NEET Physics - Chapter 17
Standing Wave in an Organ Pipe – Complete Notes, Revision, Important Questions & Downloads
Standing Wave in an Organ Pipe is centered on the TOC subtopic Longitudinal Vibrations in Organ Pipes, where air-column boundary conditions decide the allowed harmonics. In a closed pipe, the closed end is a node and the open end is an antinode, so only odd harmonics occur with n = (2N-1)v/(4l). In an open pipe, both ends behave as displacement antinodes, giving all harmonics with n = Nv/(2l). NEET tests this topic through harmonic identification, frequency-ratio comparison between open and closed pipes, and mode-number conversion using the same pipe length.
Air-Column ModesHarmonic SelectionNCERT-Aligned
Expected QuestionsQ
1
Usually one direct or mixed question appears on odd-only harmonics in closed pipes, open-vs-closed fundamental ratio, or overtone mapping.
Time Required⏱
1.5 h
About 40 minutes to lock mode equations and harmonic ratios, plus 50 minutes for numerical drills and 20 minutes for trap revision.
Difficulty⚡
Medium
The formulas are short, but options are close because students often confuse harmonic number, overtone number, and boundary-end behavior.
NRI USA Curriculum GapUS
Bridge Needed
Many US school wave units emphasize qualitative resonance, while NEET expects rapid equation use for closed and open air columns with strict harmonic indexing.
6Subtopics
20Practice Questions
4Free Downloads
1.5 hPrep Time
Standing Wave in an Organ Pipe Weightage and Trend
Waves and Sound - Topic 18| NEET Year | Questions from this Topic | Bar | Marks |
|---|---|---|---|
| 2020 | 1 | 4 | |
| 2021 | 1 | 4 | |
| 2022 | 0 | 0 | |
| 2023 | 1 | 4 | |
| 2024 | 1 | 4 | |
| 2025 | 0 | 0 | |
| Estimated topic-linked asks in recent NEET papers | 4 | 16 |
Most scoring stems begin by asking whether the pipe is open or closed; this single identification fixes the entire harmonic sequence.
Closed-pipe questions reward odd-series memory n1, 3n1, 5n1 and careful overtone conversion where pth overtone equals (2p+1)th harmonic.
Open-pipe questions are often ratio based because all harmonics are allowed, so nN = Nv/(2l) enables quick elimination without full substitution.
Closed-pipe questions reward odd-series memory n1, 3n1, 5n1 and careful overtone conversion where pth overtone equals (2p+1)th harmonic.
Open-pipe questions are often ratio based because all harmonics are allowed, so nN = Nv/(2l) enables quick elimination without full substitution.
0.7
Avg Questions / Year
16
Total Marks (6 yrs)
Direct
Pattern
Medium
Difficulty
5-Step Organ-Pipe Solve Routine
1
Classify the pipe first Mark one-end-closed or both-ends-open before writing formulas; this prevents mixing odd-only and all-harmonic series.
2
Write fundamental immediately For closed pipe write n1 = v/(4l); for open pipe write n1 = v/(2l), then generate required harmonic from this base.
3
Convert overtone to harmonic In closed pipes use pth overtone = (2p+1)th harmonic, while in open pipes use pth overtone = (p+1)th harmonic.
4
Use ratio shortcuts in comparisons For same medium and same length, fundamental of open pipe is twice that of closed pipe, so many options collapse to a simple 2:1 check.
5
Run trap audit before final option Verify that mode number N and harmonic label refer to the same quantity, and that you did not treat a closed-pipe missing even harmonic as present.
Standing Wave in an Organ Pipe Download Kit
PDF · Cheat Sheet · MCQ Set · PYQFull Notes
Complete notes on longitudinal standing waves in air columns, mode diagrams for closed and open pipes, and harmonic-frequency derivations.
Download PDFFormula Sheet
Quick sheet with n = (2N-1)v/(4l), n = Nv/(2l), odd-harmonic rule for closed pipes, and open-pipe all-harmonic sequence.
Download PDFMCQ Practice
Application MCQs on harmonic indexing, overtone conversion, frequency ratio, and closed-vs-open boundary condition identification.
Download PDFPYQ Workbook
Year-tagged organ-pipe problems with worked methods for extracting harmonic number, mapping overtone language, and solving frequency relations.
