# Organ Pipes Numericals > Closed and open pipe harmonics with v/4L and v/2L fundamentals, end correction and resonance for NEET Physics. - Canonical URL: https://prepelephant.com/topics/neet-ug/physics/organ-pipes-numericals-neet - Exam / course: NEET-UG · Subject: Physics - Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team - First published: 2026-10-02 - Last updated: 2026-10-02 - How to cite: "Organ Pipes Numericals", PrepElephant, https://prepelephant.com/topics/neet-ug/physics/organ-pipes-numericals-neet ## Direct answer A closed pipe (one end stopped) sounds an octave lower and only odd harmonics: the sealed end forces a displacement node, the open mouth a displacement antinode, giving fundamental f1 = v/4L and overtones at 3f1, 5f1, 7f1... An open pipe, antinodes at both ends, sounds f1 = v/2L with all harmonics (2f1, 3f1...) — its fundamental is double the closed pipe's on equal length. With v ≈ 340 m/s, a half-metre closed pipe gives 170 Hz (then 510, 850 Hz) while a half-metre open pipe gives 340 Hz (then 680, 1020 Hz). Real mouths add an end correction of roughly 0.6 times the radius per open end, so a pipe plays slightly lower than its measured length suggests. ## What you must remember - **Closed pipe modes:** f_n = (2n − 1)v/4L — odd harmonics only; the first overtone is the third harmonic, the second the fifth. - **Open pipe modes:** f_n = nv/2L — all harmonics present; the first overtone is the second harmonic (the octave). - **Equal-length ratio:** open fundamental : closed fundamental = 2 : 1; conversely, a closed pipe needs half the length to match an open pipe's note. - **End correction:** about 0.6 r per open end; effective length L_eff = L + 0.6r (closed) or L + 1.2r (open), lowering all frequencies slightly. - **Speed of sound:** about 340 m/s at room temperature in NEET conventions, rising roughly 0.6 m/s per °C; v ∝ √T in kelvin. - **Resonance tube pairing:** a fork of frequency f over a closing water column resonates first at L = v/4f, next at 3v/4f; the separation of successive resonances is λ/2 — the standard way to measure v. - **Numbering trap:** "fifth harmonic" and "fifth overtone" differ by one; a closed pipe has no second harmonic at all. ## Walking down a half-metre pipe Close one end of a 0.5 m pipe: f1 = 340/(4 × 0.5) = 170 Hz, and the only overtones are 3 × 170 = 510 Hz and 5 × 170 = 850 Hz — the even numbers 340 and 680 are forbidden, because the closed node cannot support them. Open both ends: f1 = 340/(2 × 0.5) = 340 Hz with 680 and 1020 Hz — the octave and the third harmonic return. Now invert to the resonance tube: hold a 340 Hz fork over a water column; the shortest resonant length is L = v/4f = 340/1360 = 0.25 m, the next comes at 0.75 m, their difference being λ/2 = 0.5 m (λ = 1 m). Add the end correction for a tube of radius 2 cm: each open end contributes about 1.2 cm, so the true resonance sits at 26.2 cm — and a student who ignores it will compute v about 5% too low. ## Where NEET sets the trap The even-harmonic ban is the chapter's assertion-reason favourite: "a closed pipe can never sound the second harmonic" is true, and the reason is the permanent node, not the pipe's material. Length-versus-frequency inversions punish proportional reasoning: halving the length doubles every frequency, and questions ask it backwards ("a pipe gives 512 Hz; what after halving?"). Diagram questions show a pipe with nodes and antinodes marked and ask for the mode number — count the quarter-wavelengths. The end correction's direction is worth one mark alone: real pipes sound flatter (lower) than v/4L predicts because the effective length is longer. Finally, temperature items note that a warmer day raises v and sharpens every pipe's pitch — a fact that pairs naturally with a musician's complaint. ## Frequently asked questions ### What is the fundamental of a closed pipe 50 cm long at 340 m/s? f1 = v/4L = 340/(4 × 0.5) = 170 Hz, with overtones possible only at 510 Hz and 850 Hz — odd multiples. ### Which harmonics are absent from a closed organ pipe? All even harmonics; the closed end must remain a displacement node, so only odd multiples of the fundamental fit the pipe. ### An open and a closed pipe of equal length have fundamentals in what ratio? 2 : 1 — v/2L against v/4L; the open pipe sounds an octave higher on the same length. ### What is end correction and how large is it? The antinode forms slightly outside the mouth, adding about 0.6 times the radius per open end to the effective length — making real pipes sound marginally flatter than geometry suggests. ### A 340 Hz fork resonates with a closed tube at 25 cm. What is the next resonance length? 75 cm: successive closed-tube resonances sit half a wavelength apart, here λ = 1 m from λ = 4 × 0.25 m.