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The superposition principle
If in a stretched string two impulses are applied at the two ends, these propagate in two opposite directions, meet one another, for some time they are superimposed, then they go on following the original paths. In the area in which the superposition occurs, and for the time necessary to reach separation of the two impulses, every point of the string undergoes in every given instant a shift of the equilibrium position equal to the sum (algebric sum, since we must take into account the fact that the two impulses might well consist in motions of the points of the string both “upwards” and “downwards” with respect to the undisturbed equilibrium position) of the two shifts they would have undergone, at that time, had each of the two been propagating alone. This behaviour presents a particular case of the very important superposition principle which presides over each motion of wave propagation and states: in every point of a medium where more than one wave propagate the resulting perturbation is given at each instant by the sum of the single perturbations. From the principle of superposition it follows that different waves can continue to propagate one by one undisturbed whether or not local superpositions occur. Returning now to the case of light, it is well known that “crossing” the beams of two torches causes an increase of luminosity of the objects contained in the superposition area, while outside this area (considering each torch separately) the two beams appear completely undisturbed.
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