Q: What is the resonance tube experiment formula for speed of sound? A: For two adjacent resonances in a closed resonance tube, use v=2f(L2−L1). The interval L2−L1
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Fast answer for formula questions In a closed resonance tube, adjacent resonance lengths differ by half a wavelength, so L2−L1=λ/2. Therefore λ=2(L2−L1) and v=fλ=2f(L2−L1). 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 L1, L2, and L3 in metres. Calculate L2−L1 and L3−L2, average those two intervals if they agree, then use v=2f(mean interval). 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 v.
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resonance tube experiment
Use a closed air column above water, find two loud adjacent resonance lengths, then calculate v=2f(L2−L1).
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 L1 and L2 for the same tuning fork, use λ=2(L2−L1)
resonance tube formula
Closed tube resonances occur at odd quarter-wavelengths; adjacent resonance lengths differ by λ/2.
equation to determine wavelength of sound in a closed tube
For adjacent resonances, λ=2(L2−L1). 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 L2−L1.
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.
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.
The Physics of Pipe Resonance
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.
Core Theory and Equations
Standing Waves in Tubes
For a tube closed at one end:
Closed end: Displacement node (pressure antinode)
Open end: Displacement antinode (pressure node)
Resonance condition:L=4(2n−1)λ
Where:
L = Effective length of air column
n = 1, 2, 3... (resonance number)
λ = Wavelength
Speed of Sound Calculation
Since v=fλ:
v=2f(L2−L1)
Where L2−L1 is the distance between successive resonances.
If the question gives first and third resonance positions instead, then L3−L1=λ, so use v=f(L3−L1).
Temperature Dependence
v=331.31+273.15T m/s
Or approximately: v≈331.3+0.606T for T in °C
Equipment Setup
Method 1: Traditional Water Column
Materials:
Clear tube (1-1.5m long, 3-5cm diameter)
Water reservoir with flexible tube
Tuning forks (256Hz, 512Hz typical)
Meter ruler
Thermometer
Striking pad (rubber/cork)
Assembly:
Mount tube vertically with ruler alongside
Connect water reservoir to bottom
Fill system (no air bubbles!)
Practice raising/lowering water level
Method 2: Modern PVC Pipe
Simpler alternative:
PVC pipe (1-2m, smooth interior)
Moveable piston (tight-fitting disc)
Marked rod attached to piston
No water needed!
Method 3: Smartphone Speaker
21st century approach:
Frequency generator app
Bluetooth speaker
Any tube
Sound meter app for detection
Experimental Procedure
Finding First Resonance
Strike tuning fork firmly (consistent amplitude)
Hold vibrating fork above tube (~1cm gap)
Lower water level slowly (or move piston out)
Listen for sudden amplification
Fine-tune position for maximum sound
Record positionL1 carefully
Finding Subsequent Resonances
Continue lowering water/extending tube:
Second resonance at L2≈3L1
Third at L3≈5L1
Pattern: Odd multiples
Critical: Use same tuning fork throughout!
Measurements to Record
For each resonance:
Position (±1mm)
Which resonance (1st, 2nd, etc.)
Room temperature
Tuning fork frequency
Background noise level
Resonance Reading Workflow
Use this sequence to keep the calculation defensible:
Record L1, L2, and L3 in metres, not only centimetres.
Calculate L2−L1 and L3−L2.
Average the two intervals if both are reliable.
Use λ=2×mean interval.
Use v=fλ, then compare with the temperature-adjusted expected value.
Use a table like this in Paper 4 practice:
Resonance
Measured length / m
Difference from previous / m
Use in calculation
First, L1
0.162
-
Do not calculate v from this alone unless end correction is known
Second, L2
0.500
0.338
Adjacent interval
Third, L3
0.839
0.339
Adjacent interval
Mean interval
-
0.3385
v=2f(0.3385)
For a 512Hz tuning fork, this gives:
v=2(512)(0.3385)=347m⋅s−1
This is why adjacent-resonance calculations are popular: the unknown end correction appears in both measured lengths and cancels when you subtract.
The End Correction Mystery
Why It Matters
The effective length extends beyond the tube opening:
Leffective=Lmeasured+e
Where end correction e≈0.3d to 0.6d (d = 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 L1 directly without e underestimates wavelength and speed.
Experimental Determination
Since L2−L1=2λ:
Measure multiple (Ln+1−Ln) intervals
These equal 2λ regardless of e
Calculate v=f×2(Ln+1−Ln)
End correction cancels out!
Verifying End Correction
Plot Ln vs n:
Gradient = 2λ
Y-intercept = −e
Typical result: e≈0.4d
Data Collection Best Practices
Maximizing Precision
Approach resonance from both directions
Note positions approaching from above/below
Average for best estimate
Multiple frequency method
Use 2-3 different tuning forks
Plot v vs f (should be horizontal)
Confirms wave equation
Temperature monitoring
Record at start and end
Calculate expected change in v
Apply correction if needed
Common Measurement Pitfalls
"Can't hear clear resonance"
Fork not vibrating strongly enough
Holding fork too far from tube
Background noise interference
Tube diameter too small/large
"Multiple resonance positions"
Temperature gradients in water
Tube not perfectly vertical
Air bubbles in water column
Alternative Methods
Method 1: Two-Microphone Phase
Using smartphones/computers:
Place mics at known separation
Generate pure tone
Measure phase difference
Calculate wavelength
Method 2: Kundt's Tube (Visual)
Classic demonstration:
Horizontal tube with speaker at one end
Sprinkle cork dust/lycopodium powder
Dust forms patterns at nodes
Measure node spacing = 2λ
Method 3: Echo Timing
Direct time-of-flight:
Sharp sound pulse (clap/click)
Measure echo time from distant wall
v=t2d
Need d>50m for accuracy
Smartphone App Experiments
Frequency Generator + Spectrum Analyzer
Modern approach benefits:
Any frequency (not limited to tuning forks)
See resonance peak on screen
Precise frequency control
Record data automatically
Recommended apps:
Frequency Generator: "Signal Generator"
Analysis: "Spectroid" (Android) or "SpectrumView" (iOS)
✓ 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 (L2−L1) method to eliminate e ✓ 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.
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