A measured acoustic benchmark plan
Eight tubes, a low-frequency validity check, independent holdout lengths and explicit uncertainty requirements.
A conventional benchmark, ready for a pilot
Status: no new acoustic measurements collected. The corrected protocol uses eight separate tubes and an untouched three-tube test set. Three remounts per tube measure repeatability; they do not create 144 independent experiments.
fₙ = n g v(T, RH, P, CO₂) / [2 (L + 2ηa)] Reference: g = 1, η ≈ 0.6133 per unflanged end
Levine–Schwinger gives a low-frequency end correction. Silva et al. (2009) treats frequency-dependent radiation. Constant end correction across all six harmonics is not justified.
Check the planned mode before collecting data
The proposed conservative limit is ka ≤ 0.3. It is a design rule, not a guaranteed error bound. Of 48 candidate tube/mode combinations, 17 pass at the nominal geometry. Freeze modes before seeing their measured agreement.
The displayed speed is an assumption. Cramer’s environmental model is implemented in the Python tool with explicit temperature, humidity, local pressure and CO₂ inputs. FFT spacing alone is not frequency uncertainty.
Calibration and holdout
| Role | Tube IDs | Requirement |
|---|---|---|
| Calibration | T01, T03, T04, T06, T08 | Joint g and η fit with an identified measurement-error model |
| Untouched test | T02, T05, T07 | Predictions and uncertainty frozen before inspecting peaks |
| Technical repeats | Three remounts per tube | Retain within-tube correlations and shared calibration errors |
Measure geometry, wall thickness, end clearance and per-run environment; preserve raw audio and calibration records. Pilot work must establish clock/peak uncertainty and parameter identifiability. A naive AICc based on correlated peaks is not a suitable primary gate.
Decision rules before collection
Proposed tolerances are ±1% for g, ±0.05 for η, and a held-out relative RMS upper uncertainty bound of 0.5%. They require a feasible pilot uncertainty budget and registration before confirmation. A point estimate within a tolerance is not enough to establish equivalence.
Complete corrected protocol · Mode eligibility and split · Blank run template · Blank peak template · Design calculation code
No fitted measured coefficients are supplied. Future-data fitting remains gated on calibrated uncertainty and covariance inputs.