Dynamic Wave Interference Calculator

Understanding Dynamic Wave Interference

Wave Interference Fundamentals

y(x,t) = A₁sin(ωt - kx + φ₁) + A₂sin(ωt - kx + φ₂)

where:

  • A = Wave amplitude
  • ω = Angular frequency (2πf)
  • k = Wave number (2π/λ)
  • φ = Phase angle
  • x = Position
  • t = Time

Types of Wave Interference

Constructive Interference

  • Phase difference = 0°, 360°
  • Maximum amplitude = A₁ + A₂
  • Energy enhancement
  • Standing wave antinodes

Destructive Interference

  • Phase difference = 180°
  • Minimum amplitude = |A₁ - A₂|
  • Energy cancellation
  • Standing wave nodes

Partial Interference

  • Intermediate phase differences
  • Beats phenomenon
  • Wave packets
  • Group velocity effects

Wave Properties

Wave Parameters

  • Wavelength λ = v/f
  • Period T = 1/f
  • Wave number k = 2π/λ
  • Phase velocity v = ω/k

Energy Transport

  • Power ∝ A²
  • Energy density
  • Poynting vector
  • Radiation pressure

Applications

Acoustics

  • Sound wave interference
  • Noise cancellation
  • Room acoustics
  • Musical instruments

Optics

  • Light interference
  • Interferometry
  • Holography
  • Fiber optics

Quantum Mechanics

  • Matter waves
  • Double-slit experiment
  • Quantum interference
  • Decoherence