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In phase / antiphase
● VERBATIM — examined word-for-wordIn phase: Δφ = 0 (or 2nπ) — same displacement AND same direction of motion; particles nλ apart. Antiphase: Δφ = π — always opposite; particles (n + ½)λ apart. Same amplitude NOT required.
What this actually means
In phase is stricter than 'same displacement': the two particles must also be moving the same way. Two particles crossing zero in opposite directions share a displacement but are in antiphase.
Separations translate directly: whole-wavelength gaps mean in phase; odd half-wavelength gaps mean antiphase.
Amplitude is irrelevant. Two waves of different heights can still be perfectly in phase.
The trap
Calling two adjacent zero crossings 'in phase' — they move opposite ways: antiphase, λ/2 apart.
Prove it — watch it be true
- Snap P and Q to λ apart: Δφ = 0, and they move together frame by frame
- Snap to λ/2: they mirror each other at every instant — Δφ = π
- Now pick two adjacent zero crossings: same displacement, opposite motion — antiphase, not in phase