derivation of principle of super position by taking cos
Answers
Answer:
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Explanation:
Explanation:
The principle of superposition states that, when two or more waves of the same type cross at some point, the resultant displacement at that point is equal to the sum of the displacements due to each individual wave.
The displacements are added vectorially. However, usually the vibrations or oscillations are in a single plane, so the displacements can be added algebraically (just including the +/− sign).
The principle depends on the medium behaving linearly when the waves pass through; i.e. when the parts of the medium have twice the displacement then it has twice the restoring force. (For very large amplitudes this breaks down and harmonics are obtained).
The idea and the language transfers across to electromagnetic waves in a vacuum, even though there is no mechanical displacement of the medium.
When the waves pass beyond that point of intersection, they separate out again and the waves are completely unchanged (unless the medium has been overstretched).
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∝E∝A2.
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.
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