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feat: atmospheric refraction by ray tracing and the parabolic equation#231

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jmrplens merged 6 commits into
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feat/atmospheric-refraction
Jul 19, 2026
Merged

feat: atmospheric refraction by ray tracing and the parabolic equation#231
jmrplens merged 6 commits into
mainfrom
feat/atmospheric-refraction

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@jmrplens

@jmrplens jmrplens commented Jul 19, 2026

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Summary

The refracting-atmosphere counterpart of the underwater numerical solvers, for the environmental domain, clean-room from Salomons (Computational Atmospheric Acoustics) and Attenborough and Van Renterghem.

  • linear_sound_speed_profile and log_linear_sound_speed_profile: effective sound-speed profiles (sound speed plus wind).
  • atmospheric_ray_paths: Snell's-law ray tracing with ground reflection, turning points and travel times, plus the closed-form ray_curvature_radius and shadow_zone_distance for a linear gradient.
  • atmospheric_parabolic_equation: the Green's-function PE (GFPE) returning the relative-level field over range and height, with a finite-impedance ground, a Gaussian starter and its ground image, a refraction phase screen and an absorbing top layer.

The submarine PE and ray cores are reused rather than duplicated: the GFPE is the same range-marching split-step family as the ocean solver, adapted for air with a full FFT and the plane-wave ground reflection in place of the pressure-release surface, and the ground impedance is resolved through the existing porous and ground-effect machinery.

Validation

In a homogeneous atmosphere the GFPE reproduces the independent Weyl-Van der Pol spherical ground effect to 0.10-0.13 dB over grassland from 50 to 1000 m, and the coherent two-ray +6 dB over hard ground to 0.44 dB. The ray curvature radius matches its closed form exactly, and source-receiver reciprocity holds to 0.25 dB. Three new conformance checks (327 total, byte-exact report).

Checks

ruff, mypy, bandit, full pytest (3851 passed, no new warnings), conformance byte-exact, figures within tolerance (856, four new variants), api-docs with no drift, site i18n parity and full build clean. Adversarially reviewed with no bugs found.

Review in cubic

Summary by CodeRabbit

  • New Features

    • Added atmospheric refraction modeling for outdoor sound propagation, including effective sound-speed profiles, ray tracing, shadow-zone calculations, and a GFPE-based parabolic-equation solver.
    • Exposed new result types with helpers for evaluating and plotting ray paths and relative sound levels.
  • Documentation

    • Added English and Spanish guides, API reference pages, and new atmospheric refraction figures.
    • Updated the documentation sidebar and conformance reporting.
  • Tests

    • Added validation coverage for profile helpers, ray geometry, propagation/ground effects, reciprocity, and plot “smoke” checks.

jmrplens added 5 commits July 19, 2026 17:08
Add phonometry.environmental.atmospheric_refraction, the refracting-atmosphere
counterpart of the underwater numerical-propagation solvers.

- Effective sound-speed profiles: linear c(z)=c0+g z and the logarithmic
  surface-layer profile c(z)=c0+b ln(1+z/z0) (Salomons Eq. 4.5).
- atmospheric_ray_paths: Snell's-law ray tracing (RK4, range marching, ground
  reflection), returning curved paths, turning points, travel times and ground
  reflections; reuses the ray core of the ocean ray_trace.
- ray_curvature_radius and shadow_zone_distance: closed forms for the linear
  gradient (exact circular arcs, upward-refraction shadow boundary).
- atmospheric_parabolic_equation: the Green's Function PE (split-step Fourier,
  Gaussian starter with ground image, finite-impedance ground reflection,
  absorbing top layer), returning the relative-level field over range/height.
  In the homogeneous limit it reproduces the spherical-wave ground effect.

Results expose .plot() renderers (profile, ray paths, relative-level field).
…cles

Add three checks (ray turning height vs the circular-arc geometry, the GFPE
relative level vs the exact spherical-wave ground effect over grassland, and
vs the coherent two-ray field over a rigid ground) and place the module in the
environmental section of the API taxonomy. Regenerate the report.
A single-concept, two-panel figure: the upward-refracting ray fan leaving a
near-ground shadow, and the GFPE relative-level field over the range-height
plane showing the same acoustic shadow. Rendered as PNG (the imshow field) in
the four language x theme variants.
Add the nine public names to the quick-reference table and regenerate the
Starlight API pages, sidebar and llms-full.txt.
Add the GitHub guide and the bilingual site guides (typed APA references,
ThemeImage figure, dual-snippet figure code), index and sidebar entries, and
the [Unreleased] changelog note.

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Review Change Stack

No actionable comments were generated in the recent review. 🎉

ℹ️ Recent review info
⚙️ Run configuration

Configuration used: Organization UI

Review profile: ASSERTIVE

Plan: Pro

Run ID: e76a619d-f070-493e-99ea-d827a8907495

📥 Commits

Reviewing files that changed from the base of the PR and between 2a5bfd2 and 3d63590.

📒 Files selected for processing (2)
  • src/phonometry/_plot/environmental.py
  • src/phonometry/environmental/atmospheric_refraction.py

📝 Walkthrough

Walkthrough

Adds atmospheric refraction modeling with effective sound-speed profiles, ray tracing, a GFPE solver, result plotting, conformance checks, public exports, generated figures, and English/Spanish documentation.

Changes

Atmospheric refraction

Layer / File(s) Summary
Profiles and ray tracing
src/phonometry/environmental/atmospheric_refraction.py, tests/environmental/test_atmospheric_refraction.py, src/phonometry/__init__.py, src/phonometry/environmental/__init__.py
Adds linear and log-linear profiles, ray-geometry helpers, RK4 Snell-law tracing, result dataclasses, public exports, and analytical ray tests.
GFPE solver and conformance
src/phonometry/environmental/atmospheric_refraction.py, scripts/conformance_report.py, tests/environmental/test_atmospheric_refraction.py
Adds split-step GFPE propagation with impedance handling, absorbing boundaries, relative-level results, oracle comparisons, reciprocity checks, shadowing checks, and input validation.
Visualization and API wiring
src/phonometry/_plot/environmental.py, scripts/generate_graphs.py, scripts/api_taxonomy.py
Adds profile, ray, and PE plotters and registers atmospheric-refraction figure generation and API taxonomy entries.
Documentation and site integration
docs/*, site/src/content/docs/*, site/astro.config.mjs, llms-full.txt
Adds guides, API references, navigation, generated API text, conformance results, figure examples, and changelog coverage in English and Spanish.

Estimated code review effort: 4 (Complex) | ~45 minutes

Sequence Diagram(s)

sequenceDiagram
  participant Caller
  participant Profile as EffectiveSoundSpeedProfile
  participant RayModel as atmospheric_ray_paths
  participant PEModel as atmospheric_parabolic_equation
  participant Results
  Caller->>Profile: create effective sound-speed profile
  Profile->>RayModel: provide sampled speeds
  RayModel->>Results: return ray paths and diagnostics
  Profile->>PEModel: provide refracting profile
  PEModel->>Results: return GFPE relative-level field
  Results-->>Caller: evaluate or plot propagation results
Loading

Possibly related PRs

  • jmrplens/phonometry#180: Extends the API taxonomy and documentation-generation structures used to register the new atmospheric-refraction module.

Poem

A rabbit traced rays through the breeze,
Then marched sound waves under the trees.
Profiles bent light—
GFPE shone bright,
While docs hopped along with great ease.

🚥 Pre-merge checks | ✅ 4 | ❌ 1

❌ Failed checks (1 warning)

Check name Status Explanation Resolution
Docstring Coverage ⚠️ Warning Docstring coverage is 43.14% which is insufficient. The required threshold is 80.00%. Write docstrings for the functions missing them to satisfy the coverage threshold.
✅ Passed checks (4 passed)
Check name Status Explanation
Description Check ✅ Passed Check skipped - CodeRabbit’s high-level summary is enabled.
Title check ✅ Passed The title clearly matches the main change: adding atmospheric refraction modeling via ray tracing and the parabolic equation.
Linked Issues check ✅ Passed Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check ✅ Passed Check skipped because no linked issues were found for this pull request.
✨ Finishing Touches
📝 Generate docstrings
  • Create stacked PR
  • Commit on current branch
🧪 Generate unit tests (beta)
  • Create PR with unit tests
  • Commit unit tests in branch feat/atmospheric-refraction

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Code Review

This pull request introduces a new module, phonometry.environmental.atmospheric_refraction, which implements ray tracing and a Green's Function Parabolic Equation (GFPE) solver to model sound propagation in a refracting atmosphere. It includes effective sound-speed profiles (linear and logarithmic), closed-form geometric calculations, validation tests, and comprehensive documentation. One review comment suggests optimizing the ray-tracing loop by performing the specular ground reflection check before calculating the travel time increment, which avoids clipping negative heights and improves accuracy.

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Comment on lines +400 to +406
# Travel time increment (dt/dr = 1/(xi c^2)) at the new height.
cc = _speed_at(np.clip(z, 0.0, None))
ray_t[:, s] = ray_t[:, s - 1] + dr / (xi * cc**2)
# Specular ground reflection: fold z < 0 back up and flip zeta.
below = z < 0.0
z = np.where(below, -z, z)
zeta = np.where(below, -zeta, zeta)

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medium

Evaluating the effective sound speed cc before the specular ground reflection clamps any negative intermediate heights to 0.0 via np.clip. Specular reflection maps z < 0 to -z (the actual physical height of the reflected ray). By performing the ground reflection check first, we can evaluate cc at the true physical height z without needing np.clip, which improves the accuracy of the travel time calculation.

