Wave Interference
BeginnerExplore how waves combine to create constructive and destructive interference patterns.
Theory
Principle of Superposition
When two or more waves overlap in space, the resulting displacement at any point is the algebraic sum of the individual wave displacements.
ytotal = y1 + y2
y1 = A1 sin(k₁x - ω₁t + φ₁)
y2 = A2 sin(k₂x - ω₂t + φ₂)
Constructive Interference
Occurs when two waves are in phase (phase difference = 0°, 360°, etc.). The waves reinforce each other, creating a larger amplitude:
- Maximum amplitude = A₁ + A₂
- Path difference = nλ (n = 0, 1, 2, ...)
- Phase difference = 2πn radians
- Bright fringes in interference patterns
Destructive Interference
Occurs when two waves are out of phase (phase difference = 180°, 540°, etc.). The waves cancel each other:
- Minimum amplitude = |A₁ - A₂|
- Path difference = (n + ½)λ (n = 0, 1, 2, ...)
- Phase difference = (2n + 1)π radians
- Dark fringes in interference patterns
Key Parameters
Wavelength (λ)
Distance between successive crests or troughs. Determines the spacing of interference patterns.
Frequency (f)
Number of wave cycles per second. Related to wavelength by v = fλ.
Amplitude (A)
Maximum displacement from equilibrium. Determines wave intensity.
Phase (φ)
Position within the wave cycle. Phase difference determines interference type.
Real-World Applications
- Noise-canceling headphones - Use destructive interference to reduce ambient noise
- Thin film interference - Creates colors in soap bubbles and oil slicks
- Radio astronomy - Interferometers combine signals for higher resolution
- Holography - Records interference patterns to create 3D images
- Seismic analysis - Understanding earthquake wave interactions
- Acoustic engineering - Designing concert halls and reducing echoes