Superposition Principle

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Superposition applies when waves are?

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1. **The Principle**: For linear media, the resultant displacement at any point is the vector sum of individual displacements of waves at that point: $y = y_1 + y_2 + \dots$.
2. **Condition: Linearity**: The restoring forces in the medium must be proportional to the displacement ($F \propto x$). This is typically true for small amplitude waves.
3. **Independence**: Waves do not interact with or scatter each other; they pass through each other unaffected.
4. **Failure**: Superposition fails in non-linear media (high-intensity laser pulses) where the properties of the medium change due to the wave itself.

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Superposition Principle

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