Physics · Waves · NEET
A closed pipe has a NODE at the closed end (air cannot move there) and an ANTINODE at the open end. Only wave patterns with a node at one end and antinode at the other fit inside — these correspond to lengths L = lambda/4, 3lambda/4, 5lambda/4... That gives frequencies v/4L, 3v/4L, 5v/4L, i.e. only 1, 3, 5 times the fundamental. Even multiples (2f, 4f) would need an antinode-antinode or node-node fit, which the closed end forbids. So a closed pipe = odd harmonics only.
The OPEN pipe. Open pipe fundamental = v/2L, closed pipe fundamental = v/4L. Dividing: (v/2L)/(v/4L) = 4/2 = 2. So the open pipe's fundamental is exactly 2 times (one octave higher) than the closed pipe of the same length. This exact result was asked directly in NEET 2023 (answer 2 : 1).
A HARMONIC is any allowed frequency counted as a multiple of the fundamental (1st, 2nd, 3rd...). An OVERTONE is any allowed frequency ABOVE the fundamental, counted in order (1st overtone = the next one after fundamental). For an OPEN pipe all harmonics exist, so 1st overtone = 2nd harmonic, 2nd overtone = 3rd harmonic. For a CLOSED pipe only odd harmonics exist, so 1st overtone = 3rd harmonic, 2nd overtone = 5th harmonic, 3rd overtone = 7th, 4th overtone = 9th. Mixing these up is the single biggest error in pipe PYQs.
For a closed pipe use harmonic = 2 x (overtone number) + 1. So 1st overtone -> 2(1)+1 = 3rd harmonic, 2nd overtone -> 5th, 4th overtone -> 9th harmonic. For an open pipe it is simpler: harmonic = overtone number + 1. Write this conversion FIRST before you equate frequencies, and the ratio problems become one line.
No. If an open (both ends open) pipe is dipped so the water closes its lower end, it becomes a closed pipe but with a shorter air column. NEET 2025 asked exactly this: an open pipe of length L (f = v/2L) dipped so air column becomes L/2 turns into a closed pipe with f' = v/(4 x L/2) = v/2L = f. The fundamental frequency stays the SAME. This trap works because two changes (closed end + half length) cancel out.
The ratio of the fundamental frequency of an open pipe to that of a closed pipe of the same length is:
The fundamental frequency of an open organ pipe equals the third harmonic of a closed organ pipe. If the length of the closed pipe is 20 cm, the length of the open pipe is:
The 4th overtone of a closed organ pipe has the same frequency as the 3rd overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
An open pipe is open at both ends and has antinodes at both ends; it produces ALL harmonics with fundamental f = v/2L. A closed pipe is closed at one end (node) and open at the other (antinode); it produces only ODD harmonics with fundamental f = v/4L. For the same length the open pipe's fundamental is twice that of the closed pipe.
A closed pipe needs only a quarter wavelength (L = lambda/4) to fit its lowest mode, giving lambda = 4L and f = v/4L. An open pipe needs half a wavelength (L = lambda/2), giving lambda = 2L and f = v/2L. A larger wavelength means a lower frequency, so the closed pipe is lower-pitched (exactly half) for the same length.
Open pipe: 1f, 2f, 3f, 4f, 5f... (all integer harmonics). Closed pipe: 1f, 3f, 5f, 7f... (only odd harmonics). This is why an open pipe (like a flute) sounds richer while a closed pipe (like a clarinet's lowest register) has a different, hollower tone.
Open pipe: nth overtone = (n+1)th harmonic. Closed pipe: nth overtone = (2n+1)th harmonic. Example: closed pipe 2nd overtone = 5th harmonic; open pipe 2nd overtone = 3rd harmonic. Always convert to the harmonic number before writing the frequency formula.
Temperature changes the speed of sound v (v increases with temperature), so every frequency of both pipes shifts by the same factor. But because v appears in both f = v/2L and f = v/4L, the RATIO between open and closed pipe frequencies (and between their harmonics) does not change with temperature. Only the actual Hz values change.
