Waves: Oscillations, Superposition, Interference, Diffraction and Stationary Waves
Wave basics
For a progressive wave v = fλ and T = 1/f. Phase difference = 2π Δx/λ. Superposition adds displacements. Two sources are coherent if they have a constant phase difference and the same frequency; laser light or a single slit feeding two slits gives coherence.
Interference and diffraction
Young's double slit fringe spacing w = λD/s, where s is slit separation and D is slit-to-screen distance. A diffraction grating obeys d sinθ = nλ, with d = 1/(lines per metre). Diffraction is significant when the gap is comparable to λ. Polarisation shows that light is transverse.
Stationary waves
A stationary wave has nodes (zero amplitude) and antinodes (maximum amplitude), spaced λ/2 apart. On a string fixed at both ends, f_n = nv/(2L). In a pipe closed at one end, only odd harmonics occur and the fundamental has λ = 4L. In an open pipe, all harmonics occur with λ = 2L for the fundamental.
Worked example
A grating has 500 lines per mm, so d = 1/(500 × 10^3) = 2.0 × 10^-6 m. For λ = 600 nm, first order: sinθ = (1 × 600 × 10^-9)/(2.0 × 10^-6) = 0.30, θ = 17.5°. Second order: sinθ = 0.60, θ = 36.9°. Third order: sinθ = 0.90, θ = 64.2°. Fourth order would need sinθ = 1.20, which is impossible.
Traps
Using slit width instead of slit separation; mixing degrees and radians in phase calculations; forgetting that path difference must be measured in the same units as λ; using λ = 2L for a closed pipe; claiming nodes move.