Speed of Sound from an Open–Open Resonance Tube
A fixed air column open at both ends; the model hides the true speed of sound. Tune to harmonic n, read noisy resonance frequencies fₙ, recover v from v = 2 fₙ L / n and average.
Goal
Determine the speed of sound v in air from the open–open resonance condition fₙ = n v / (2L) using several harmonics n and the sample mean of vₙ = 2 fₙ L / n.
Equipment
- Resonance tube (open–open), L = 1.1 m
- Sine excitation / frequency readout (simulated)
- Harmonic selector n
Theory
For a tube open at both ends, pressure nodes occur at the ends; allowed standing waves have harmonics fₙ = n v / (2L) with n = 1, 2, 3, … Rearranging gives v = 2 fₙ L / n. Small frequency-reading error is modelled on each measurement.
Procedure
- The apparatus uses a fixed column length L = 1.1 m (shown on the card) with both ends open, matching the “open at both ends” case in the related simulator.
- Select the harmonic index n with the slider (use several different values from 1 upward).
- Press “Record measurement” to log (n, fₙ): the frequency reading carries small tuner noise.
- Repeat for at least 5 distinct harmonics spread across the available n range.
- The table adds v = 2 fₙ L / n for each row. Take the sample mean of v as your result.
- Compare with the reference speed of sound in air and write the conclusion.
Experiment
Open–open air column: standing pressure pattern for harmonic n; true v is hidden — you recover it from noisy fₙ readings.
Air column length L = 1.1 m is fixed for this lab — the same L used in v = 2 fₙ L / n and in the exported CSV.
Both ends are open (organ-pipe harmonics). The related simulator also explores open–closed pipes — this worksheet uses only the open–open formula.
Ideal resonance (model): fₙ = n v / (2L) ≈ 155.91 Hz
Record ≥5 different harmonics. Each row estimates v = 2 fₙ L / n; the result card uses the mean. Avoid repeating the same n if you want independent samples.
Measurements
| № | Harmonic n | Resonance frequency fₙ Hz | Speed estimate v m/s | |
|---|---|---|---|---|
| No measurements yet — take your first reading. | ||||
Data processing
Uncertainty
Instrument uncertainty (simple propagation)
±0.90 Hz
With v = 2 f L / n and fixed L, n, first-order δv/v ≈ Δf/|f| on each row (ignoring tiny end corrections).
Take measurements to estimate propagated uncertainty.
The lab result is the mean of v estimates; this is a quick frequency-reading budget, not a full acoustic model.
Lab report
Opens the system print dialog — choose “Save as PDF” or your printer. Header and footer are hidden when printing.
One click opens the print dialog — choose “Save as PDF”.
Speed of Sound from an Open–Open Resonance Tube
Generated: 23 Apr 2026, 05:35
Goal
Determine the speed of sound v in air from the open–open resonance condition fₙ = n v / (2L) using several harmonics n and the sample mean of vₙ = 2 fₙ L / n.
Measurement table
| # | Harmonic n | Resonance frequency fₙ (Hz) | Speed estimate v (m/s) |
|---|---|---|---|
| No measurements yet — take your first reading. | |||
Fit and derived value
Add at least 2 trials to compute the sample mean.
Conclusion
The mean speed of sound agrees with the reference value within tolerance. Main uncertainties: tuning/readout of fₙ, end corrections not included, and assuming a uniform air column at room temperature.
PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.
Conclusion
The mean speed of sound agrees with the reference value within tolerance. Main uncertainties: tuning/readout of fₙ, end corrections not included, and assuming a uniform air column at room temperature.