# P01-A — open-pipe benchmark, prospective protocol draft

Status: design and intake tools implemented; no new acoustic data collected. Freeze
pilot-dependent decisions and register before collecting confirmatory observations.
This is a test of a conventional acoustic approximation, not evidence of new physics.

## Geometry, scope and independent units

For a thin-walled unflanged open pipe, the low-frequency correction is approximately
0.6133 times inner radius a per open end (Levine & Schwinger 1948). For two comparable
open ends, f_n = n*g*v(T,RH,P,CO2)/(2*(L+2*eta*a)), with reference g=1, eta=0.6133.
The constant correction is a low-ka approximation; Silva et al. (journal 2009,
preprint 2008) treats frequency-dependent radiation impedance. Higher modes, thick
walls, baffles, nearby surfaces and blocked ends require different modeling.

Eight separate tubes T01–T08, proposed lengths 0.30–1.00 m in 0.10 m increments,
inner radius 0.025 m. Measure actual radius, ovality, wall thickness, length, end
clearance, and microphone/speaker geometry. Recutting one tube is not eight independent
specimens. Randomize run order; three remounts per tube measure technical repeatability.
Calibration IDs: T01,T03,T04,T06,T08. Untouched test IDs: T02,T05,T07.

Screen candidate modes 1–6 by predicted ka=n*pi*a/(L+1.2266*a) <= 0.3, before looking
at measured peaks. This is a conservative design choice, not a certified error bound.
At the nominal dimensions, 17 of 48 candidate tube/mode combinations pass. Six modes
at every length do not pass: n=6 on the 0.30 m tube has ka about 1.425. The number of
independent experimental units is eight tubes, not 144 peaks or remounts. Freeze how
geometry uncertainty is handled near the eligibility boundary; do not select modes
by agreement with the desired model. Higher modes can support a separate comparison
using frequency-dependent radiation and viscothermal losses.

## Measurements and uncertainty

Record per-run air temperature, RH, actual local pressure and CO2 (or a declared CO2
assumption with a defensible uncertainty). Cramer (1993) speed calculation is provided
for 0–30 C, 75–102 kPa, CO2 below 10,000 ppm and water fraction <=0.06. Do not use
sea-level-corrected weather pressure as chamber pressure. Calibrate instruments.
Define whether every uncertainty is a standard uncertainty, tolerance or coverage
interval; retain correlations and shared calibration errors.

At 48 kHz/16384 samples, FFT bin spacing is 2.9296875 Hz. Half a bin is not a complete
frequency uncertainty. Zero padding does not increase information. Characterize clock
accuracy, windowing, signal-to-noise, linewidth, estimator bias and remount variation.
Use a phase/clock-calibrated acquisition chain and known-tone checks. Peak uncertainty
must come from the validated estimator and repeatability/systematic budget. Keep raw
waveforms, instrument settings and rejected-peak reasons. Blank CSV templates are
headers only and must not be read as measured zeros.

## Analysis and claim gate

Estimate g and eta only from calibration tubes using a measurement-error likelihood
that includes length/radius/environment uncertainty and shared calibration terms.
Estimate identifiability/profile intervals; carry their joint uncertainty into held-out
predictions. A five-tube calibration set is small: pilot simulation must establish
whether eta and g can be separated at the required precision. Do not quietly fix
one parameter after a failed fit. Repeated peaks are correlated within tubes; naive
AICc with N=144 is inappropriate. The primary comparison is untouched-tube predictive
error with uncertainty, not the training residual alone.

Proposed engineering tolerances (to be justified and frozen after a separate pilot):
95% interval for g wholly inside [0.99,1.01]; interval for eta wholly inside
[0.5633,0.6633]; upper uncertainty bound for held-out relative RMS error <=0.5%.
If those precision goals cannot be reached, revise the design before registration.
An estimate merely inside a tolerance is not equivalence; a nonsignificant residual
trend is not evidence that no trend exists. A failure can expose instrument or model
limitations and does not by itself establish a different physical law.

Use protocol_tools.py to regenerate acoustic-design.csv. Analysis of future data is
gated on a calibrated covariance/uncertainty model; no fitted experimental coefficients
are supplied in this release. Costs and delivery times require actual quotations;
the original low-cost estimate is not a precision guarantee.

Primary sources: https://doi.org/10.1103/PhysRev.73.383 ;
https://doi.org/10.1016/j.jsv.2008.11.008 ; https://arxiv.org/html/0811.3625v1 ;
https://doi.org/10.1121/1.405827 .