Superposition of Waves

​This principle was given by Huygen. If two or more waves arrive simultaneously, the particles in the medium are subjected to two or more simultaneous displacements. As a result, a new resultant wave is formed. This phenomenon of intermixing of two or more waves to produce a new wave is called superposition of waves.

Principle of superposition of waves states that the resultant displacement of the particle is equal to the algebraic sum of individual displacements due to different waves.

Superposition of waves figure (1)
Superposition of Waves figure (2)

Let $y_1, y_2, y_3, …$ be the displacements of the particle due to individual waves and let the resultant displacement be $y$. Then, according to the principle of superposition of waves, \[y=y_1+y_2+y_3+… \] \[y=\sum_{i=1}^n y_i\] The principle of superposition of waves can be applied to all types of waves as long as the amplitude of the wave is not too large.

In this principle, amplitude of resultant wave is different from interfering waves but it is the same if two waves of same amplitude superimpose at $120°$. Similarly, frequency may or may not be changed.

Principle of superposition of waves can be applied in the followings; 
1. Interference of waves: Two waves of the same frequency moving in the same direction. 
2. Stationary waves: Two waves of the same frequency moving in the opposite direction.
3. Beats: Two waves of slightly different frequency moving in the same direction. 

More on Wave And Wave Motion

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