Suggested change
# Travel time increment (dt/dr = 1/(xi c^2)) at the new height.
cc = _speed_at(np.clip(z, 0.0, None))
ray_t[:, s] = ray_t[:, s - 1] + dr / (xi * cc**2)
# Specular ground reflection: fold z < 0 back up and flip zeta.
below = z < 0.0
z = np.where(below, -z, z)
zeta = np.where(below, -zeta, zeta)
# Specular ground reflection: fold z < 0 back up and flip zeta.
below = z < 0.0
z = np.where(below, -z, z)
zeta = np.where(below, -zeta, zeta)
# Travel time increment (dt/dr = 1/(xi c^2)) at the new height.
cc = _speed_at(z)
ray_t[:, s] = ray_t[:, s - 1] + dr / (xi * cc**2)
bounces += below.astype(np.int_)

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Applied in 3d63590: the ground reflection is now evaluated at the true folded height (-z, specular per Salomons) before sampling the effective sound speed, and the clip is gone. It improves the reflected-step travel time without affecting the trajectories; the free-field travel-time test is unchanged.

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Codecov Report

❌ Patch coverage is 96.44128% with 10 lines in your changes missing coverage. Please review.
✅ Project coverage is 96.12%. Comparing base (6d39a09) to head (3d63590).

Files with missing lines Patch % Lines
...phonometry/environmental/atmospheric_refraction.py 95.70% 10 Missing ⚠️
Additional details and impacted files
@@           Coverage Diff            @@
##             main     #231    +/-   ##
========================================
  Coverage   96.11%   96.12%            
========================================
  Files         135      136     +1     
  Lines       18041    18322   +281     
========================================
+ Hits        17341    17612   +271     
- Misses        700      710    +10     

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Actionable comments posted: 1

🤖 Prompt for all review comments with AI agents
Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Inline comments:
In `@src/phonometry/environmental/atmospheric_refraction.py`:
- Around line 603-610: Update the nonpositive-range branch in the relative-level
field calculation to assign NaN instead of positive infinity. Preserve the
existing finite-range computation and ensure the resulting first column of
AtmosphericPEResult.relative_level and downstream
level_at_height/plot_atmospheric_pe usage receives NaN.
🪄 Autofix (Beta)

Fix all unresolved CodeRabbit comments on this PR:

  • Push a commit to this branch (recommended)
  • Create a new PR with the fixes

ℹ️ Review info
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Configuration used: Organization UI

Review profile: ASSERTIVE

Plan: Pro

Run ID: e2c169c0-503d-45b4-b636-42128d5aa5ee

📥 Commits

Reviewing files that changed from the base of the PR and between 6d39a09 and 2a5bfd2.

⛔ Files ignored due to path filters (5)
  • .github/images/atmospheric_refraction.png is excluded by !**/*.png
  • .github/images/atmospheric_refraction_dark.png is excluded by !**/*.png
  • .github/images/atmospheric_refraction_es.png is excluded by !**/*.png
  • .github/images/atmospheric_refraction_es_dark.png is excluded by !**/*.png
  • site/src/generated/api-sidebar.mjs is excluded by !**/generated/**
📒 Files selected for processing (19)
  • CHANGELOG.md
  • docs/CONFORMANCE.md
  • docs/README.md
  • docs/api-reference.md
  • docs/atmospheric-refraction.md
  • llms-full.txt
  • scripts/api_taxonomy.py
  • scripts/conformance_report.py
  • scripts/generate_graphs.py
  • site/astro.config.mjs
  • site/src/content/docs/es/guides/atmospheric-refraction.mdx
  • site/src/content/docs/guides/atmospheric-refraction.mdx
  • site/src/content/docs/reference/api/environment/atmospheric-refraction.md
  • site/src/content/docs/reference/api/index.md
  • src/phonometry/__init__.py
  • src/phonometry/_plot/environmental.py
  • src/phonometry/environmental/__init__.py
  • src/phonometry/environmental/atmospheric_refraction.py
  • tests/environmental/test_atmospheric_refraction.py

Comment thread src/phonometry/environmental/atmospheric_refraction.py
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Numerical conformance report

327/327 conformance checks pass across 41 domains and 201 standards - filters class 1 - weightings within IEC 61672-1 class 1.

Each row pins a standard clause to its expected normative value and the value the library computes. Every section below is collapsible and stays collapsed while all of its rows pass; a section with any failing row opens automatically.

Numerical validation - filters & weightings: class showcase (IEC 61260-1 · IEC 61672-1 · ISO 7196)

IEC 61260-1:2014 class per filter architecture (order 6, one-third-octave, 100 Hz-10 kHz, fs = 48 kHz). For each architecture the table shows, at its binding band, the measured relative attenuation and the class-1 limit it must clear, so the number and the range it must sit in are both visible. A positive margin means the acceptance limits are met with that much room.

Architecture Class verdict Binding band Measured rel. atten. Class-1 limit Margin cl.1 Margin cl.2
butter Class 1 (default) 100 Hz +0.00 dB ≥ -0.40 dB +0.400 dB +0.600 dB
cheby1 By design (passband ripple) 6310 Hz +0.19 dB ≥ +1.44 dB -1.246 dB -0.837 dB
cheby2 Class 1 100 Hz +0.00 dB ≥ -0.40 dB +0.400 dB +0.600 dB
ellip By design (passband ripple) 10000 Hz +0.10 dB ≥ +1.32 dB -1.218 dB -0.813 dB
bessel By design (soft rolloff) 100 Hz +12.46 dB ≥ +16.60 dB -4.133 dB -3.133 dB

Only Butterworth (the library default) and Chebyshev-II are class-compliant architectures. Chebyshev-I and elliptic trade the mask for passband ripple, and Bessel for a maximally-flat group delay (soft rolloff); they cannot satisfy the IEC 61260-1 Class 1/2 attenuation mask by construction, so they are labelled By design - this is expected, not a failure or regression.

Frequency-weighting conformance (A/C: IEC 61672-1 Table 3; G: ISO 7196 A.3). The max deviation from nominal is informational (it falls at a frequency extreme where the tolerance is widest and asymmetric); compliance is judged at the binding frequency - the one with the least headroom - where the deviation, the applicable tolerance band and the headroom are shown together.

