Interference of waves

Among the phenomena characteristic of wave processes is interference of waves, which consists in the fact that when two waves are superimposed, amplification and attenuation of oscillations can occur.

To get acquainted with this phenomenon, let us consider what happens if waves of the same length arrive at a certain point in space.

We observe this phenomenon using the example of waves propagating on the water surface. We will continuously create waves on its surface at two points. To do this, in the immediate vicinity of the surface of the water we place the ends of two wires attached to an elastic metal plate. When the plate vibrates, the ends of the wires will periodically dive into the water, and excite oscillations that propagate in the form of waves of equal length along its surface. Each of the wires excites its own system of waves. Two wave systems, superimposed on each other, will interact, and hence interference of the waves will occur.

It is important that the two wave systems are matched, that is, that at the same length they exit from the vibration centers in the same phases, or if they are phase shifted (for example, appeared in opposite phases, for example), then the phase shift with time Should not change. Such waves are called coherent. In this experiment, the coherence is ensured by the fact that both ends of the wire periodically touch the water surface simultaneously - the waves leave the vibration centers in the same phases.

Let us construct a superposition of two systems of coherent waves. Solid circles denote the crests of the ring waves propagating along the surface of the water from the sources, and the dotted lines are the depressions. The points where the waves of both systems meet in the same phases, the depression with the depression and the crest with the crest, are the points of the amplified oscillations (maxima). The points of weakened oscillations (minima) are located in places where the depression of one wave meets the crest of another. In the presence of coherence of waves, the pattern of alternation of maxima and minima will be stable. In fact, if at the moment there is a crest with a crest at some point , then in half a period there will be a depression with a depression, and in another half-period again a crest with a crest, etc., i.e. At this point there will be a maximum of oscillations all the time. Such a change in the minima and maxima of the oscillation amplitudes is called an interference pattern. And the phenomenon of superposition of waves, which forms an interference pattern, is called interference of waves.

To solve the problem of the phases in which interfering waves meet at a given point, it is necessary to take into account the difference in their course. To do this, it is sufficient to calculate the number of waves of the corresponding system that fit at distances between the points of maxima and minima of interest to us and the vibration centers. We will see that the maxima will be at those points that either are at equal distances from both centers, or at points where the path difference corresponds to an even number of half-waves, while the minima correspond to an odd number.

Using the example of this experiment, we considered such a phenomenon as the interference of mechanical waves.

Nevertheless, the phenomenon of interference is peculiar not only to waves arising on the surface of water, but also to all types of waves: sound, electromagnetic and other. Therefore, if light has wave properties, then when two of its beams are superimposed, interference of light waves will arise.

Sources emitting such waves are called coherent. In optics, coherent sources can only be created artificially.

It should not be forgotten that interference of waves (any, including light waves) occurs only when the waves that interact have the same frequency and a time-independent phase shift at any point.