Wavefronts, Rays & Phase Geometry
A wavefront joins in-phase points, spaced λ apart, with rays perpendicular to fronts.
controls
v = 0.5 m/s fixed → f = 0.63 Hz, T = 1.60 s. θ, d: oblique mode only.
wavefront facts (live)
- Sliding amber caliper: consecutive same-type fronts (crest → crest) are exactly λ = 0.80 m apart — the caliper rides outward with the pattern and never changes length. Drag λ and every gap changes together.
- Two amber beads sit on the same front (same distance from the source) — they rise and fall in perfect sync: a wavefront joins in-phase points.
- Grey bead sits λ/2 further along the travel direction — it bobs in antiphase, proving the sync of the amber pair is geometry, not coincidence.
- Rays point radially outward — perpendicular to every circular front; orbit the camera to verify from any angle.
phase protractor — the trig method (no axis values needed)
trig method — marker Q
y/y₀ = +0.50 → sin θ = 0.50 → θ = 30.0°
Q at half amplitude → 30° · actual position on axis: 30°
phase difference P ↔ Q
Δφ = |φ_Q − φ_P| = 30° = 0.52 rad
separation = 0.083 λ
what this confirms — from “Wave Motion — Everything to Memorise”
- ✓
“Wavefront & ray” — rays are perpendicular to wavefronts (radial arrows cross every ring at 90°, from any camera angle); a front joins in-phase points (the two amber beads on one front bob in sync); consecutive same-type fronts are spaced exactly λ (the sliding caliper).
- ✓
“Wavelength, λ” — λ is the shortest distance between consecutive in-phase points — visible as the constant crest-to-crest gap on the rings; move the λ slider and every gap rescales together while the bead λ/2 off the front stays antiphase.
- ✓
“Oblique wavefronts → effective separation Δx” — two points separated by d along a boundary met at angle θ have path difference Δx = d·sinθ (the amber leg of the drawn right triangle), giving Δφ = (Δx/λ)·2π; as θ → 0 the fronts lie parallel to the wall and the posts fall in phase.
- ✓
“Trig method — no axis values” — a displacement fraction alone fixes the phase angle via sin θ = y/y₀: half amplitude → 30°, y₀/√2 → 45°, full amplitude → 90° — drag P and Q or use the snap buttons and read the worked line.