← Wave Systems

3 Wave basics & superposition

Watch: Wave basics & superposition Opens a YouTube search: pick a video that clicks for you Wave equation v=f\lambda v = speed (m s⁻¹), f = frequency (Hz), λ = wavelength (m). Period T=\frac{1}{f} Superposition: when waves meet, displacements add. Constructive interference where they’re in phase (crest meets crest); destructive where out of phase (crest meets trough).

Path difference conditions

  • Constructive: path difference = n λ (whole number of wavelengths).
  • Destructive: path difference = (n + ½) λ.
  • Two sources must be coherent (constant phase relationship, same frequency) to give a stable interference pattern.

Two-source / double-slit interference

Bright fringes (maxima) d sin θ = n λ d = slit separation, θ = angle to the fringe, n = order (0,1,2…). Fringe spacing (small angles) x=\frac{\lambda L}{d} x = fringe separation on a screen distance L away. Worked example Double-slit wavelength Slits 0.20 mm apart; the 3rd-order maximum is at θ = 0.90°. Find λ. d sin θ = n λ → λ = d sin θ / n. λ = (0.20×10⁻³ × sin0.90°) / 3 = (0.20×10⁻³ × 0.0157) / 3. λ = 1.05×10⁻⁶ m ≈ 1.0×10⁻⁶ m. ✓ λ ≈ 1.0 µm (infra-red-ish: check the source!).

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