🎻 Standing Waves & Harmonics
📖 The Physics
A standing wave forms when a wave reflects off a fixed end and overlaps the incoming wave. Unlike a normal wave, the pattern doesn't travel anywhere — it just swings in place, like a skipping rope.
Some points, the nodes (blue), never move at all; others, the antinodes (red), swing the most. Only whole numbers of half-wavelengths fit between the two fixed ends, which is why an instrument can only play certain notes.
y = A·sin(nπx/L)·cos(ωt)
Allowed wavelengths: λₙ = 2L / n Frequencies: fₙ = n·f₁ (n = 1, 2, 3 …)
Step through the harmonics: n = 1 is the fundamental, n = 2 doubles the frequency, and so on. This is exactly how a guitar or violin string produces its notes.
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