Closed Pipe Harmonics (One End Closed) (νₙ = (2n-1)v/(4L), n = 1, 2, 3, further terms (only odd)
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νₙ = (2n-1)v/(4L), n = 1, 2, 3, ... (only odd harmonics)
What each symbol means
| Symbol | What it stands for |
|---|---|
| L | Length of pipe (m) |
| n | Mode number (positive integer) |
| v | Speed of sound in air (m/s) |
| νₙ | Frequency of nth allowed mode (Hz) |
| (2n-1) | Gives odd multiples: 1, 3, 5, 7, ... |
When to use this
Closed end = node, open end = antinode. Fundamental: ν₁ = v/(4L). Only ODD harmonics present: ν₁, 3ν₁, 5ν₁, ... Frequency ratios are 1:3:5:7:... Fundamental of closed pipe is half that of same-length open pipe. Closed pipe sounds 'hollow' due to missing even harmonics. NCERT Eq. 14.44.