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Q: What does Resonance Tubes: Finding Speed of Sound for H2 Physics Practicals cover?A: Master the resonance tube experiment using tuning forks, PVC pipes, and smartphone apps.TL;DR 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:
Wave properties and standing waves
Boundary conditions (closed vs open ends)
Temperature dependence of sound speed
Practical applications (organ pipes, wind instruments)
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:
Resonance condition:
L = ( 2 n − 1 ) λ 4 L = \frac{(2n-1)\lambda}{4} L = 4 ( 2 n − 1 ) λ
L L L = Effective length of air column
n n n = 1, 2, 3... (resonance number)
Speed of Sound Calculation Since v = f λ v = f\lambda v = f λ
v = f × 4 ( L 2 − L 1 ) v = f \times 4(L_2 - L_1) v = f × 4 ( L 2 − L 1 )
Where L 2 − L 1 L_2 - L_1 L 2 − L 1
Temperature Dependence v = 331.3 1 + T 273.15 m/s v = 331.3\sqrt{1 + \frac{T}{273.15}} \text{ m/s} v = 331.3 1 + 273.15 T m/s
Or approximately: v ≈ 331.3 + 0.606 T v ≈ 331.3 + 0.606T v ≈ 331.3 + 0.606 T T T T
Equipment Setup
Method 1: Traditional Water Column 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)
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 PVC pipe (1-2m, smooth interior)
Moveable piston (tight-fitting disc)
Marked rod attached to piston
No water needed!
Method 3: Smartphone Speaker
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 position L 1 L_1 L 1 carefully
Finding Subsequent Resonances Continue lowering water/extending tube:
Second resonance at
L 2 ≈ 3 L 1 L_2 ≈ 3L_1 L 2 ≈ 3 L 1 Third at
L 3 ≈ 5 L 1 L_3 ≈ 5L_1 L 3 ≈ 5 L 1 Pattern: Odd multiples
Critical : Use same tuning fork throughout!
Measurements to Record
The End Correction Mystery
Why It Matters The effective length extends beyond the tube opening:
L effective = L measured + e L_\text{effective} = L_\text{measured} + e L effective = L measured + e
Where end correction e ≈ 0.3 d e ≈ 0.3d e ≈ 0.3 d 0.6 d 0.6d 0.6 d d d d
Experimental Determination Since L 2 − L 1 = λ 2 L_2 - L_1 = \frac{\lambda}{2} L 2 − L 1 = 2 λ
Measure multiple
( L n + 1 − L n ) (L_{n+1} - L_n) ( L n + 1 − L n ) intervals
These equal
λ 2 \frac{\lambda}{2} 2 λ regardless of
e e e Calculate
v = f × 2 ( L n + 1 − L n ) v = f \times 2(L_{n+1} - L_n) v = f × 2 ( L n + 1 − L n ) End correction cancels out!
Verifying End Correction Gradient =
λ 2 \frac{\lambda}{2} 2 λ Typical result: e ≈ 0.4 d e ≈ 0.4d e ≈ 0.4 d
Data Collection Best Practices
Maximizing Precision Approach resonance from both directions
Multiple frequency method
Temperature monitoring
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) Horizontal tube with speaker at one end
Sprinkle cork dust/lycopodium powder
Dust forms patterns at nodes
Measure node spacing =
λ 2 \frac{\lambda}{2} 2 λ
Method 3: Echo Timing Sharp sound pulse (clap/click)
Measure echo time from distant wall
v = 2 d t v = \frac{2d}{t} v = t 2 d Need
d > 50 m d > 50m d > 50 m 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
Set generator to pure tone (start ~500Hz)
Place phone speaker at tube opening
Position analyzer mic inside tube
Vary tube length watching amplitude
Screenshot at resonances
Automated Sweep Method Some apps can sweep frequency:
Fix tube length