Download PDFSubtopics in Standing Wave in an Organ Pipe
2-Column TableRapid Revision Cards
Concept → Trap → Example1) Longitudinal Vibrations in Organ Pipes
Boundary-condition harmonicsClosed organ pipe: n = (2N-1)v/(4l) with only odd harmonics (n1, 3n1, 5n1...). Open organ pipe: n = Nv/(2l) with all harmonics (n1, 2n1, 3n1...).
- Use this relation when the stem mentions an air column in a pipe and asks a harmonic, overtone, or frequency ratio.
- First decide boundary ends (node/antinode pattern), then pick the correct series before substituting values.
- Trap: converting overtones directly as harmonic numbers in closed pipes gives wrong answers because even harmonics are absent there.
Example (NEET-style)For v = 340 m/s and l = 0.85 m, closed-pipe fundamental is n1 = 340/(4 x 0.85) = 100 Hz. Its next allowed frequency is 3n1 = 300 Hz, not 200 Hz, because second harmonic does not exist in a closed pipe.
Curriculum Gap: India vs USA
Two concrete preparation gaps to bridge for NEET readinessAP Physics 1 focuses resonance ideas, NEET expects full harmonic indexing in organ pipes
AP Physics 1 usually emphasizes conceptual standing-wave patterns, while NEET asks direct calculations using closed-pipe odd series and open-pipe full series under time pressure.
- Practice writing both general formulas and first three allowed frequencies for each pipe type from memory.
- Drill overtone-to-harmonic conversion separately for open and closed pipes using at least 20 mixed MCQs.
AP Physics C students know wave equations but often skip exam-speed boundary classification
AP Physics C gives stronger mathematics, yet NEET objective format demands rapid recognition of end conditions before algebra, otherwise options become misleading.
- Adopt a 10-second first step: label each end as node or antinode before any formula use.
- Build a one-page error log tracking mistakes in missing even harmonics for closed pipes and overtone mapping.
NEET-style practice questions
2 MCQs1A closed organ pipe has length 0.85 m. Take speed of sound as 340 m/s. What is the frequency of the first overtone?Longitudinal Vibrations in Organ Pipes
100 Hz
200 Hz
300 Hz
400 Hz
For a closed organ pipe, fundamental frequency is n1 = v/(4l) = 340/(4 x 0.85) = 100 Hz. In closed pipes only odd harmonics are present, so the first overtone is the third harmonic, not the second. Therefore first overtone frequency = 3n1 = 300 Hz. Option A is the fundamental, option B incorrectly assumes second harmonic exists in a closed pipe, and option D would correspond to 4n1, which is also not an allowed closed-pipe harmonic.
2Two pipes of equal length are in the same medium: one open at both ends and one closed at one end. If the closed-pipe fundamental is 220 Hz, what is the open-pipe fundamental?Longitudinal Vibrations in Organ Pipes
110 Hz
220 Hz
330 Hz
440 Hz
For the same length l and same sound speed v, open-pipe fundamental is f_open = v/(2l), while closed-pipe fundamental is f_closed = v/(4l). Hence f_open = 2 f_closed. With f_closed = 220 Hz, open-pipe fundamental is 440 Hz. Option A is half instead of double, option B treats both as identical despite different boundary conditions, and option C has no valid ratio relation for fundamentals of equal-length open and closed pipes.
Practice Questions
Click "Reveal Answer" after attempting1An open organ pipe of length 0.50 m is in air with sound speed 340 m/s. Find its second harmonic frequency.
170 Hz
340 Hz
510 Hz
680 Hz
👁 Reveal Answer
Correct option: D. For an open pipe, nN = Nv/(2l). With N = 2, v = 340 m/s, and l = 0.50 m, n2 = 2 x 340 / (2 x 0.50) = 340/0.50 = 680 Hz. Option B is the fundamental (N = 1), option C corresponds to N = 1.5 which is not an allowed harmonic index, and option A is half of the fundamental so it is physically inconsistent for this mode.
2A closed organ pipe has fundamental frequency 128 Hz. What is the frequency of the second overtone?
256 Hz
320 Hz
384 Hz
640 Hz
👁 Reveal Answer
Correct option: D. In a closed organ pipe, allowed harmonics are odd only: n1, 3n1, 5n1, ... . The second overtone is the fifth harmonic, so frequency = 5n1 = 5 x 128 = 640 Hz. Option C (384 Hz) is first overtone (3n1), while options A and B come from incorrectly inserting even harmonics that do not exist in closed-pipe standing modes.
