A Conditions For Destructive Interference

Matter is the basis for everything in the universe. From observable matter to dark matter, it is the very foundation of why the universe exists. Therefore the study of matter and its form is very important. One notable theory is about the concept of the matter wave and how a stream of particles, when small enough, can be constituted as a wave.

Matter, according to the Particle Theory, is rigid, and the motion of its constituent particles can be distinctly measured. But according to the Wave Theory, particles, when small enough, cannot be distinctly identified. This is in part because of Heisenberg’s principle too. Therefore in order to identify the motion of these particles, the disturbance they create in the medium can be measured. Let us have a deeper insight into what is Wave Theory.

Wave Function Theory and Schrodinger’s equation

Let us assume we are observing a tennis ball being thrown between two friends playing catch. The tennis ball is roughly the size of our hand, and it is very easy to identify the position and motion of the ball at any given time. Let us now assume that the size of the tennis ball keeps decreasing constantly. What would happen then?

As the size of the tennis ball decreases, it would become more and more difficult for us to observe the exact position and motion of the ball. A point would come, after which we cannot say with any amount of credibility about the position or the path being followed by the ball. Similarly, in physics, as the particle becomes smaller and smaller, it becomes nearly impossible to give the exact position and path being followed by the particle. For example, an electron inside a nucleus is a very tiny particle, and due to Heisenberg’s principle, it is impossible to tell the exact position of the electron when it is treated as a particle. But what if we measure the disturbance caused by the electron as it moves through the medium?

This disturbance that is created by a particle when it moves through a medium in space is called a wave. For a particle like an electron, the wave function is a special quantity that gives the probability of a particle being in a specific place, provided that the particle behaves like a matter wave.

But physics is incomplete without mathematical proof. Erwin Schrodinger postulated a mathematical equation giving a physical form to the hypothesis of De Broglie that stated that matter behaves as a wave. Widely applied to quantum mechanics and to atoms and their innate entities, a popular example of the usage of Schrodinger’s wave function is to find the probability that an electron is present in a given space.

What is Interference of Waves?

Now that we know particles can also travel as waves, the next important concept is to understand the interaction between them. When two forces are applied to a body, they undergo vector addition to yield the total force on the body. When two bodies collide with each other, they undergo elastic or inelastic collision. But what happens when two waves meet each other when travelling in a medium?

Waves are made up of crests and troughs. When two waves meet, their crests and troughs clash with each other to yield a completely new set of crests and troughs. This phenomenon is called the interference of waves. In other words, the disturbance that is caused in a medium due to two waves interacting with each other is a net total of the effect that the two waves have on the medium.

The interference of waves can be observed when they are in the visible spectrum and the pattern that is formed is called the interference pattern. Waves can interact such that they cause two types of interference, constructive and destructive interference. Constructive interference occurs when the net interference becomes a sum of the individual interferences caused by the wave whereas destructive interference is caused when the individual disturbances of two waves cancel each other out.

Destructive Interference

Destructive interference occurs when waves conjoin in such a way that they totally neutralise each other. In the instance the waves destructively interfere, they possess the identical magnitude in the inverted directions.

There have been several compulsive wave phenomena that have occurred naturally, which cannot be described by a single wave. To understand the destructive phenomena, we should inspect them on the basis of combining the waves. For inspecting these, we use the principle of superposition that states:

“If two or more waves are travelling in a medium, the resulting wave function is the algebraic total of the individual wave function.”

If the same frequency and equal magnitude are superimposed, the procedure of interference comes into place. When two waves of the same frequency traverse in a medium at an identical time and in the same way, because of both of the waves’ superpositions, the intensity of the medium at a specified point is not the same as the total of their intensities. At random points, the power of the end wave holds a big value, while for particular points, it is very little. In this part, we have to focus exponentially towards destructive interference.

Conditions for Destructive Interference

Destructive interference will happen when the peaks of one of the waves are at the same place as the troughs of the other wave. That will happen only when the path difference is some odd multiple of r. There must be half a wave between them or one-half wave in addition to any number of complete waves, so the path difference will need to be the difference of an integral multiple of the wavelength of the wave and half of the wavelength.

Conclusion

This disturbance that is created by a particle when it moves through a medium in space is called a wave. For a particle like an electron, the wave function is a special quantity that gives the probability of a particle being in a specific place, provided that the particle behaves like a matter wave.

Destructive interference occurs in instances where waves conjoin in such a way that they totally neutralise each other. When waves destructively interfere, they should possess identical magnitude in the inverted directions.

Several compulsive wave phenomena have occurred naturally, which cannot be described by a single wave.