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What is the superposition principle? What is interference?

Question:

What is the superposition principle?

What is interference?

Superposition of Waves

There are two fundamental types of energy-momentum transporting entities in the universe. They are the particle and the wave. A particle occupies a finite extension in space. Other particles are excluded from the space it occupies. A wave has an infinite extension. Any number of waves can occupy the same region in space at the same time. That is, particles cannot be superposed while any number of waves can be superposed.

Answer and Explanation:

Since more than one wave can occupy the same region at the same time without excluding the others, it follows that the displacement of the medium will be a superposition of the individual displacements due to all the waves present simultaneously. This is called the superposition principle. Since a wave has an amplitude and a phase it may be mathematically represented by a phasor. The total displacement may be determined by phasor addition. This is just like vector addition with the direction angle replaced by the relative phase angle and the magnitude replaced by the amplitude.

Now the intensity of a wave is the average energy crossing unit perpendicular area per second. This is proportional to the square of the amplitude. Therefore it follows from the superposition principle for displacement that intensities cannot be superposed. When two waves are present the total intensity is the sum of the individual intensities with an additional term. This additional term is called the interference term. If the waves are superposed with a fixed phase difference then it is called coherent addition. In this case, the interference term is observable. Then we have the phenomenon of interference. On the other hand, if random phases are present then the interference term may average out to zero. In this case, which is more common, intensities are additive. Coherent addition will generate characteristic fringe patterns. Coherent addition of light is achieved using a Young's double-slit arrangement.


Learn more about this topic:

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The Resultant Amplitude of Two Superposed Waves

from MEGA Physics: Practice & Study Guide

Chapter 15 / Lesson 10
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