Curve fs Max dev. from nominal (info) Binding freq Deviation there Tolerance band Headroom
A 48 kHz -0.867 dB @ 19953 Hz 1000 Hz +0.000 dB [-0.70, +0.70] dB +0.700 dB
A 96 kHz -0.482 dB @ 19953 Hz 1000 Hz +0.000 dB [-0.70, +0.70] dB +0.700 dB
C 48 kHz -0.900 dB @ 19953 Hz 1000 Hz +0.000 dB [-0.70, +0.70] dB +0.700 dB
G 48 kHz +0.047 dB @ 1 Hz 1 Hz +0.047 dB [-1.00, +1.00] dB +0.953 dB
Filters & weightings: 100% (7/7)
Standard Quantity Expected (norm) Computed Δ Status
IEC 61260-1:2014 Table 1 Octave-band filter class (butterworth, fs=48 kHz) class 1 class 1 (margin +0.400 dB) +0.400 dB
IEC 61260-1:2014 Table 1 One-third-octave filter class (butterworth, fs=48 kHz) class 1 class 1 (margin +0.400 dB) +0.400 dB
IEC 61260:1995 / ANSI S1.11-2004 Table 1 Class 0 (strictest) octave-band filter (butterworth, fs=48 kHz) class 0 class 0 (margin +0.150 dB) +0.150 dB
IEC 61260-1:2014 Table F.1 Formula (9) breakpoint mapping, b=3, Omega at G**(1/2) 1.12202 (+/-0.00001) 1.12202 0
IEC 61672-1:2013 Table 3 A-weighting deviation vs class-1 limits (fs=48 kHz) deviation within limits @ 1000 Hz +0.000 dB in [-0.70, +0.70] dB headroom +0.700 dB
IEC 61672-1:2013 Table 3 C-weighting deviation vs class-1 limits (fs=48 kHz) deviation within limits @ 1000 Hz +0.000 dB in [-0.70, +0.70] dB headroom +0.700 dB
ISO 7196:1995 Table 2 / A.3 G-weighting deviation vs +/-1 dB tolerance (fs=48 kHz) deviation within limits @ 1 Hz +0.047 dB in [-1.00, +1.00] dB headroom +0.953 dB
Levels & dosimetry: 100% (6/6)
Standard Quantity Expected (norm) Computed Δ Status
IEC 61672-1:2013 (Leq) Leq of a 1 Pa 1 kHz sine 90.97 dB (+/-0.05 dB) 90.969 dB -0.001 dB
IEC 61252:1995 (LEX,8h) 8 h exposure to 90 dB(A) noise 90 dB (+/-0.05 dB) 90.008 dB 0.008 dB
ISO 1996-1:2016 3.6.4 Lden, constant 60 dB in day/evening/night 66.3952 dB (+/-0 dB) 66.3952 dB 0 dB
ISO 1996-2:2007 Annex C.5 Example 1 Tonal audibility ΔLta (Formula C.3), 4 kHz tone 13.7 dB (+/-0.05 dB) 13.66 dB -0.044 dB
ISO 1996-2:2007 Annex C.5 Example 1 Tonal adjustment Kt (Formulae C.4-C.6) 6 dB (+/-0 dB) 6 dB 0 dB
ISO 1996-2:2017 Annex G.2 Combined measurement uncertainty u = √(Σ(cj·uj)²) 2.18 dB (+/-0.01 dB) 2.18 dB -0.002 dB
Room acoustics: 100% (12/12)
Standard Quantity Expected (norm) Computed Δ Status
Sabine (W. C. Sabine, 1922) Reverberation time T = k·V/A (V=120 m³, S=158 m², α=0.2) 0.611825 s (+/-0.000001 s) 0.611825 s 0 s
Everest, Master Handbook of Acoustics 4th ed, Fig. 7-22 Sabine RT, worked Example 1 @ 1 kHz (untreated 23.3×16×10 ft room, SI) 3.39 s (+/-0.02 s) 3.402 s 0.012 s
Eyring (Norris-Eyring, 1930) Reverberation time T = k·V/(-S·ln(1-ᾱ)) (α=0.2) 0.548369 s (+/-0.000001 s) 0.548369 s 0 s
Arau-Puchades (Acustica 65, 1988, Formula 18) T (α=0.5/0.1/0.1 per wall pair, dims 8×5×3 m) 0.812147 s (+/-0.000001 s) 0.812147 s 0 s
Model identity (uniform absorption) Arau-Puchades ≡ Eyring when ᾱ is uniform 0.548369 s (= Eyring) 0.548369 s 0 s
Vorlander Auralization 2e, Eq. (11.38)-(11.39) Image-source direct-sound amplitude 1/(4πr) and delay r/c (r = 4 m) 0.0198944 (+/-0) 0.0198944 0
Kuttruff Room Acoustics 6e, Eq. (9.23) Audible shoebox image count up to order 10 (= 1560) 156 (+/-0) 156 0
Kuttruff Room Acoustics 6e, Eq. (4.6) Temporal reflection density dN/dt = 4πc³t²/V (t = 0.1 s, V = 120 m³) 42258.2 1/s (+/-0 1/s) 42258.2 1/s 0 1/s
Bies Engineering Noise Control 5e, Eq. (6.44) Room constant R = Sᾱ/(1-ᾱ) (S = 100 m², ᾱ = 0.2 → 25 m²) 25 m² (+/-0 m²) 25 m² 0 m²
Bies Engineering Noise Control 5e, Eq. (6.43) Critical distance rc: direct field = reverberant field (R = 25, Q = 1) 0.160000 (= reverberant term) 0.16 0
Kuttruff Room Acoustics 6e, Eq. (3.44) Schroeder frequency f_s = 2000√(T/V) (V = 200 m³, T = 1 s) 141.421 Hz (+/-0 Hz) 141.421 Hz 0 Hz
Bies Engineering Noise Control 5e, Eq. (6.43) Steady-state SPL Lp = Lw + 10lg(Q/4πr² + 4/R) (Lw=90, r=1, R=25, Q=1) 83.7945 dB (+/-0 dB) 83.7945 dB 0 dB
Psychoacoustics: 100% (12/12)
Standard Quantity Expected (norm) Computed Δ Status
ISO 532-1:2017 Annex B.2 Zwicker loudness N, stationary test signal 1 83.2957 sone (+/-0.1%) 83.2957 sone 0 sone
ISO 532-1:2017 Annex B.5 Time-varying loudness Nmax, technical signal 14 (aircraft, free field) 22.6399 sone (+/-0.1%) 22.6399 sone 0 sone
ISO 532-1:2017 Annex B.5 Time-varying loudness Nmax, technical signal 15 (vehicle interior, diffuse field) 9.6059 sone (+/-0.1%) 9.6059 sone 0 sone
DIN 45692:2009 Clause 6 Sharpness of the standard 1 kHz reference signal 1 acum (+/-0 acum) 1 acum 0 acum
DIN 45692:2009 Table A.2 Sharpness of critical-band noise at 2.5 kHz (2320-2700 Hz, 4 sone) 1.78 acum (+/-0.089 acum) 1.747 acum -0.033 acum
ISO 226:2023 Table B.1 Equal-loudness contour, 60 phon @ 100 Hz 78.5 dB SPL (+/-0.05 dB SPL) 78.504 dB SPL 0.004 dB SPL
ECMA-418-2:2025 Clause 5.1.8 HMS loudness of a 1 kHz / 40 dB tone (c_N=0.0211964) 1 sone_HMS (+/-0.03 sone_HMS) 0.9843 sone_HMS -0.016 sone_HMS
ECMA-418-2:2025 Clause 6.2.8 HMS tonality of a 1 kHz / 40 dB tone (c_T=2.8758615) 1 tu_HMS (+/-0.03 tu_HMS) 0.9998 tu_HMS 0 tu_HMS
ECMA-418-2:2025 Clause 7 HMS roughness of a 1 kHz / 70 Hz / m=1 / overall 60 dB tone (c_R=0.0180685) 1 asper (+/-0.01 asper) 0.9999 asper 0 asper
ISO 532-2:2017 Clause 3.17 / Annex B.1 Moore-Glasberg loudness of a 1 kHz / 40 dB tone (C=0.0617) 1 sone (+/-0.01 sone) 1.0001 sone 0 sone
ISO 532-3:2023 Annex C.1 Moore-Glasberg-Schlittenlacher peak LTL, steady 1 kHz / 40 dB 1 sone (+/-0.02 sone) 0.9996 sone 0 sone
ECMA-418-2:2025 Clause 9 HMS fluctuation strength of a 1 kHz / 4 Hz / m=1 / overall 60 dB tone (c_F=0.003840572) 1 vacil_HMS (+/-0.01 vacil_HMS) 0.9931 vacil_HMS -0.007 vacil_HMS
Speech transmission (IEC 60268-16): 100% (9/9)
Standard Quantity Expected (norm) Computed Δ Status
IEC 60268-16:2020 A.2.2 STI weighting-factor pair (500 Hz + 1 kHz bands) 0.398 (+/-0.001) 0.398 0
IEC 60268-16:2020 A.3.1.2 Uniform MTF m=0.5 maps to STI=0.5 0.5 (+/-0.01) 0.5 0
IEC 60268-16:2020 C.3.2 STIPA direct method, Formula (C.1) signal at m=0.2 0.3 (+/-0.01) 0.2992 -0.001
IEC 60268-16:2020 C.3.2 STIPA direct method, Formula (C.1) signal at m=0.5 0.5 (+/-0.01) 0.4998 0
IEC 60268-16:2020 C.3.2 STIPA direct method, Formula (C.1) signal at m=0.8 0.7 (+/-0.01) 0.7002 0
IEC 60268-16:2020 C.3.3 Indirect method: exponential decay RT60=1 s vs Schroeder MTF 0.5885 (+/-0.005) 0.5885 0
IEC 60268-16:2020 C.4.2 Filter-bank slope: +41 dB unmodulated tone one octave below 125 Hz m >= 0.5 (C.4.2 pass criterion) 0.9812 0.481
IEC 60268-16:2020 A.2.2 (audio path) Weighting factors: modulated 500 Hz + 1 kHz pair through stipa() 0.398 (+/-0.005) 0.398 0
IEC 60268-16:2020 A.3.1.2 (audio path) Filter-bank phase: half-octave edge carriers at TI=0.9 0.9 (+/-0.01) 0.8975 -0.003
Intensity & sound power: 100% (4/4)
Standard Quantity Expected (norm) Computed Δ Status
