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What Is Superposition? Discuss The Concept Behind This Term In Detail

Referencing Styles : MLA | Pages : 1

The theory of superposition-

In general terms the principle of superposition states that when two or more than two waves of equal type cross at the same point, the resultant displacement at that particular point is equal to the sum of the displacements due to each to each individual wave.  When superposition occurs, for slow mechanical waves the amplitude can be observed. For high frequency waves, such as sound or EM waves, the intensity is usually measured, which is a measure of the energy of the wave in the region: the energy is proportional to the square of the amplitude.

 Intensity∝2

The resulting intensity at the point of intersection can be greater or smaller than the intensity due to each of the superposing waves. Superposition is important for explaining phenomena such as interference, diffraction and standing waves

In mathematical terms, Superposition is principle which is also referred as superposition property which states that for all the linear system, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus is the sum of the response that would have been caused by each stimulus individually. So that if input A produces response X and input B produces responses Y then input (A+B) produces response (X+Y). Superposition is basically the ability of a quantum system to be in multiple states at the same time until it is measured. Since, the concept is difficult to understand the essential principle of quantum mechanics is often illustrated by an experiment carried out in 1801 by the English physicist. Thomas Young. Young's double-slit experiment was intended to prove that light consists of waves. Today, the experiment is used to help people understand the way that electrons can act like waves and create interference patterns. In order to assess the experiment a beam of light is aimed at a barrier with two vertical slits. The light passes through the slits and the resulting pattern is recorded on a photographic plate. When one slit is covered, the pattern is what would be expected: a single line of light, aligned with which even slit is open. Intuitively, one would expect that if both slits are open, the pattern of light will reflect two lines of light aligned with the slits. In fact, what happens is that the photographic plate separates into multiple lines of lightness and darkness in varying degrees. What is being illustrated by this result is that interference is taking place between the waves going through the slits, in what, seemingly, should be two non-crossing trajectories. Each photon not only goes through both slits; it simultaneously takes every possible trajectory en route to the photographic plate.

In order to see how this might possibly occur, other experiments have focused on tracking the paths of individual photons. Surprisingly, the measurement in some way disrupts the photons' trajectories and somehow, the results of the experiment become what would be predicted by classical physics: two bright lines on the photographic plate each aligned with the slits in the barrier. This has led scientists to conclude that superposition cannot be directly observed; one can only observe the resulting consequence, interference.

In computing, the concept of superposition has important implications for the way information will be processed and stored in the future. For example, today's classical computers process information in bits of one or zero, similar to a light switch being turned on or off.  The quantum supercomputers of tomorrow, however, will process information as qubits -- one, zero or a superposition of the two states. The principle has many applications in physics and engineering because many physical systems can be modeled as liner systems. For example a beam can be modeled as a linear system where the input stimulus is the load on the beam and the output response is the deflection of the beam. The importance of linear systems is that they are easier to analyze mathematically; there is a large body of mathematical techniques, frequency domain linear transform methods such as Fourier, Laplace transforms, and linear operator theory, that are applicable. Because physical systems are generally only approximately linear, the superposition principle is only an approximation of the true physical behavior.

The superposition principle applies to any linear system, including algebraic equations, linear differential equations, and systems of equations of those forms. The stimuli and responses could be numbers, functions, vectors, vector fields, time-varying signals, or any other object that satisfies certain axioms. Note that when vectors or vector fields are involved, a superposition is interpreted as a vector sum.

The wave superposition concept

Waves are generally described by variations in some of the parameter through time and space for example, pressure in sound wave, height in a water wave, or the electromagnetic field in a light wave. The value of this parameter is called the amplitude of the wave, and the wave itself is a function specifying the amplitude at each point. In any system with waves, the waveform at a given time is function of the source (that is external forces, if any that creates or affects the wave) and the initial condition of the system. In many cases especially in classic wave equation the equation describing the wave is linear. When this is true, the superposition principle can be applied. That means that the net amplitude caused by two or more waves traversing the same space is the sum of the amplitudes that would have been produced by the individual waves separately. For example, two waves traveling towards each other will pass right through each other without any distortion on the other side.

The superposition of waves can lead to the following three effects:

Whenever two waves having the same frequency travel with the same speed along the same direction in a specific medium, then they superpose and create an effect termed as the interference of waves.

In a situation where two waves having similar frequencies move with the same speed along opposite directions in a specific medium, then they superpose to produce stationary waves.

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