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The resonance tube is one of the few school experiments where you can measure a basic physical quantity, the speed of sound, to within about one percent with a tuning fork, a glass tube and some water. It also has a correction, the "end correction", that confuses students in the viva. This post explains the method, works a full set of readings, shows how to get the end correction from your own data and lists what examiners ask.
Which exams include the experiment?
The CBSE Physics curriculum for 2026-27 lists it as a Class 11 experiment: "to find the speed of sound in air at room temperature using a resonance tube by two resonance positions". The JEE (Main) 2026 syllabus and the NEET (UG) 2026 syllabus both include it in their experimental skills lists, and the JEE (Advanced) 2026 brochure lists "speed of sound using resonance column". Check the current year's documents.
Why is the vibrating air column longer than the tube?
The water surface closes the bottom of the tube, so there is a displacement node there. The top is open, so there is an antinode near the top. The first loud resonance happens when the column is about a quarter wavelength long. But the antinode sits slightly above the rim, so the vibrating column is a little longer than the length you measure.
The NCERT Class 11 physics laboratory manual (Experiment 16) writes this as:
First resonance: λ/4 = l₁ + e
Second resonance: 3λ/4 = l₂ + e
where e is the end correction, about 0.6r for a tube of radius r. Subtracting gives λ = 2(l₂ − l₁), so v = 2ν(l₂ − l₁) and the end correction cancels. That is the whole reason for finding two resonances.
The 0.6 is not a guess. Levine and Schwinger (1948) solved sound radiation from an unflanged circular pipe and found that, at low frequencies, the pipe behaves as if lengthened by a fraction of its radius, with an exact end correction of 0.6133.
Worked example: from readings to the speed of sound
A student uses a 512 Hz tuning fork in a tube of inner diameter 3.0 cm, at a room temperature of 25 °C. The mean readings (falling and rising water levels averaged) are l₁ = 16.0 cm and l₂ = 49.8 cm.
Wavelength: λ = 2(49.8 − 16.0) = 67.6 cm = 0.676 m.
Speed: v = νλ = 512 × 0.676 ≈ 346 m/s.
End correction from your data: subtract three times the first equation from the second: e = (l₂ − 3l₁)/2 = (49.8 − 48.0)/2 = 0.9 cm.
Check against theory: r = 1.5 cm, so 0.6r = 0.9 cm. The data agree.
Correct to 0 °C if asked. From Laplace's formula in the NCERT chapter Waves, v = √(γP/ρ), and for an ideal gas this is proportional to √T. So v₀ = 346.1 × √(273/298) ≈ 331 m/s. NCERT quotes 331.3 m/s at STP from Laplace's formula, so the result is consistent.
What if you had used only the first resonance and ignored the end correction? Then v = 4νl₁ = 4 × 512 × 0.160 ≈ 328 m/s, about 1 percent low. That is why the two-position method is preferred.
How precise is your answer?
If each length is read to ±0.1 cm, the difference l₂ − l₁ is uncertain by up to ±0.2 cm out of 33.8 cm, about ±0.6 percent. That gives v = 346 ± 2 m/s. The frequency printed on the fork has its own uncertainty too. Our guide to error propagation in measurements shows how to combine them.
Which mistakes cost marks in the lab?
Reading only with the water falling. The lab manual asks for readings with the level falling and rising, then the mean. Averaging the two directions reduces the error in judging where the sound is loudest.
Holding the fork badly. Keep the prongs parallel to the ground, one above the other, about 1 cm above the rim, and never let them touch the tube.
Looking for the second resonance too close. It lies near three times l₁. The manual also notes that it is quieter than the first.
Calling the second resonance an overtone. The lab manual is explicit: with the same fork the frequency, wavelength and speed do not change, so the second resonance is not an overtone.
Ignoring the room. Measure the temperature two or three times. The manual lists humid air, a non-uniform tube and wind in the room as sources of error.
What does the viva ask?
Expect: Why do we need two resonance positions? What is the end correction and what does it depend on? Why is the second resonance fainter? Does the speed of sound depend on temperature, and how? Would humidity raise or lower your value? (Humid air gives a higher speed, the lab manual notes.) What changes with an open pipe? Our post on preparing for the practical exam and viva has a broader checklist.
A practice routine
Derive v = 2ν(l₂ − l₁) and e = (l₂ − 3l₁)/2 from the two equations without notes.
Solve NCERT Waves exercise 14.15, which gives resonance at 25.5 cm and 79.3 cm with a 340 Hz source, and then find the end correction from the same numbers.
Before the lab, predict l₁ and l₂ for your fork using v ≈ 346 m/s and e = 0.6r, so you know where to listen.
For the theory behind closed pipes, read our post on standing waves in strings and pipes.
If closed-pipe harmonics still feel shaky, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can revise standing waves on their own before the practical.
Before your next lab session, write the five viva answers above in one line each.