IEC 61043:1994 Clause 5 Plane-wave intensity I = p^2 / (rho c) 0.00238 W/m^2 (+/-1.5%) 0.00239 W/m^2 0 W/m^2
ISO 3744:2010 Eq. 18 Monopole hemisphere recovers LW (r=4 m) 95 dB (+/-0 dB) 95 dB 0 dB
ISO 9614-2:1996 Eq. 12 Intensity scan recovers LW of an enclosed source 90 dB (+/-0.000001 dB) 90 dB 0 dB
ISO 3741:2010 Eq. 20 Reverberation-room method inverts to a known LW 0 dB error 0 dB 0 dB
Room & building acoustics: 100% (50/50)
Standard Quantity Expected (norm) Computed Δ Status
ISO 3382-2:2008 5.3.3 T30 from a synthetic exponential decay (T=1.0 s) 1 s (+/-1%) 1 s 0 s
ISO 18233:2006 (swept-sine method) Sweep deconvolution recovers a known IIR response 0 dB in-band error (+/-0.1 dB) 0.0006 dB 0.001 dB
ISO 717-1 Annex C, Table C.1 Weighted sound reduction index Rw (C;Ctr) Rw 30 (C -2; Ctr -3) Rw 30 (C -2; Ctr -3) sum 31.8 dB
ISO 717-1:2020 Annex C, Table C.2 Enlarged range 50-5000 Hz: Rw (C; Ctr; C50-5000; Ctr,50-5000) Rw 30 (C -2; Ctr -3; C50-5000 -2; Ctr,50-5000 -4) Rw 30 (C -2; Ctr -3; C50-5000 -2; Ctr,50-5000 -4) exact
ISO 717-2 Annex C, Table C.1 Weighted impact sound pressure level Ln,w (CI) Ln,w 79 (CI -11; sum 28.0 dB) Ln,w 79 (CI -11; sum 28.0 dB) +0 dB
ISO 717-2 Annex C, Table C.1 (covered) Weighted impact level of the floor WITH covering Ln,w (CI) Ln,w 64 (CI -3; sum 30.0 dB) Ln,w 64 (CI -3; sum 30.0 dB) +0 dB
ISO 717-2 Annex C, Table C.2 Floor-covering improvement ΔLw and CI,Δ (Formulae (2)/(A.4); CI,Δ from the normative Table 4 floor, not the 2020 print's misprinted C.2 chain) ΔLw 15 dB; CI,Δ -9 dB (Table 4 reference floor) ΔLw 15 dB; CI,Δ -9 dB +0 dB
ISO 354:2003 Eq. 5/8 Sabine inversion recovers absorption area 9.212828 m^2 (+/-0 m^2) 9.212828 m^2 0 m^2
ISO 3382-3:2012 Clause 6.2 Open-plan spatial decay rate D2,S (-6 dB/doubling) 6 dB (+/-0 dB) 6 dB 0 dB
ISO 16283-3:2016 Clause 3.12 Facade R'45 isolates the -1.5 dB incidence correction (S=A) 38.5 dB (+/-0 dB) 38.5 dB 0 dB
ISO 10140-2:2010 Formula (2) Lab airborne R on the ISO 717-1 reference shape -> Rw = 54 Rw 54 dB Rw 54 dB +0 dB
ISO 10140-5:2010+A1 Annex B, Table B.1 Reference elements end-to-end: printed Rw (C; Ctr) of all three Rw(C;Ctr) = 53(-1;-5) / 52(-1;-5) / 33(-1;-2) 53(-1;-5) / 52(-1;-5) / 33(-1;-2) exact
ISO 10140-5:2010+A1 Annex C, Table C.1 Reference floors end-to-end: printed Ln,t,r,0,w (CI) of both Ln,t,r,0,w(CI) = 72(0) / 75(-3) 72(0) / 75(-3) exact
ISO 15186-1:2000 Formula (7) Intensity RI on the ISO 717-1 reference shape -> RI,w = 30 RI,w 30 dB (scalar anchor RI = 34 dB) RI,w 30 dB (RI = 34 dB) +0 dB
ISO 15186-1:2000 Annex B, Table B.1 Adaptation term Kc: all 18 printed rows; (B.1) reduces to (B.2) max abs(Kc - Table B.1) <= 0,05 dB (1 dp print) 0.046 dB (B.1 vs B.2: 4.33e-04 dB) 0.046 dB
ISO 10052:2021 Clause 3.6 Survey R' applies the V/7,5 minimum-area rule 26.197888 dB (+/-0 dB) 26.197888 dB 0 dB
ISO 10052:2021 Clause 3.16 Service-equipment LXY is the 3-position energy average 32.823329 dB (+/-0 dB) 32.823329 dB 0 dB
ISO 10052:2021 Table 4 Reverberation-index estimate (35 <= V < 60, type g) k = [4.5, 5.0, 5.5, 5.5, 5.5] dB k = [4.5, 5.0, 5.5, 5.5, 5.5] dB exact
ISO 717-2:2020 Table 4 / Clause 5.2 Reference-floor weighted level Ln,r,0,w and CI (ISO 16251-1 ΔLw anchor) Ln,r,0,w = 78 dB, CI = -11 dB Ln,r,0,w = 78 dB, CI = -11 dB exact
ISO 16251-1:2014 / ISO 717-2 Formula (2) Floor-covering ΔLw: zero improvement gives ΔLw = 0 ΔLw = 0 dB (ΔL = 0 -> Ln,r = Ln,r,0) ΔLw = 0 dB exact
ISO 10848-1:2006 Formula (14) Flanking Kij (simplified) matches closed form Kij = 1.9897 dB Kij = 1.9897 dB exact
ISO 10848-1:2006 Formula (12) Flanking equivalent absorption length aj at f_ref aj = 1.2661 m aj = 1.2661 m exact
ISO 10848-1:2006 Clause 7.3.1 Flanking total loss factor η = 2,2/(f·Ts) η = 0.0044 η = 0.0044 exact
EN 29052-1:1992 Formula 4 Apparent dynamic stiffness s't = 4π²·m't·fr² (m't=200 kg/m², fr=25 Hz) 4.934802 MN/m³ (+/-0.000001 MN/m³) 4.934802 MN/m³ 0 MN/m³
EN 29052-1:1992 clause 8.2 NOTE Enclosed-gas stiffness s'a·d = 111 MN·mm/m³ (p₀=0,1 MPa, ε=0,9) 5.55556 MN/m³ (+/-0.0001 MN/m³) 5.55556 MN/m³ 0 MN/m³
EN 29052-1:1992 Formula 2 Floating-floor natural frequency f0 = (1/2π)√(s'/m') (s'=10 MN/m³, m'=100 kg/m²) 50.32921 Hz (+/-0 Hz) 50.32921 Hz 0 Hz
ISO 7626-1:2011 Table 1 / 3.1.2 Closed-form SDOF driving-point mobility peak mag(Y(f0)) = 1/c (c=5 N·s/m) 0.2 m/(N·s) (+/-0.000001 m/(N·s)) 0.2 m/(N·s) 0 m/(N·s)
ISO 7626-1:2011 Table 1 / 3.1.2 Closed-form SDOF static receptance H(0) = 1/k (k=8000 N/m) 0.000125 m/N (+/-0.0001%) 0.000125 m/N 0 m/N
ISO 7626-1:2011 Table 1 FRF reciprocity: impedance × mobility = 1 (at 37 Hz) 1 (= Z·Y) 1 0
ISO 10846-2:2008 3.17 Transfer-stiffness level Lk = 20 lg( k /k0), k0 = 1 N/m ( k = 1 MN/m)
ISO 10846-3:2002 Formula (1) Indirect method k2,1 = -(2πf)²·m2·T (f=500 Hz, m2=10 kg, T=0,01) -986960.4 N/m (+/-0.1%) -986960.4 N/m 0 N/m
ISO 10846-1:2008 Table A.2 FRF relation k = jω·Z at 250 Hz ( k recovered from impedance) 1001249.2 N/m (+/-0.0001%) 1001249.2 N/m
ISO 7626-2:2015 7.5.2 Rigid-mass calibration: accelerance mag(A) = 1/m (m=10 kg) 0.1 1/kg (+/-0 1/kg) 0.1 1/kg 0 1/kg
ISO 7626-2:2015 7.5.2 Rigid-mass calibration: mobility mag(Y) = 1/(2πf·m) at 100 Hz (m=10 kg) 0.0001592 m/(N·s) (+/-0.001%) 0.0001592 m/(N·s) 0 m/(N·s)
ISO 7626-2:2015 Annex A Normalized random error ε = √((1−γ²)/(2nγ²)): γ²=0,8, n=75 → 4,08 % (< 5 %) 4.08 % (+/-0.01 %) 4.08 % 0.002 %
ISO 7626-1:2011 Table 1 Rigid 1 kg mass at ω = 1000 rad/s: mobility 1e-3, compliance 1e-6 (decades) 0.001 m/(N·s) (+/-1e-07%) 0.001 m/(N·s) 0 m/(N·s)
ISO 10846-3:2002 6.1 Inequality (2) Indirect-method validity limit mag(T) = 0,1 ↔ ΔL1,2 = 20 dB 20 dB (+/-0 dB) 20 dB 0 dB
ISO 10846-3:2002 6.1 Model bias at the validity limit: k_ind/k = 1,1 (0,83 dB ≤ 1 dB, 10 % ≤ 12 %) 1.1 (+/-1e-07%) 1.1 0
ISO 10846-1:2008 Equation (6) Delivered/blocking force F2/F2,b = 1/1,1 at mag(k2,2/kt) = 0,1 (within 10 %) 0.9091 (+/-0) 0.9091 0
ISO 10846-2:2008 / -3:2002 7.6 Linearity: ΔLk ≤ 1,5 dB for input spectra 10 dB apart (linear element: 0) ΔLk ≤ 1,5 dB (7.6 c) 0 dB 0 dB
ISO/TS 7849-1:2009 Formula (8) Calibration L_v from â = 9,81 m/s² at 100 Hz (standard's EXAMPLE) 106.9 dB (+/-0.1 dB) 106.9 dB -0.02 dB
ISO/TS 7849-2:2009 Formula (15) L_W from L_v via measured radiation factor = 10 lg(P/P0) (round-trip) 84.771 dB (+/-0 dB) 84.771 dB 0 dB
ISO/TS 7849-1:2009 Formula (12) Impedance term: L_W − L_v = 10 lg(411/400) at ε = 1, S = S0 0.1178 dB (+/-0 dB) 0.1178 dB 0 dB
EN 15657:2018 Formula (14) Reception-plate L_Ws = resonant-plate power P = ωη(mS)⟨v²⟩ (round-trip) 55.545 dB (+/-0 dB) 55.545 dB 0 dB
EN 15657:2018 Formula (13) Plate loss factor η = 2,2/(f·Ts) at 1 kHz, Ts = 0,3 s 0.0073 (+/-0) 0.0073 0
EN 15657:2018 Formulae (15)/(17) + EN 12354-5 Annex I.3 Source conversion chain reproduces Table I.8 (wall, installed) max abs(L_Ws,inst - Table I.8) <= 0,15 dB 0.055 dB 0.055 dB