Sweep 100-1000Hz slowly
Note frequencies of amplitude peaks
Calculate wavelengths and average
v v v
Advanced Analysis
Uncertainty Calculations Position measurement:
δ L = ± 1 \delta L = ±1 δ L = ± 1 mm
Frequency uncertainty:
δ f = ± 0.5 \delta f = ±0.5 δ f = ± 0.5 Hz (tuning fork)
Temperature:
δ T = ± 0.5 \delta T = ±0.5 δ T = ± 0.5 °C
For speed of sound:
δ v v = ( δ f f ) 2 + ( 2 δ L L 2 − L 1 ) 2 \frac{\delta v}{v} = \sqrt{\left(\frac{\delta f}{f}\right)^2 + \left(\frac{2\delta L}{L_2-L_1}\right)^2} v δ v = ( f δ f ) 2 + ( L 2 − L 1 2 δ L ) 2
Typical achievement: δ v ≈ ± 2 \delta v ≈ ±2 δ v ≈ ± 2
Temperature Correction Graph Measure
v v v at different room temperatures
Compare gradient to theory (0.606 m/s/°C)
Extrapolate to find
v 0 v_0 v 0 at 0°C
Dispersion Investigation Does v v v
Use multiple tuning forks (256, 512, 1024 Hz)
Should be constant (non-dispersive medium)
Common Exam Questions
Q1: "Why must the tube be open at one end?" Open end allows pressure variations
Creates pressure node (displacement antinode)
Closed end would give different resonance pattern
Explains why
L = ( 2 n − 1 ) λ 4 L = \frac{(2n-1)\lambda}{4} L = 4 ( 2 n − 1 ) λ not
n λ 2 \frac{n\lambda}{2} 2 nλ
Q2: "Explain the end correction"
Q3: "How would results change in helium?" v He ≈ 3 × v air v_\text{He} ≈ 3 \times v_\text{air} v He ≈ 3 × v air (lower density)
Same frequency → 3x wavelength
Resonances at 3x distances
Pitch changes in voice explained
Practical Tips for Success
Getting Clear Resonances Strike tuning fork correctly
Minimize damping
Reduce interference
Data Recording Template Tuning-fork frequency f = 512 Hz f = 512 \space \text{Hz} f = 512 Hz Ambient temperature T = 23.5 ∘ C T = 23.5 \space ^{\circ}\text{C} T = 23.5 ∘ C Resonance Position \(\pu{L_n (cm)}\)**\(\pu{L_{n+1}-L_n (cm)}\) Wavelength \(\pu{\lambda (m)}\)Speed \(\pu{v (m/s)}\)1st \(16.8 \pm 0.1\) - - - 2nd \(50.3 \pm 0.1\) \(33.5\) \(0.670\) \(343.0\) 3rd \(83.9 \pm 0.1\) \(33.6\) \(0.672\) \(344.1\)
v ‾ = 343.6 ± 2 ; m/s
\overline{v} = 343.6 \pm 2 ;\text{m/s}
v = 343.6 ± 2 ; m/s
v theory ( 23.5 ∘ C ) = 345.5 ; m/s
v_{\text{theory}}(23.5^{\circ}\text{C}) = 345.5 ;\text{m/s}
v theory ( 23. 5 ∘ C ) = 345.5 ; m/s
Percentage difference = ∣ v ‾ − v theory ∣ v theory × 100 % = 0.5 %
\text{Percentage difference}
= \frac{\lvert \overline{v} - v_{\text{theory}} \rvert}{v_{\text{theory}}}\times 100\%
= 0.5\%
Percentage difference = v theory ∣ v − v theory ∣ × 100% = 0.5%
Links to A-Level Topics
Waves and Superposition Standing wave formation demonstrated
Nodes and antinodes visible through resonance
Constructive interference at specific lengths
Boundary Conditions
Sound and Music
Extensions and Investigations
1. Humidity Effects
2. Open-Open Tube
3. Real Wind Instruments
4. Acoustic Impedance
Your Lab Success Checklist ✓ Check tuning fork frequency (often stamped on it)Measure tube diameter for end correctionRecord temperature at start and endApproach resonance slowly from both directionsMeasure multiple resonances (at least 3)Use ( L 2 − L 1 ) (L_2-L_1) ( L 2 − L 1 ) to eliminate e e e Calculate uncertainty propagationCompare 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.
Resonance Tubes: Finding Speed of Sound for H2 Physics Practicals
