Waves
Waves tests the language and mathematics of wave motion: the wave equation, superposition, coherence, standing waves, two-source interference and the electromagnetic spectrum. Expect quantitative items on the diffraction grating and Young's double slit, plus conceptual items on phase and path difference.
Core rules
- v = fλ applies to all waves. On refraction the frequency is fixed by the source, so speed and wavelength change together.
- Transverse oscillations are perpendicular to energy transfer, longitudinal are parallel. Polarisation is possible only for transverse waves, which is direct evidence that sound is longitudinal.
- Superposition adds displacements. Coherent sources have the same frequency and a constant phase difference; constructive interference needs path difference nλ, destructive needs (n + ½)λ.
- In a standing wave, adjacent nodes (or antinodes) are λ/2 apart; a fixed end is a node, a free end an antinode.
- Young's double slit fringe spacing: w = λD/s, where s is the slit separation and D the slit-to-screen distance.
- Diffraction grating: d sinθ = nλ, with d = 1/N when N is the number of lines per metre.
- Intensity is proportional to amplitude squared; for a point source intensity falls as 1/r².
- In the electromagnetic spectrum, all members travel at c in vacuum; order from radio to gamma is by increasing frequency and decreasing wavelength.
Worked example
A grating has 300 lines per mm. The second-order maximum is observed at 18°. Find the wavelength. d = 1 / (3.00 × 10⁵ lines per metre) = 3.33 × 10⁻⁶ m. λ = d sinθ / n = (3.33 × 10⁻⁶ × sin 18°) / 2 = (3.33 × 10⁻⁶ × 0.309) / 2 ≈ 5.15 × 10⁻⁷ m = 515 nm, a green line.
Traps that cost marks
- Entering d in millimetres while λ is in nanometres, or forgetting to invert lines per mm.
- Using n = 0 or forgetting n when asked for the second order.
- Claiming frequency changes when light enters glass.
- Confusing fringe spacing w with slit separation s in the double-slit formula.
- Treating intensity as proportional to amplitude rather than amplitude squared.
- Leaving the calculator in radian mode for grating problems.