9. Superposition

Principle of Superposition

When two or more waves of the same type meet at a point, the resultant displacement is the algebraic sum of the individual displacements

Interference and Coherence

Interference: the formation of points of cancellation and reinforcement where 2 coherent waves pass each other
Coherence: waves having a constant phase difference
Constructive
- Phase difference = even π\frac{\lambda}{2}
- Path difference = even λ/2
- Destructive
  - Phase difference = odd π \frac{\lambda}{2}
  - Path difference = odd λ/2 \
- \

Conditions for Two-Source Interference:
- Meet at a point
- Must be of the same type
- Must have the same plane of polarization
Demonstrating Two-Source Interference:

A stationary wave is formed when two progressive waves of the same frequency, amplitude and speed, travelling in opposite directions are superposed.
Node: region of destructive superposition where waves always meet out of phase by \pi,\ \thereforeπ, ∴ displacement = zero
Antinode: region of constructive superposition where waves meet in phase \therefore∴ particle vibrate with max amp
- Neighboring nodes & antinodes separated by \frac{1}{2}\lambda½λ
- Between 2 adjacent nodes, particles move in phase and they are out of phase with the next two nodes by \piπ
- Stationary wave at different times:

Diffraction: the spreading of waves as they pass through a narrow slit or near an obstacle.
For diffraction to occur, the size of the gap should be equal to the wavelength of the wave.