ISO 9611:1996 eq. (9) Mean free velocity level (energy mean, v0 = 5e-8 m/s) 72.3017 dB (+/-0 dB) 72.3017 dB 0 dB
EN 12354-5:2009 Formula (19b/19c) Coupling term → force-source limit 10 lg(mag(Ys)/Re{Yi}) as mag(Ys) ≫ mag(Yi) 40 dB (+/-0.01 dB) 40.001 dB 0.001 dB
EN 12354-5:2009 Annex I.3, Table I.9 Flushing cistern: four paths + Formula (17) total -> 29 dB(A) max path/total dev <= 0.15 dB; total 29 dB(A) 0.055 dB; 29.3 dB(A) 0.055 dB
EN 12354-5:2009 Annex I.2, Table I.6a Whirlpool floor component: mobility correction + path 11 max abs(dev vs Table I.6a) <= 0,15 dB 0.1 dB 0.1 dB
Building prediction & uncertainty: 100% (15/15)
Standard Quantity Expected (norm) Computed Δ Status
EN 12354-1:2000 Annex H.3 Airborne prediction R'w (direct + 12 flanking paths) R'w 52 dB (13 paths) R'w 52 dB (13 paths, 52.17) +0.17 dB
EN 12354-1:2000 Annex H.3 (paths) All 12 printed flanking-path values Rij,w max abs(Rij,w - printed) <= 0,05 dB 0.042 dB 0.042 dB
EN 12354-1:2000 Formula (5b) / Annex H.3 DnT,w closure from R'w (both H.3 examples -> 54 dB) DnT,w 54 dB (printed 53,8/54,3) DnT,w 53.63 / 54.13 dB -0.17 dB vs printed
EN 12354-2:2000 Annex E.3 Impact prediction L'n,w = Ln,w,eq - dLw + K 45 dB (+/-0 dB) 45 dB 0 dB
EN 12354-2:2000 Formula (3) / Annex E.3 Standardized impact level L'nT,w (exact 0,032 V form -> 43 dB) L'nT,w 43 dB (exact 42,96; E.3 prints 42,8) L'nT,w 42.96 dB -0.001 dB
EN 12354-3:2000 Annex F Facade airborne prediction (R'tr,s,w / D2m,nT,w single numbers) R'tr,s,w 31 (Ctr -3); D2m,nT,w 33 dB R'tr,s,w 31 (Ctr -3); D2m,nT,w 33 dB 0
EN 12354-4:2000 Annex G / Formula (2) Radiated LW of a wall+door segment (side 1, low bands) LW 63/125 Hz [59.8, 61.2] dB (+/-0.1) LW [59.8, 61.2] dB 0.038 dB
EN 12354-4:2000 Annex E / Table G.9 Exterior level of all four Table G.9 reception cells Lp 36,6 / 28,5 / 44,6 / 37,3 dB (+/-0,05) Lp 36.6 / 28.5 / 44.6 / 37.3 dB 0.046 dB
ISO 12999-1:2020 Table 2 Airborne band uncertainty, situation A @ 1 kHz 1.8 dB (+/-0 dB) 1.8 dB 0 dB
ISO 12999-1:2020 Annex B, Table B.2 One-decimal single numbers Rw / Rw+C50-5000 / Rw+Ctr,50-5000 57.4 / 56.4 / 51.1 dB 57.4 / 56.4 / 51.1 dB +0.00 dB
ISO 12999-1:2020 Annex B, Formulae (B.2)/(B.6) Single-number uncertainties (uncorrelated 0,6/0,8; correlated u(Rw) 1,9) u_uncorr 0.6 / 0.8 dB; u_corr(Rw) 1.9 dB 0.60 / 0.79 dB; 1.90 dB -0.00 dB
ISO 12999-1:2020 Clause 8 / Table 8 Expanded uncertainty U = 1.96 u (95 % two-sided, Rw sit. A) 2.352 dB (+/-0 dB) 2.352 dB 0 dB
ISO 12999-2:2020 Table 4 / Formula (1) Absorption coefficient +/-U (k=2), reproducibility, 20 x 1/3-oct bands U(k=2) = [0.33, 0.26, 0.22, 0.17, 0.13, 0.11, 0.09, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.09, 0.09, 0.09, 0.1, 0.11, 0.13, 0.16] U(k=2) = [0.33, 0.26, 0.22, 0.17, 0.13, 0.11, 0.09, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.09, 0.09, 0.09, 0.1, 0.11, 0.13, 0.16] exact
ISO 12999-2:2020 Table 5 / Formula (4) Practical coefficient +/-U (k=2), reproducibility, 5 octave bands U(k=2) = [0.09, 0.08, 0.08, 0.08, 0.1] U(k=2) = [0.09, 0.08, 0.08, 0.08, 0.1] exact
ISO 12999-2:2020 Clause 7, Examples 1/2 Single-number U (k=2): alpha_w and DLalpha,NRD alpha_w +/-0.07, DLalpha +/-1.6 dB alpha_w +/-0.07, DLalpha +/-1.6 dB exact
Outdoor propagation & occupational exposure: 100% (10/10)
Standard Quantity Expected (norm) Computed Δ Status
ISO 9613-1:1993 Table 1 Air attenuation @ 10 degC, 70 %, 1 kHz 3.66 dB/km (+/-0.01 dB/km) 3.658 dB/km -0.002 dB/km
ISO 9613-1:1993 Table 1 Air attenuation @ 0 degC, 20 %, 2 kHz 34.6 dB/km (+/-0.1 dB/km) 34.64 dB/km 0.04 dB/km
ISO 9613-2:1996 Table 2 Atmospheric attenuation grid, 6 conditions x 8 octave bands, dB/km all 48 cells within half a printed digit worst residual 0.939 x tolerance 0.939 x
ISO 9613-2:1996 Eq. (7) Geometrical divergence Adiv = 20 lg(d/d0) + 11 at 100 m 51 dB (+/-0 dB) 51 dB 0 dB
ISO 9613-2:1996 Table 3 Ground b'(0) porous limit -> Agr(250 Hz) = 2(-1.5 + 10.1) 17.2 dB (+/-0 dB) 17.2 dB 0 dB
ISO 9613-2:1996 clause 7.4 Single-edge diffraction saturates at the 20 dB cap 20 dB (+/-0 dB) 20 dB 0 dB
ISO 9613-2:1996 clause 7.4 Double-edge diffraction saturates at the 25 dB cap 25 dB (+/-0 dB) 25 dB 0 dB
ISO 9612:2009 Annex D Task-based LEX,8h + U (welder day, case a) LEX,8h 84.3; U 2.7 dB LEX,8h 84.3; U 2.7 dB -0.01; +0.02 dB
ISO 9612:2009 Annex E Job-based LEX,8h + U (production line, 18 workers) LEX,8h 88.1; U 3.8 dB LEX,8h 88.2; U 3.8 dB +0.06; -0.03 dB
ISO 9612:2009 Annex F Full-day LEX,8h + U (forklift drivers) LEX,8h 90.1; U 3.4 dB LEX,8h 90.1; U 3.4 dB +0.02; +0.03 dB
Materials: absorption, airflow & impedance: 100% (6/6)
Standard Quantity Expected (norm) Computed Δ Status
ISO 11654:1997 Annex A.1 Weighted absorption alpha_w (no indicator) 0.60 (class C, no indic.) 0.60 (class C, '') 0
ISO 11654:1997 Annex A.2 Weighted absorption alpha_w with M indicator 0.60(M) 0.60(M) 0
ISO 9053-2:2020 Annex A.3 Thermal boundary-layer thickness b 0.00183 m (+/-0.00001 m) 0.00183 m 0 m
ISO 9053-2:2020 Annex A.3 Effective ratio of specific heats kappa' 1.37 (+/-0.001) 1.37 0
ISO 10534-1:1996 Eqs (9)/(13)/(14) Absorption from standing-wave ratio s=3 alpha 0.75 (+/-0), |r| 0.5 alpha 0.75, |r| 0.5000 0
ISO 10534-2 Eq. (17) / Annex D Two-microphone round trip recovers a known reflection factor abs(r - (0.3-0.4j)) = 0 (identity, +/-1e-9) 0 0
Scattering & diffusion (ISO 17497): 100% (5/5)
Standard Quantity Expected (norm) Computed Δ Status
ISO 17497-1:2004 Eq (2) Reference speed of sound at 20 C 343.2 m/s (+/-0 m/s) 343.2 m/s 0 m/s
ISO 17497-1:2004 Eqs (1)/(4)/(5) Scattering coefficient (synthetic chain) 0.0931 (+/-0) 0.0931 0
ISO 17497-1:2004 Annex A.5 Expanded uncertainty of scattering coefficient 0.02971 (+/-0) 0.02971 0
ISO 17497-2:2012 Formula (5) Diffusion coefficient (autocorrelation) 0.7367 (+/-0) 0.7367 0
ISO 17497-2:2012 Formula (8) Zenith area factor (radians convention) 1.57105 (+/-0) 1.57105 0
In-situ road absorption (ISO 13472): 100% (3/3)
Standard Quantity Expected (norm) Computed Δ Status
ISO 13472-1:2002 Clause 4.2 Geometrical-spreading factor Kr 0.6667 (+/-0) 0.6667 0
ISO 13472-1:2002 Annex A Maximum-sampled-area radius 1.3425 m (+/-0 m) 1.3425 m 0 m
ISO 13472-2:2010 Clause 5.4.1 Spot-tube upper usable frequency f_u 1989.4 Hz (+/-0.1 Hz) 1989.4 Hz 0 Hz
Precision sound power (ISO 3745 / 9614-3): 100% (4/4)
Standard Quantity Expected (norm) Computed Δ Status
ISO 3745:2012 Clause 10.5 EXAMPLE Expanded uncertainty U (k=2) 4.123 dB (+/-0.001 dB) 4.123 dB 0 dB
ISO 3745:2012 Eq (11) K1 background floor (6 dB edge band) 1.2563 dB (+/-0.0001 dB) 1.2563 dB 0 dB
ISO 3745:2012 Eq (16) Meteorological C1 at 23 C reference -0.1282 dB (+/-0.0001 dB) -0.1282 dB 0 dB
ISO 9614-3:2002 Eqs (5)/(8)/(9) Uniform-intensity LW recovery 80 dB (+/-0 dB) 80 dB 0 dB
Human vibration (ISO 8041 / 2631 / 5349): 100% (15/15)
Standard Quantity Expected (norm) Computed Δ Status
