Wave Behaviour: Oscillations, Waves, Sound, Light, Superposition, Interference and Diffraction
Wave behaviour covers oscillations, wave properties, sound, light, superposition, interference and diffraction. The exam tests SHM definitions, the wave equation, standing waves, two-source interference, diffraction gratings and the Doppler effect. HL questions often require you to link phase difference to path difference and to interpret intensity patterns.
Core rules
- SHM: a = −ω²x; T = 2π√(m/k) for a mass–spring, T = 2π√(l/g) for a small-angle pendulum.
- Wave speed v = fλ; phase difference = 2π × path difference / λ.
- Superposition adds displacements; standing waves have nodes and antinodes.
- Double slit: fringe spacing x = λD/a, where a is slit separation and D is screen distance.
- Grating: nλ = d sinθ, with d = 1/(lines per metre).
- Doppler for sound: f′ = f(v ± v_o)/(v ∓ v_s), with signs giving approach a higher frequency.
Worked example
A grating has 500 lines per mm, so d = 1/(5.00 × 10⁵) = 2.00 × 10⁻⁶ m. For λ = 600 nm and n = 1, sinθ = nλ/d = (6.00 × 10⁻⁷)/(2.00 × 10⁻⁶) = 0.300. Thus θ = 17.5°. The second order would give sinθ = 0.600, θ = 36.9°, still physically possible.
Traps
Check that sinθ ≤ 1; if not, that order does not exist. Fringe spacing is the distance between adjacent bright fringes, not the distance from the centre to the first fringe. Intensity is proportional to amplitude squared. In pipe problems, distinguish a node at a closed end from an antinode at an open end.