Wave Properties and Interference

Wave interference occurs when two or more waves overlap, combining through the principle of superposition. This leads to either reinforcement (constructive interference) or cancellation (destructive interference).

Superposition Principle

When waves overlap, their amplitudes add algebraically at each point:

ytotal=y1+y2y_{total} = y_1 + y_2

Types of Interference

Constructive Interference

Phase difference: 2πn (n = 0, 1, 2, ...)

Δx=nλ\Delta x = n\lambda

Destructive Interference

Phase difference: π + 2πn (n = 0, 1, 2, ...)

Δx=(n+12)λ\Delta x = (n + \frac{1}{2})\lambda

Applications

  • Double-slit experiment
  • Noise cancellation
  • Thin film interference
  • Interferometers