Acoustic Resonance

standing waves in pipes · open/closed ends · harmonics

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open/open
Physics: Open-open pipe: L = nλ/2, f_n = nc/(2L) — all harmonics present. Closed-one-end pipe: L = (2n−1)λ/4, f_n = (2n−1)c/(4L) — only odd harmonics. Speed of sound c = 343 m/s in air at 20°C. Pressure node at open end, antinode at closed end. Pipe organ: closed "stopped" pipes produce flatter pitch, full harmonic content from open pipes. Kundt's tube uses cork dust patterns to visualize standing waves. Resonance Q = f₀/Δf measures sharpness.