Key Concepts: Wave Superposition & Interference

Principle of Superposition

• When two or more waves overlap, the resultant displacement at any point is the sum of the individual displacements.

Constructive Interference

• Occurs when waves are in phase (crests align with crests).
• Resultant amplitude = sum of amplitudes.
• Path difference = 0, λ, 2λ, ... (nλ).

Destructive Interference

• Occurs when waves are out of phase (crests align with troughs).
• Resultant amplitude = difference of amplitudes. Complete cancellation if amplitudes are equal.
• Path difference = λ/2, 3λ/2, ... ((n + ½)λ).

Applications

• Young's double-slit experiment shows interference fringes (bright and dark bands).
• Noise-canceling headphones use destructive interference.