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Q: What is the resonance tube experiment formula for speed of sound?
A: For two adjacent resonances in a closed resonance tube, use . The interval
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Fast answer for formula questions
In a closed resonance tube, adjacent resonance lengths differ by half a wavelength, so . Therefore and . End correction affects each measured length, but it cancels when you subtract two adjacent resonance positions.
Fast answer for setup questions
Use a vertical resonance column with water at the bottom, a ruler beside the tube, and a tuning fork of known frequency above the open end. Lower or raise the water level until the sound is loudest, record that air-column length, then repeat for the next loud resonance. The setup measures the wavelength of the sound in air; the frequency comes from the tuning fork.
Reading-table answer
Record , , and in metres. Calculate and , average those two intervals if they agree, then use . Use end correction only when working from one resonance length directly.
Fast answer for theory and setup checks
The closed end of the tube is a displacement node and the open end is a displacement antinode. Keep the tuning fork just above the open end, move the water level slowly, and listen for the loudest sound. If the question asks for setup, name the water column, ruler, tuning fork, thermometer, and repeated adjacent resonance readings before calculating .
| If the query asks for... | Write this first |
| resonance tube experiment | Use a closed air column above water, find two loud adjacent resonance lengths, then calculate . |
| resonance column apparatus | Use a vertical tube, water reservoir or movable water level, ruler, tuning fork, thermometer, and repeated adjacent resonance lengths. |
| determine the speed of sound in air | Find and for the same tuning fork, use |
| resonance tube formula | Closed tube resonances occur at odd quarter-wavelengths; adjacent resonance lengths differ by . |
| equation to determine wavelength of sound in a closed tube | For adjacent resonances, . For the first resonance alone, include the end correction. |
| resonance tube experiment setup | Keep the tuning fork just above the open end, move the water level slowly, and record the loudest point, not the first faint change in volume. |
| end correction | Use adjacent resonances when possible because the same end correction is present in both lengths and cancels in . |
For the wider Paper 4 logbook route, pair this page with the H2 Physics Paper 4 technique file and the H2 Physics Practical 2026 guide.
SEAB's 2026 H2 Physics 9478 syllabus places standing waves in air columns and determination of the wavelength of sound in the Waves learning outcomes. Paper 4 is the practical paper, so keep both the physics formula and the measurement method clear.
TL;DR
Turn a PVC pipe and tuning fork into a sound speed measurement device. This guide shows how to find resonance positions carefully, apply end corrections properly, account for temperature variations, and compare your result against the expected ~343 m/s at room temperature. Plus smartphone alternatives that can support the same concepts.
| Search intent | Open this next |
| Resonance tube experiment setup | Use the traditional water-column setup below, then compare it with the H2 Physics Paper 4 technique file. |
| Resonance tube experiment formula | Start with , then check the graph and uncertainty habits in the H2 Physics Practical 2026 guide. |
| Speed of sound practical | Keep this as the waves practical, then route wider Paper 4 revision through the H2 Physics practicals hub. |
Need the full Paper 4 sequence first? Start with our H2 Physics Practical 2026 guide, then keep a reusable H2 Physics Paper 4 technique file for resonance readings, graph habits, uncertainty comments, and ACE fixes. Use our JC H2 Physics tuition if you want weekly coaching around the same practical cycle.
Add this resonance-tube workflow to our H2 Physics practical experiments so your timing notes, data tables, and ACE language match the rest of your Paper 4 prep.
When sound waves bounce inside a tube, magic happens at specific lengths - the reflected waves reinforce the original, creating resonance. This experiment elegantly connects:
Your measurement of sound speed will be as accurate as professional equipment, using basic materials.
For a tube closed at one end:
Resonance condition:
Where:
Since :
Where is the distance between successive resonances.
If the question gives first and third resonance positions instead, then , so use .
Or approximately: for in °C
Materials:
Assembly:
Simpler alternative:
21st century approach:
Continue lowering water/extending tube:
Critical: Use same tuning fork throughout!
For each resonance:
Use this sequence to keep the calculation defensible:
Use a table like this in Paper 4 practice:
| Resonance | Measured length / m | Difference from previous / m | Use in calculation |
| First, | 0.162 | - | Do not calculate from this alone unless end correction is known |
| Second, | 0.500 | 0.338 | Adjacent interval |
| Third, | 0.839 | 0.339 | Adjacent interval |
| Mean interval | - | 0.3385 |
For a tuning fork, this gives:
This is why adjacent-resonance calculations are popular: the unknown end correction appears in both measured lengths and cancels when you subtract.
The effective length extends beyond the tube opening:
Where end correction to ( = tube diameter)
If a question asks why the first resonance alone is less reliable, say this: the measured air-column length is shorter than the effective vibrating length because the displacement antinode forms just outside the open end. The difference is the end correction, so using directly without underestimates wavelength and speed.
Since :
Plot vs :
Typical result:
"Can't hear clear resonance"
"Multiple resonance positions"
Using smartphones/computers:
Classic demonstration:
Direct time-of-flight:
Modern approach benefits:
Recommended apps:
Procedure:
Some apps can sweep frequency:
Main contributions:
For speed of sound:
Typical achievement: m/s (0.6%)
Plot your results:
Does depend on frequency?
Key points:
Model answer:
Consider:
| Resonance | Position ** | Wavelength | Speed | |
| 1st | - | - | - | |
| 2nd | ||||
| 3rd |
Add humidity sensor:
Both ends open:
Analyze recorder/flute:
Advanced topic:
✓ Check tuning fork frequency (often stamped on it)
✓ Measure tube diameter for end correction
✓ Record temperature at start and end
✓ Approach resonance slowly from both directions
✓ Measure multiple resonances (at least 3)
✓ Use method to eliminate
✓ Calculate uncertainty propagation
✓ Compare with theory at measured temperature
Master this experiment and you'll understand how pipe organs work, why your voice sounds different in helium, and how submarines use sonar. You're measuring the same property that lets you hear - the speed at which pressure waves travel through air.