N beads on a stretched string. Watch how high mode numbers alias onto the low fundamental modes.
Only N distinct standing-wave patterns can exist on N beads. Asking for a mode number higher than N folds back ("aliases") onto one of those fundamentals — the beads (black dots) trace exactly the same motion even though the continuous blue curve wiggles faster. The small graph plots the dispersion relation ωn ∝ sin(nπ/2(N+1)).
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