Open Pipe Harmonics (Both Ends Open) (νₙ = nv/(2L), n = 1, 2, 3, further terms)
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νₙ = nv/(2L), n = 1, 2, 3, ...
What each symbol means
| Symbol | What it stands for |
|---|---|
| L | Length of pipe (m) |
| n | Harmonic number (positive integer) |
| v | Speed of sound (m/s) |
| νₙ | Frequency of nth harmonic (Hz) |
When to use this
Both ends are antinodes. Fundamental: ν₁ = v/(2L). ALL harmonics present (same as string). Frequency ratios: 1:2:3:4:... Open pipe fundamental is TWICE that of same-length closed pipe. End correction: effective L = L + 2e where e ≈ 0.6r (r = radius of pipe). NCERT derives from Fig. 14.15.