ISO 8041-1:2017 Table B.8 Wk design-goal factor at 6,31 Hz 1.054 (+/-0.1%) 1.0544 0
ISO 8041-1:2017 Table B.9 Wm design-goal factor at 1,585 Hz 0.9342 (+/-0.1%) 0.9342 0
ISO 8041-1:2017 Table 1 Wh factor at the 500 rad/s reference 0.202 (+/-0.15%) 0.202 0
ISO 8041-1:2017 Table B.1 Wb design-goal factor at 6,31 Hz 1.054 (+/-0.1%) 1.0545 0
ISO 8041-1:2017 Table B.1 Wb design-goal factors at 1 / 100 Hz max rel dev ≤ 0,1 % 0.000267 0
ISO 8041-1:2017 Table 1 Wc factor at the 100 rad/s reference 0.5145 (+/-0.1%) 0.5145 0
ISO 8041-1:2017 Table 1 + Table B.3 Wd factors at the 100 rad/s reference and 1 Hz max rel dev ≤ 0,1 % 0.000162 0
ISO 8041-1:2017 Table B.4 We design-goal factor at 8 Hz 0.1263 (+/-0.1%) 0.1263 0
ISO 8041-1:2017 Table B.5 Wf design-goal factors at 0,1585 / 0,1 Hz max rel dev ≤ 0,1 % 0.000098 0
ISO 8041-1:2017 Table B.7 Wj design-goal factors at 6,31 / 8 Hz max rel dev ≤ 0,1 % 0.00001 0
ISO 8041-1:2017 Table 5 + Annex B All nine weightings inside the tolerance envelope (318 printed bands) 0 bands outside the Table 5 tolerances 0 0
ISO 5349-2:2001 Example E.2.1 Single-tool daily exposure A(8) 4.1 m/s^2 (+/-0.05 m/s^2) 4.14 m/s^2 0.037 m/s^2
ISO 5349-2:2001 Example E.3 Forestry three-task A(8) 3.6 m/s^2 (+/-0.05 m/s^2) 3.61 m/s^2 0.01 m/s^2
ISO 5349-1:2001 Eq. (C.1) VWF 10 % lifetime Dy at A(8)=7 4 yr (+/-0.1 yr) 4.04 yr 0.042 yr
Directive 2002/44/EC Art. 3 HAV/WBV action & limit values HAV 2.5/5.0, WBV 0.5/1.15 m/s^2 HAV 2.5/5.0, WBV 0.5/1.15 m/s^2 0
Speech intelligibility (ANSI S3.5-1997): 100% (7/7)
Standard Quantity Expected (norm) Computed Δ Status
ANSI S3.5-1997 Table 3 Band-importance function normalisation 1 (+/-0) 1 0
ANSI S3.5-1997 clause 5.4 Equivalent masking spectrum level at 200 Hz -1.665 (+/-0.001) -1.665 0
ANSI S3.5-1997 clause 5.6 Equivalent disturbance in quiet at 5000 Hz -23.6 dB (+/-0.01 dB) -23.6 dB 0 dB
ANSI S3.5-1997 clause 6 SII, noise 30 dB plus hearing loss 40 dB 0.2185 (+/-0.0001) 0.2185 0
R CRAN 'SII' Example C.2 One-third-octave method, independent oracle 0.851375 (+/-0.0001) 0.851375 0
ANSI S3.5-1997 clause 6 SII, standard speech in quiet, normal hearing 0.99582517 (+/-0.000001) 0.99582517 0
ANSI S3.5-1997 Table 3 Loud-effort speech spectrum level at 1 kHz 42.16 dB (+/-0 dB) 42.16 dB 0 dB
Objective intelligibility (STOI / ESTOI): 100% (3/3)
Standard Quantity Expected (norm) Computed Δ Status
Taal et al. 2011 (Eq. 6, degenerate) STOI of a signal against itself = 1 (perfect correlation) 1 (+/-0.000001) 1 0
Jensen & Taal 2016 (Eq. 8, degenerate) ESTOI of a signal against itself = 1 (perfect spectral correlation) 1 (+/-0.000001) 1 0
Taal et al. 2011 (monotonicity with SNR) STOI rises from -15 dB to +25 dB SNR speech-shaped noise STOI(+25 dB) - STOI(-15 dB) > 0.2 0.462 (0.389 -> 0.851) 0
Impulsive-sound prominence (NT ACOU 112): 100% (2/2)
Standard Quantity Expected (norm) Computed Δ Status
NT ACOU 112:2002 Formula 1 Predicted prominence, OR=1000 dB/s, LD=30 dB 11.9542 (+/-0.0001) 11.9542 0
NT ACOU 112:2002 Formula 2 Adjustment KI to LAeq at prominence P=10 9 dB (+/-0 dB) 9 dB 0 dB
Room noise (ANSI S12.2-2019): 100% (3/3)
Standard Quantity Expected (norm) Computed Δ Status
ANSI S12.2-2019 Table 1 NC-40 curve, tangency self-consistency 40 (+/-0) 40 0
ANSI S12.2-2019 Table D.1 RC-31 Mark II curve, 63 Hz level 51 (+/-0) 51 0
ANSI S12.2-2019 clause D.4 RC-35 curve, mid-frequency average LMF 35 (+/-0) 35 0
Hearing threshold (ISO 7029 / ISO 389-7): 100% (3/3)
Standard Quantity Expected (norm) Computed Δ Status
ISO 7029:2017 Table 1 Median threshold, male age 60 at 4 kHz 20.209 dB (+/-0.001 dB) 20.208 dB 0 dB
ISO 7029:2017 Table 2 Upper spread su, male age 60 at 1 kHz 10.153 dB (+/-0.001 dB) 10.153 dB 0 dB
ISO 389-7:2005 Table 1 Free-field reference threshold at 1 kHz 2.4 dB (+/-0 dB) 2.4 dB 0 dB
Measurement uncertainty (GUM / Supplement 1): 100% (7/7)
Standard Quantity Expected (norm) Computed Δ Status
ISO/IEC Guide 98-3-1 clause 9.2 Combined uncertainty, additive model 2 (+/-0) 2 0
ISO/IEC Guide 98-3 Table G.2 Coverage factor, p=0.99, v=16 2.92 (+/-0.005) 2.921 0.001
ISO/IEC Guide 98-3 Annex G.4 Welch-Satterthwaite effective dof 40 (+/-0) 40 0
ISO/IEC Guide 98-3 Annex H.1 End-gauge combined uncertainty uc, nm 31.71 nm (+/-0.01 nm) 31.71 nm 0.001 nm
ISO/IEC Guide 98-3 Annex H.1 End-gauge expanded uncertainty U99, nm 92.1 nm (+/-0.1 nm) 92.1 nm 0.04 nm
ISO/IEC Guide 98-3 Annex H.2 (Table H.3) Correlated V/I/phi budget: uc(R), ohm 0.071 ohm (+/-0.001 ohm) 0.071 ohm 0 ohm
ISO/IEC Guide 98-3-1 Table 3 (clause 9.2.3) Seeded Monte Carlo, rectangular sum: 95 % interval endpoint +/-3.88 (u = 2.0) +/-3.886 (u = 2.002) 0.006
Noise-induced hearing loss (ISO 1999): 100% (3/3)
Standard Quantity Expected (norm) Computed Δ Status
ISO 1999:2013 Table D.2 Median NIPTS, 4 kHz, 90 dB, 20 yr 13 dB (+/-0.5 dB) 12.9 dB -0.057 dB
ISO 1999:2013 Table D.2 Worst-10 % NIPTS, 4 kHz, 90 dB, 20 yr 18 dB (+/-0.5 dB) 17.8 dB -0.239 dB
ISO 1999:2013 Table D.4 Worst-10 % NIPTS, 3 kHz, 100 dB, 40 yr 60 dB (+/-0.5 dB) 59.8 dB -0.172 dB
Multiple-shock whole-body vibration (ISO 2631-5): 100% (6/6)
Standard Quantity Expected (norm) Computed Δ Status
ISO 2631-5:2018 Formula 3 Daily acceleration dose, 5 x 40 m/s2 peaks 55.97 m/s2 (+/-0.01 m/s2) 55.97 m/s2 -0.002 m/s2
ISO 2631-5:2018 Formula C.3 Stress variable R, Annex C male example 1.22 (+/-0.01) 1.22 0
ISO 2631-5:2018 Formula C.5 Injury probability, Annex C male example 0.37 (+/-0.01) 0.37 -0.003
ISO 2631-5:2018 Annex C NOTE 5 Compressive stress Sd, female example 1.4 MPa (+/-0.01 MPa) 1.4 MPa -0.001 MPa
ISO 2631-5:2018 Annex C NOTE 5 Stress variable R, female example 0.97 (+/-0.01) 0.96 -0.008
ISO 2631-5:2018 Formula 1 vs Annex D Table D.1 Seat-to-spine transfer vs the 256 Hz digital filter (0,5-80 Hz) max abs(Formula 1 - filter) ≤ 0,04 0.001 0.001
Sound absorption in enclosed spaces (EN 12354-6): 100% (2/2)
Standard Quantity Expected (norm) Computed Δ Status
EN 12354-6:2003 Formula 1 Equivalent absorption area, Annex E bare room 2.26 m2 (+/-0.01 m2) 2.26 m2 0.003 m2
EN 12354-6:2003 Formula 5 Reverberation time, Annex E bare room 2.1 s (+/-0.1 s) 2.1 s 0.003 s
Prominent discrete tones (ECMA-418-1): 100% (2/2)
Standard Quantity Expected (norm) Computed Δ Status
ECMA-418-1:2024 Clause 10 Formula (2) Critical band at 1 kHz (f1,c / f2,c / dfc) dfc 162.2 Hz (+/-0.05 Hz); edges 922.2-1084.4 Hz dfc 162.22 Hz; edges 922.2-1084.4 Hz 0.017 Hz
ECMA-418-1:2024 Clause 11.6 Formula (14) Proximity spacing dfprox at 150 / 850 Hz 23 Hz @ 150 Hz; 63.8 Hz @ 850 Hz (+/-0.5 Hz) 23.0 Hz; 63.8 Hz +0.004; +0.044 Hz
Tonal audibility (ISO/PAS 20065): 100% (11/11)
Standard Quantity Expected (norm) Computed Δ Status
ISO/PAS 20065:2016 Formulae (12)-(14) Audibility at 137.3 Hz, Annex E spectrum 1 4.99 dB (+/-0.05 dB) 5.01 dB 0.022 dB
