Overview
This lecture explains the phenomena of interference and diffraction in waves, focusing on the principles of superposition and wave behavior at boundaries.
Superposition and Interference
- Mechanical waves can occupy the same space, leading to the principle of superposition.
- Superposition results in interference patterns when two or more waves overlap.
- Interference can produce new patterns, observed easily with water, sound, and light waves.
- Constructive interference occurs when overlapping waves add to produce greater amplitude.
- Destructive interference happens when waves combine to produce reduced or zero amplitude.
- Complete destructive interference results when waves are exactly out of phase, cancelling each other.
Phase Relationships in Periodic Waves
- Waves exactly in phase (peaks and troughs align) result in constructive interference with doubled amplitude.
- Waves exactly out of phase (crests align with troughs) result in complete destructive interference, cancelling the waves.
- Noise-cancelling headphones use destructive interference by generating out-of-phase sound waves that reduce unwanted noise.
- Real-world interference patterns are complex but always follow the superposition principle.
Wave Behavior at Boundaries
- At a free boundary, waves reflect back with the same amplitude.
- At a fixed boundary, waves reflect back inverted (opposite sign amplitude).
- When encountering a small gap, waves bend around edges, a process called diffraction.
Diffraction and Its Significance
- Diffraction occurs when waves pass through or around obstacles, creating a series of maxima and minima.
- Diffraction patterns are a type of interference pattern found in all wave types, including light and sound.
Key Terms & Definitions
- Superposition — The process where two or more waves occupy the same space and combine their amplitudes.
- Interference — The pattern resulting from the overlap of two or more waves.
- Constructive Interference — When overlapping waves combine to produce a wave of greater amplitude.
- Destructive Interference — When overlapping waves combine to produce a wave of smaller or zero amplitude.
- Complete Destructive Interference — When two waves combine to cancel each other completely (zero amplitude).
- In Phase — Waves whose crests and troughs align.
- Out of Phase — Waves whose crests align with the other's troughs.
- Diffraction — The bending of waves around obstacles or through gaps, producing interference patterns.
Action Items / Next Steps
- Review the principle of superposition and practice identifying constructive and destructive interference in wave diagrams.
- Prepare for a future lesson on the quantum implications of wave diffraction.