Wave Interference Calculator
Understanding Wave Interference
Wave Interference Principles
Resultant Wave = y₁(x,t) + y₂(x,t)
y(x,t) = A₁sin(ωt + φ₁) + A₂sin(ωt + φ₂)
where:
- A = Amplitude
- ω = Angular frequency (2πf)
- φ = Phase angle
- t = Time
Types of Interference
Constructive Interference
- Waves in phase (Δφ = 0°, 360°)
- Maximum amplitude = A₁ + A₂
- Enhanced wave intensity
- Bright fringes in optics
Destructive Interference
- Waves out of phase (Δφ = 180°)
- Minimum amplitude = |A₁ - A₂|
- Reduced wave intensity
- Dark fringes in optics
Partial Interference
- Intermediate phase differences
- Variable amplitude
- Common in real systems
Applications
Optics
- Young's double-slit
- Thin film interference
- Interferometers
- Antireflection coatings
Acoustics
- Noise cancellation
- Room acoustics
- Musical instruments
- Sound barriers
Electronics
- Signal processing
- Antenna arrays
- RF systems
- Phase-locked loops
Advanced Concepts
Coherence
- Temporal coherence
- Spatial coherence
- Coherence length
- Coherence time
Multiple Wave Interference
- N-slit diffraction
- Diffraction gratings
- Bragg diffraction