ISO/PAS 20065:2016 Formula (13) Masking index av at 137.3 / 592.2 Hz -2.02 dB @ 137.3 Hz; -2.4 dB @ 592.2 Hz (+/-0.005 dB) -2.017 dB; -2.400 dB +0.003; +0.000 dB
ISO/PAS 20065:2016 Formula (20) Mean audibility of the five spectra, Annex E 6.96 dB (+/-0.05 dB) 6.98 dB 0.018 dB
ISO/PAS 20065:2016 Formula (6) Mean narrow-band level LS from spectrum, Table E.1 49.22 dB (+/-0.02 dB) 49.22 dB -0.001 dB
ISO/PAS 20065:2016 Clause 6 Extended uncertainty U of the 137.3 Hz tone, Table E.2 2.79 dB (+/-0.02 dB) 2.8 dB 0.006 dB
ISO/PAS 20065:2016 Formulae (28)-(29) Extended uncertainty of the mean audibility, Annex E Step 4 1.38 dB (+/-0.01 dB) 1.38 dB -0.003 dB
ISO/PAS 20065:2016 Formula (8) Tone level LT from spectrum, Table E.1 67.96 dB (+/-0.02 dB) 67.96 dB -0.005 dB
ISO/PAS 20065:2016 Clause 5.3.8 Tone detection over the spectrum, Table E.1 tones at [118.4, 137.3, 158.8] Hz tones at [118.4, 137.3, 158.8] Hz exact
ISO/PAS 20065:2016 Clause 5.3.8 Step 3 Same-band FG combination inside analyze_spectrum, Table E.2 row 2 FG 72.15 dB (+/-0.02 dB) 72.15 dB -0.002 dB
ISO/PAS 20065:2016 Formula (17) Multi-tone FG combination, Table E.1 72.15 dB (+/-0.02 dB) 72.15 dB -0.002 dB
ISO/PAS 20065:2016 Formulae (18)/(19) Two-tone separation fD (DIN 45681 Annex J), 137.3 / 212 Hz fD(137.3)=24.09, fD(212)=21.0 Hz; Annex E pair combined fD(137.3)=24.09, fD(212)=21.00 Hz; Annex E pair combined exact
Psychoacoustic annoyance & fluctuation strength (Fastl & Zwicker): 100% (3/3)
Standard Quantity Expected (norm) Computed Δ Status
Fastl & Zwicker Eqs (16.2)-(16.4) Psychoacoustic annoyance, worked (N5,S,F,R) tuple 37.0478 (+/-0.001) 37.0477 0
Fastl & Zwicker Eq (10.2) Fluctuation strength of AM broadband noise (60 dB, m=1, 4 Hz) 3.6943 vacil (+/-0.001 vacil) 3.6943 vacil 0 vacil
Fastl & Zwicker Ch. 10 / Osses et al. 2016 Fluctuation-strength calibration: 1 kHz / 60 dB / m=1 / 4 Hz AM tone 1 vacil (+/-0.05 vacil) 1 vacil 0 vacil
Electroacoustics: distortion & frequency response: 100% (14/14)
Standard Quantity Expected (norm) Computed Δ Status
IEC 60268-3:2013 (14.12.3.2) THD (rel. total RMS, the R convention the clause defines) 0.112853 (+/-0.0001) 0.112853 0
Closed-form harmonic synthesis (THD_F convention) THD (rel. fundamental, the widespread datasheet convention) 0.113578 (+/-0.0001) 0.113578 0
IEC 60268-3:2013 (14.12.5) 2nd-order harmonic distortion d2 (rel. total) 0.099361 (+/-0.0001) 0.099361 0
IEC 60268-3:2013 (14.12.7.2 g) Modulation distortion d_m,2 (arithmetic sideband sum over U_2,f2) 0.16 (+/-0.0001) 0.16 0
IEC 60268-3:2013 (14.12.7.2 h) Modulation distortion d_m,3 (arithmetic sideband sum over U_2,f2) 0.08 (+/-0.0001) 0.08 0
IEC 60268-3:2013 (14.12.8.1 a) Difference-frequency distortion d_d,2 (over U_2,ref = 2 U_2,f2) 0.03 (+/-0.0001) 0.03 0
IEC 60268-3:2013 (14.12.8.1 b) Difference-frequency distortion d_d,3 (arithmetic product sum) 0.04 (+/-0.0001) 0.04 0
IEC 60268-3:2013 (14.12.10) Total difference-frequency distortion (8 kHz / 11.95 kHz tones) 0.03605551 (+/-0.0001) 0.03605551 0
ITU-R BS.468-4 Table 1 Weighting network response at the 6.3 kHz peak (14.12.11 network) 12.2 dB (+/-0 dB) 12.2 dB 0 dB
IEC 60268-3:2013 (14.12.9) DIM of the 15 kHz / 3.15 kHz signal (Table 2, 9 products) 0.168819 (+/-0.0001) 0.168819 0
Bendat & Piersol, Random Data 4e H1 recovers a known first-order IIR gain at 1 kHz 0.8954 (+/-2%) 0.8954 0
Bendat & Piersol, Random Data 4e Ordinary coherence = 1 for a noiseless LTI path 1 (+/-0.001) 1 0
AES17-2015 (6.4.2 / 5.2.7) Idle channel noise, 1 kHz -20 dBFS tone (CCIR-RMS -5.63 dB offset) -25.63 dB (+/-0.01 dB) -25.63 dB 0 dB
AES17-2015 (6.4.1) Dynamic range, full-scale reference over a -40 dBFS residual at 2 kHz 40 dB (+/-0.6 dB) 40.41 dB 0.414 dB
Calibrated spectral analysis (Bendat & Piersol): 100% (6/6)
Standard Quantity Expected (norm) Computed Δ Status
Bendat & Piersol, Random Data 4e Eq. (5.67) White-noise autospectral density = sigma^2/(fs/2) 0.000977 (+/-3%) 0.000982 0
Bendat & Piersol, Random Data 4e Eq. (8.158) PSD random error = 1/sqrt(nd) (Monte Carlo, 100 seeded records) 0.1768 (+/-6%) 0.1764 0
Bendat & Piersol, Random Data 4e Eq. (8.163) 95% chi-square confidence interval coverage (Monte Carlo) 0.95 (+/-0.025) 0.94 -0.01
Bendat & Piersol, Random Data 4e Eqs. (9.55)/(6.39) Coherent output spectrum of a known-SNR path: gamma^2 = SNR/(1+SNR) 0.7191 (+/-0.03) 0.7255 0.006
Closed-form power-law slope (10*lg(2) dB/octave per unit exponent) Pink-noise PSD slope over 20 Hz - 20 kHz, dB/octave -3.0103 dB/oct (+/-0.05 dB/oct) -3.0116 dB/oct -0.001 dB/oct
Constant-power 1/n-octave kernel (closed form) 1/3-octave smoothed line level = Pdf/(f0(2^(1/6)-2^(-1/6))) 0.021592 (+/-1e-07%) 0.021592 0
Correlation, time delay and envelope (B&P / Knapp & Carter): 100% (7/7)
Standard Quantity Expected (norm) Computed Δ Status
Bendat & Piersol, Random Data 4e Eq. (5.21) Cross-correlation peak of a 16-sample pure delay, samples 16 (+/-0.001) 16 0
Knapp & Carter 1976, Table I (PHAT) + sub-sample interpolation GCC-PHAT estimate of an exact 12.25-sample fractional delay, samples 12.25 (+/-0.005) 12.2483 -0.002
Bendat & Piersol, Random Data 4e Eq. (5.101) Cross-spectrum phase-slope estimate of the same fractional delay 12.25 (+/-0.001) 12.2498 0
Bendat & Piersol, Random Data 4e Eq. (8.120) BLWN autocorrelation coefficient at 3 samples vs sin(2piBt)/(2piBt) -0.1559 (+/-0.02) -0.1666 -0.011
Bendat & Piersol, Random Data 4e Example 8.5 Random error of the correlation peak: B=100 Hz, T=5 s, M/S=N/S=10 0.35 (+/-0.001) 0.3493 -0.001
Bendat & Piersol, Random Data 4e Table 13.1 Hilbert transform of cos recovers sin: max interior error 0 (+/-0) 0 0
Bendat & Piersol, Random Data 4e Eq. (13.27) Envelope of an AM waveform recovers 1 + mcos(2pifm*t) exactly 0 (+/-0) 0 0
Underwater acoustics (ISO 18405/17208/18406): 100% (6/6)
Standard Quantity Expected (norm) Computed Δ Status
ISO 18405:2017 / ISO 18406 Formula 7 Sound pressure level of a synthetic tone, dB re 1 µPa 123.0103 (+/-0.0001) 123.0103 0
ISO 18405:2017 / ISO 18406 Formulae 3-4 Sound exposure level of a 2 s tone, dB re 1 µPa²·s 120 (+/-0.001) 120 0
ISO 18406:2017 (6.4.2.1.3) Peak sound pressure level of a known waveform, dB re 1 µPa 129.5424 (+/-0.0001) 129.5424 0
ISO 17208-1:2016 Radiated noise level from RMS pressure and distance, dB re 1 µPa·m 46.0206 (+/-0.0001) 46.0206 0
ISO 17208-2:2019 (Formula 3) Lloyd's-mirror surface correction ΔL at a known k·d_s -3.5211 (+/-0.0001) -3.5211 0
ISO 18406:2017 (Formulae 8-9) Cumulative SEL of N identical strikes = SEL_ss + 10·lg(N) 196.9897 (+/-0) 196.9897 0
Underwater sound propagation (transmission loss): 100% (15/15)
Standard Quantity Expected (norm) Computed Δ Status
Mackenzie (1981) nine-term equation Speed of sound at 25 °C, 35 ‰, 1000 m (canonical check value), m/s 1550.744 m/s (+/-0.01 m/s) 1550.744 m/s 0 m/s
