The principle of superposition is the additive property of any linear system or function, where the net result of multiple input variables is equal to the sum of their individual results. It is applied to linear mathematical functions and is useful for systems modeling and analysis, but is only an approximation of real-life operating conditions. It is commonly used in wave energy systems and is the technology behind noise-canceling headphones.
In physics and engineering, the principle of superposition is the additive property of any linear system or function. Given the calculated or measured result of an input variable, if one or more separate and additional variables are applied simultaneously, the resulting net result will be equal to the sum of the respective individual results of each variable. Simply stated, its basic concept can be expressed as follows: if input A results in output X and the output of input B is Y, then the superposition of both inputs A+B will result in the corresponding output X+Y. One reason for the term “superposition” is that the principle applies to a specific place and time. Given the changing state of active systems, overlapping inputs and outputs are positional events and measurements.
The superposition principle can be applied to linear mathematical functions, such as algebraic equations. When any of the input variables are affected by scalars, as with the constant coefficients of mathematical quadratic equations, the function is said to be both linear and homogeneous. For the example above, if the known scalars 1 and 2 are applied to input variables 1A+2B, the overlap is transferred to output 1X+2Y. The combined output is often called the sum.
Many mechanical and electrical products, systems, and processes are designed to be linear. If a knob is turned clockwise, the volume increases accordingly. However, in all but the simplest devices, most systems are complex and affected by many variables. They are rarely, absolutely linear. While the superposition principle is a convenient and useful tool for systems modeling and analysis, it is considered to be only an optimal approximation of real-life operating conditions.
Among the linear systems that have benefited most from the application of the superposition principle are those that use wave energy. Sound, light and other electromagnetic radiation also have highly additive properties. The shape of a wave itself can be described as a linear equation. According to the principle, two or more waves of a particular height or amplitude occupying the same space and time will transform into a single wave whose amplitude is the sum of the amplitudes of the original constituent waves. Similarly, light of the wavelength for the color red when superimposed on that of green will be additively transformed into a wavelength corresponding to the color yellow.
This overlay principle is the technology behind noise canceling headphones. A microphone analyzes the waveform of ambient sound, such as the low rumble of an aircraft engine. A loudspeaker recreates the same waveform and is phase shifted in time before adding this sound to the system. When the amplitude of the engine sound wave reaches a representative value of 1, it coincides with the depression of the added sound, the equivalent value of -1. Their sum effect is zero.
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