To determine the speed of sound in air at laboratory ambient temperature, calculate its extrapolated value at 0 °C, and measure the acoustic end correction of a cylindrical glass resonance tube using calibrated tuning forks and an adjustable water-level reservoir. Explore a virtual apparatus, collect readings and analyse a graph.
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Timing is generated from the model; a short on-screen trial represents a longer physical interval. Animation is illustrative.
The teaching model assumes an idealized inviscid acoustic gas column with perfect cylindrical planar wavefront propagation and a sharp Dirichlet boundary condition at the water meniscus. In a physical laboratory, small thermal boundary-layer conduction and viscous drag at the inner glass wall produce slight Kirchhoff-Helmholtz acoustic dispersion, water evaporation introduces a finite humidity gradient altering gas density, and finite human auditory discrimination width creates small random setting uncertainties. The resonance tube method combines boundary-value wave mechanics with acoustic impedance matching at an open aperture. By measuring the first resonance length L₁ across six calibrated tuning fork frequencies, students linearize the quarter-wave condition L₁ = (v/4)(1/f) − c. Ordinary least-squares regression isolates both the propagation velocity v = 4m = 343.2 m s⁻¹ and the boundary antinode offset c = 0.98 cm with sub-percent fidelity, confirming Helmholtz's end-correction theory.
A vertical heavy-walled borosilicate glass cylinder (length 120 cm, inner diameter 32.0 mm, radius r = 1.60 cm) graduated in millimetres, connected at its bottom outlet via heavy-gauge flexible rubber tubing to a counterweighted water reservoir mounted on an adjustable vertical support rod, enabling continuous and rapid hydrostatic manipulation of the internal water meniscus.
A precision-matched set of metallurgical acoustic tuning forks milled from high-tensile chrome-vanadium steel with stamped nominal frequencies across the musical scale (Middle C 256.0 Hz, D 288.0 Hz, E 320.0 Hz, G 384.0 Hz, B 480.0 Hz, and C' 512.0 Hz), accompanied by a soft vulcanized rubber striking mallet to excite clean, fundamental sinusoidal transverse oscillations without non-harmonic overtone chattering.
A high-contrast photo-etched metric scale bonded along the longitudinal axis of the glass tube accompanied by twin adjustable elastic rubber locator rings that slide along the tube exterior to clamp and mark the auditory loudness maxima during bidirectional meniscus searching.
A mercury-in-glass thermometer calibrated to 0.1 °C suspended adjacent to the tube mouth to measure the ambient room temperature t for adiabatic velocity calculation, alongside an aneroid barometer recording ambient atmospheric pressure P_atm.
A stainless-steel precision vernier caliper with internal knife-edge measuring jaws reading to 0.02 mm, utilized to measure the internal diameter 2r of the glass tube at multiple azimuthal angles to compute the theoretical Rayleigh end correction c = 0.6133 r.
An auxiliary digital sound pressure level (SPL) meter with decibel readout (dBA) or narrow-band microphone positioned near the tube lip to provide quantitative, objective verification of auditory resonance peaks alongside human sensory ear tuning.
To determine the speed of sound in air at laboratory ambient temperature, calculate its extrapolated value at 0 °C, and measure the acoustic end correction of a cylindrical glass resonance tube using calibrated tuning forks and an adjustable water-level reservoir. Suggested independent settings: 256.0, 288.0, 320.0, 384.0, 480.0, 512.0 Hz.
Measure the internal diameter 2r of the borosilicate glass resonance tube at three independent orthogonal orientations at the upper open aperture using precision vernier calipers reading to 0.02 mm. Record the ambient air temperature t to 0.1 °C using the calibrated laboratory thermometer mounted adjacent to the tube exterior, and verify that the laboratory is free from strong convective drafts, direct sunlight, and thermal plumes.
Accurate determination of internal tube radius r is required to compute Rayleigh's theoretical end correction c = 0.6133 r for comparison with regression intercepts, while temperature measurement governs Laplace's theoretical acoustic velocity v(T) = 331.30 √(1 + t/273.15) m/s.
Fill the adjustable leveling reservoir with distilled water until the meniscus in the resonance tube rises to approximately 8 to 10 cm below the top rim. Check that the flexible connecting hose is free from trapped air bubbles or constrictions, and verify that raising and lowering the reservoir smoothly modulates the water height across the full 100 cm active measuring span of the tube.
Eliminating air bubbles in the hydraulic linkage ensures instantaneous hydrostatic equilibration between the reservoir and the glass cylinder, preventing meniscus lag or hydrostatic oscillations during sensitive resonance tuning.
Select the 256.0 Hz tuning fork. Strike one prong cleanly approximately one-third back from its distal end using the soft rubber mallet, initiating a pure fundamental sinusoidal vibration. Immediately mount or hold the vibrating fork directly above the center of the tube aperture, orienting the prongs so that their plane of vibration is vertical and parallel to the tube axis, maintaining a clearance of approximately 5 to 8 mm (1/4 inch) above the glass lip without permitting physical contact.
Vertical prong oscillation injects alternating longitudinal compression and rarefaction wavefronts symmetrically down the tube bore; striking one-third from the tip suppresses high-frequency clang overtones that could trigger spurious higher-mode resonances.
While striking the tuning fork continuously to maintain steady acoustic power, slowly lower the water reservoir, causing the internal water level to descend. Listen intently near the tube mouth for a sudden, dramatic crescendo in sound loudness signifying acoustic resonance. Slide a rubber marker band to the approximate position. Refine the location by running the water level back and forth across a 3 cm window around the marker, clamping the marker precisely where auditory loudness reaches its sharp global maximum. Record this position as the first resonance length L₁.
Bidirectional bracketed searching eliminates human sensory hysteresis and meniscus wetting angle hysteresis, ensuring the recorded water height represents the true acoustic displacement node.
Repeat the precision resonance determination for each of the remaining tuning forks in the calibrated set: 288.0 Hz, 320.0 Hz, 384.0 Hz, 480.0 Hz, and 512.0 Hz. For each frequency, execute three independent bidirectional runs to establish reproducible first resonance lengths L₁, and record all observations in the formal laboratory notebook alongside ambient temperature readings.
Acquiring data across six widely distributed frequencies spanning an entire acoustic octave provides an extended lever arm for ordinary least-squares regression, minimizing slope variance and intercept uncertainty.
For the higher frequency forks (such as 480.0 Hz and 512.0 Hz), continue lowering the water reservoir beyond the first resonance point to locate the second resonance position L₂ (corresponding to the 3λ/4 mode). Record the distance between successive resonance points ΔL = L₂ − L₁. Compute the independent wavelength λ = 2(L₂ − L₁) and the single-fork end correction c = (L₂ − 3L₁) / 2 to cross-validate the multi-frequency regression results.
The spatial distance between successive resonance nodes ΔL = λ/2 is fundamentally independent of tube end effects, providing an internal algebraic check on both the acoustic wave speed and the validity of the open-lip boundary correction.
Points are your observations. The fit uses SI x and y values before display scaling.
| # | Tuning fork frequency f (Hz) | Resonance tube length L₁ (cm) | Inverse frequency (1 / f) | First resonance length L₁ | Remove |
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