1. Superposition Principle:
The principle of superposition states that when two or more waves meet at a point, the resultant displacement at that point is the vector sum of the displacements due to each individual wave.
2. Phase Difference:
* In Phase: If the waves are in phase (crest meets crest, trough meets trough), the amplitudes add up constructively, resulting in a larger amplitude.
* Out of Phase: If the waves are out of phase (crest meets trough), the amplitudes partially or completely cancel out, resulting in a smaller amplitude.
3. Amplitudes:
The relative amplitudes of the individual waves also play a role:
* Equal Amplitudes: If the individual waves have equal amplitudes, the resultant amplitude will be:
* Constructive interference: 2 * amplitude of individual wave (when in phase)
* Destructive interference: 0 (when completely out of phase)
* Unequal Amplitudes: If the individual waves have different amplitudes, the resultant amplitude will be somewhere between the sum and difference of the individual amplitudes, depending on the phase difference.
In Summary:
The amplitude of the resultant wave when two mechanical waves coincide can be:
* Larger than the individual amplitudes: When the waves are in phase.
* Smaller than the individual amplitudes: When the waves are out of phase.
* Equal to the sum of the individual amplitudes: When the waves are in phase and have equal amplitudes.
* Zero: When the waves are completely out of phase and have equal amplitudes.
Important Note: This analysis applies to waves of the same type (e.g., both sound waves, both water waves). The interaction of different wave types (like light and sound) is more complex.