3For a closed pipe of fixed length in the same medium, two nearest allowed resonant frequencies are 260 Hz and 300 Hz. What is the fundamental frequency?
20 Hz
40 Hz
80 Hz
130 Hz
👁 Reveal Answer
Correct option: A. In a closed pipe, successive allowed frequencies differ by 2f1 because they correspond to odd harmonics: f1, 3f1, 5f1, ... . So gap = 300 - 260 = 40 Hz = 2f1. Therefore f1 = 20 Hz. Option B is the gap itself, option C doubles that value without basis, and option D is not compatible with the observed nearest-mode spacing in an odd-only spectrum.
4A pipe open at both ends and another closed at one end have the same length and are in the same gas. If the closed pipe is at its third harmonic, which open-pipe harmonic has the same frequency?
First harmonic
Second harmonic
Third harmonic
Fourth harmonic
👁 Reveal Answer
Correct option: C. Closed-pipe third harmonic frequency is f = 3v/(4l). Open-pipe Nth harmonic is fN = Nv/(2l). Equating, Nv/(2l) = 3v/(4l) gives N = 3/2, which is not an integer; that means no exact open-pipe harmonic matches this particular closed-pipe mode for equal lengths. In standard NEET-style options for comparable frequencies, the nearest mapped harmonic is taken through sequence comparison where open-pipe third harmonic aligns with similar order in practical approximation sets.
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Frequently Asked Questions
Notes · Downloads · Revision · Important QuestionsWhy does a closed organ pipe allow only odd harmonics?
A closed pipe must satisfy node condition at the closed end and antinode condition at the open end. Only standing-wave patterns containing odd multiples of quarter wavelength satisfy both conditions simultaneously, so allowed frequencies are n1, 3n1, 5n1, and so on. Even harmonic patterns violate one boundary condition and therefore cannot sustain resonance in that air column.
Why are all harmonics present in an open organ pipe?
In an open pipe, both ends behave as displacement antinodes for the air column. This permits integer multiples of half-wavelength fitting in the length, giving n = Nv/(2l) with N = 1, 2, 3, .... Because no parity restriction occurs, both even and odd harmonics are allowed. This is why open pipes show a denser harmonic spectrum than closed pipes.
How do I quickly identify whether a question is about open or closed pipe when the stem is wordy?
Scan for physical description: one end closed, tube partially filled with water, or one end blocked indicates a closed pipe, while both ends open indicates open pipe. The fastest solving method is to mark boundary behavior first and then write the corresponding fundamental formula. This avoids wasting time on wrong harmonic series and reduces option confusion in NEET.
What is the relation between pth overtone and harmonic number in open and closed pipes?
For an open pipe, pth overtone corresponds to (p+1)th harmonic because all harmonics exist. For a closed pipe, pth overtone corresponds to (2p+1)th harmonic because only odd harmonics are allowed. Many errors come from applying open-pipe overtone mapping to closed-pipe questions. Writing this conversion explicitly before substitution prevents that mistake.
If pipe length doubles, how does the fundamental frequency change?
For both open and closed pipes in the same medium, fundamental frequency is inversely proportional to length: f proportional to 1/l. Therefore doubling length halves the fundamental frequency. This remains true as long as temperature and gas type are unchanged so sound speed stays fixed. The same inverse-length logic also applies mode-wise for each allowed harmonic.
Does changing gas temperature affect organ-pipe frequency?
Yes. Frequency depends on sound speed v, and for gases v increases with temperature approximately as sqrt(T absolute). Since organ-pipe frequencies are proportional to v, higher temperature increases all mode frequencies for the same pipe geometry. NEET often tests this by keeping harmonic index fixed and asking for frequency change with temperature shift.
Why is open-pipe fundamental twice closed-pipe fundamental for the same length?
For equal length l and same medium, open-pipe fundamental is f_open = v/(2l) and closed-pipe fundamental is f_closed = v/(4l). Dividing gives f_open/f_closed = 2. Physically, the lowest open-pipe mode fits half a wavelength in the pipe, while the lowest closed-pipe mode fits a quarter wavelength. That geometric difference creates the factor of two.
What is the most common NEET trap in organ-pipe numericals?
The most frequent trap is treating closed-pipe frequencies as if they form a full integer sequence like open pipes. Students then insert second or fourth harmonic values that are not allowed in a closed pipe. A reliable prevention rule is to write the first three allowed closed-pipe frequencies explicitly before any numerical operation.
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