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