A and B, 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 were the distance between A and B two wave-lengths, three wave-lengths, four wave-lengths—in short, any number of whole wavelengths. In all such cases we shall 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.
Fig. 151.
But if the prong B 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, the air to the right of A being reduced to quiescence. This is shown in Fig. 151, where the uniformity of shading indicates an absence both of condensations and rarefactions. When B is two half wave-lengths behind A, the waves, as already explained, support each other; when they are three half wave-lengths apart, they destroy each other. Or expressed generally, we have augmentation or destruction 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 oppose each other, and a destruction of light is the result of their coalescence.
The action here referred to, both as regards sound and light is called Interference.
§ 3. Experimental Illustrations