UNESCO/Chen-Millero vs Mackenzie Sound-speed agreement at 10 °C, 35 ‰, 1000 m (cross-model), m/s 1506.264 m/s (+/-1 m/s) 1506.524 m/s 0.261 m/s
Del Grosso (1974) vs Mackenzie Sound-speed agreement at 10 °C, 35 ‰, 1000 m (cross-model), m/s 1506.264 m/s (+/-1 m/s) 1506.313 m/s 0.049 m/s
Spherical spreading 20·lg(R) Geometrical spreading loss at R = 1000 m, dB 60 dB (+/-0 dB) 60 dB 0 dB
Thorp (1967) absorption Volume absorption α at 10 kHz (cold deep water), dB/km 1.1498 dB/km (+/-0 dB/km) 1.1498 dB/km 0 dB/km
Ainslie-McColm (1998) vs Francois-Garrison (1982) Absorption agreement at 10 kHz, 10 °C, 35 ‰, 0 m, pH 8, dB/km 0.9626 dB/km (+/-0.0963 dB/km) 0.9866 dB/km 0.024 dB/km
Francois-Garrison (1982) Part II Table IV Absorption α at 100 kHz, 10 °C, 35 ‰, 0 m, pH 8 (printed value), dB/km 33.6 dB/km (+/-0.05 dB/km) 33.63 dB/km 0.03 dB/km
Del Grosso refit (Wong-Zhu 1995 Table IV) c(t90 = 20 °C, S = 35, P = 500 bar) vs the printed check table, m/s 1603.679 m/s (+/-0.001 m/s) 1603.679 m/s 0 m/s
Wales-Heitmeyer (2002) ensemble spectrum Merchant-ship source PSD at 100 Hz (printed equation), dB re 1 µPa²/Hz 158.45 dB (+/-0.001 dB) 158.45 dB 0 dB
Passive sonar equation (Urick/Etter) Figure of merit SL − (NL − DI) − DT, dB 85 dB (+/-0 dB) 85 dB 0 dB
Seabed reflection (Rayleigh, normal incidence) Bottom loss at 90° grazing, sand ρ=1900 c=1650 over water, dB 9.0506 dB (+/-0 dB) 9.0506 dB 0 dB
Wenz wind noise (rule of fives) Wind spectrum level at 1 kHz, 5 kn (canonical anchor), dB re 1 µPa²/Hz 51.0206 dB (+/-0.0001 dB) 51.0206 dB 0 dB
Mellen thermal noise Thermal spectrum level at 50 kHz, 16.85 °C (physical), dB re 1 µPa²/Hz 19.3426 dB (+/-0 dB) 19.3426 dB 0 dB
JOMOPANS-ECHO ship source level Bulker V=13.5 kn L=211 m band level at 1 kHz (File S1 oracle), dB re 1 µPa m 161.394 dB (+/-0.01 dB) 161.394 dB 0 dB
UNESCO sound speed (EOS-80 canonical value) SVEL(S = 40, T68 = 40 °C, P = 1000 bar) vs Fofonoff & Millard 1983, m/s 1731.995 m/s (+/-0.02 m/s) 1732.004 m/s 0.009 m/s
Underwater numerical propagation (modes / rays / PE): 100% (4/4)
Standard Quantity Expected (norm) Computed Δ Status
Normal modes vs ideal waveguide Fundamental horizontal wavenumber kr1 at 20 Hz, 100 m (analytic), rad/m 0.077662 rad/m (+/-0.0001 rad/m) 0.077662 rad/m 0 rad/m
Normal modes vs image-source oracle Absolute TL at 1 km in the ideal waveguide (converged image sum), dB 48.238 dB (+/-0.02 dB) 48.239 dB 0.001 dB
Ray tracing vs linear gradient Turning depth of a 10° ray, c = 1500 + 0.05z (circular arc), m 462.8 m (+/-1 m) 462.8 m 0 m
Parabolic equation vs free field PE transmission loss at 2 km, homogeneous medium (spherical spreading), dB 66.021 dB (+/-0.1 dB) 66.021 dB 0 dB
Aircraft noise (ICAO Annex 16 / IEC 61265): 100% (14/14)
Standard Quantity Expected (norm) Computed Δ Status
ECAC Doc 29 noise fraction (half path) Finite-segment correction ΔF for a perpendicular foot at the segment start, dB -3.0103 dB (+/-0.001 dB) -3.0103 dB 0 dB
ECAC Doc 29 single-event chain SEL of a long level flyover vs the infinite-path limit LE∞ + ΔI − Λ, dB 83.444 dB (+/-0.01 dB) 83.444 dB 0 dB
ECAC Doc 29 impedance adjustment (standard atmosphere) Acoustic-impedance adjustment of NPD data at 15 °C / 101.325 kPa (Eq. 4-6/4-7), dB 0.074 dB (+/-0.0005 dB) 0.0741 dB 0 dB
ECAC Doc 29 reference workbook (segment Λ) Lateral attenuation of a climbing segment vs the ECAC Vol 3 Part 1 workbook, dB 6.3769 dB (+/-0.01 dB) 6.3769 dB 0 dB
ECAC Doc 29 start-of-roll directivity (jet) ΔSOR behind a takeoff ground-roll segment vs the Vol 3 Part 1 workbook, dB 0.3196 dB (+/-0.01 dB) 0.3196 dB 0 dB
ECAC Doc 29 start-of-roll directivity (turboprop) ΔSOR behind a takeoff ground-roll segment (turboprop, Eq. 4-24b), dB 1.0943 dB (+/-0.01 dB) 1.0944 dB 0 dB
ECAC Doc 29 workbook event assembly (JETFDS/R03, behind SOR) Energy sum of the reference per-segment SELs vs the B-1 event total, dB 74.73 dB (+/-0.01 dB) 74.733 dB 0.003 dB
SAE ARP 5534 band-attenuation continuity SAE-Method δ_B at the 150 dB branch split (Eq. 7 vs Eq. 8), dB 123.95 dB (+/-0.01 dB) 123.953 dB 0.003 dB
ECAC Doc 29 NPD interpolation Log-linear NPD level at the log-midpoint distance (Eq. 4-4), dB 97 dB (+/-0 dB) 97 dB 0 dB
SAE ARP 5534 pure-tone coefficient (ISO 9613-1) Mid-band α at 1 kHz, 25 °C, 70 % RH, 101.325 kPa, dB/m 0.006186 dB/m (+/-0 dB/m) 0.006186 dB/m 0 dB/m
ICAO Annex 16 Vol. I App. 2 Table A2-3 Perceived noisiness at SPL(b), 1 kHz band, in noys 1 (+/-0) 1 0
ICAO Doc 9501 ETM Vol. I Table 3-7 Tone correction of the turbofan example, dB 2 (+/-0) 2 0
ICAO Doc 9501 ETM Vol. I Table 4-4 Integrated-method reference EPNL, EPNdB 92.619 EPNdB (+/-0.01 EPNdB) 92.619 EPNdB 0 EPNdB
IEC 61265:1995 Table 1 Directional-response tolerance at 4 kHz / 90°, dB 2 dB (+/-0 dB) 2 dB 0 dB
Rotorcraft noise (ECAC Doc 32 / NORAH2): 100% (12/12)
Standard Quantity Expected (norm) Computed Δ Status
ECAC Doc 32 atmospheric attenuation (Table 4) ΔLa over a 1 km excess path at 1 kHz vs the NORAH2 guidance Table 4, dB 6.3 dB (+/-0.2 dB) 6.186 dB -0.114 dB
ECAC Doc 32 spherical spreading ΔLs at ten times the 60 m hemisphere reference distance (Eq. 24), dB -20 dB (+/-0 dB) -20 dB 0 dB
ECAC Doc 32 ground effect (rigid limit) ΔLg over a rigid surface at grazing incidence tends to +6 dB (Eq. 29), dB 6 dB (+/-1 dB) 6 dB 0.002 dB
ECAC Doc 32 propagation chain (NORAH2 prototype) LA of a single-hemisphere emission vs the NORAH2 prototype single-event history (R22 approach, 223.66 m slant), dB(A) 55.87 dB(A) (+/-0.1 dB(A)) 55.886 dB(A) 0.016 dB(A)
ECAC Doc 32 flight-condition interpolation (NORAH2 Eq. 8) Distance-scaled triangle blend of three uniform hemispheres, hand-checked, dB 97.0367 dB (+/-0.001 dB) 97.0364 dB 0 dB
ECAC Doc 32 flight-path kinematics (Eq. 17) Airspeed of a straight climbing track, 40 m/s ground speed at a 5° path angle, m/s 40.15279 m/s (+/-0.0001 m/s) 40.15279 m/s 0 m/s
ECAC Doc 32 retarded time (Eq. 22) Recorded-time delay at 100 m slant distance, r/c with c = 346.1 m/s, s 0.288934 s (+/-0.00001 s) 0.288934 s 0 s
ECAC Doc 32 single event (Eq. 27) SEL − LASmax of a constant-speed level flyover, 10·lg(π·d/V) closed form, dB 7.982 dB (+/-0.1 dB) 7.942 dB -0.04 dB
NORAH2 guidance mean ground plane (Eq. 36-40) Intercept of the plane fitted to a symmetric 20 m roofline, hand-checked, m 10 m (+/-0 m) 10 m 0 m
NORAH2 guidance mean flow resistivity (Eq. 41) Log-average of equal 1e4 and 1e6 Pa·s/m2 halves, hand-checked, Pa·s/m2 100000 Pa·s/m² (+/-0 Pa·s/m²) 100000 Pa·s/m² 0 Pa·s/m²
NORAH2 guidance diffraction at grazing (Eq. 42) Pure diffraction with the edge on the line of sight, 10·lg 3, dB 4.7712 dB (+/-0.0001 dB) 4.7712 dB 0 dB
NORAH2 guidance screening path difference (§A.4.5) Rubber-band delta over a 40 m hill, hand-checked geometry, m 4.2848 m (+/-0 m) 4.2848 m 0 m
Wind-turbine noise (IEC 61400-11): 100% (3/3)
Standard Quantity Expected (norm) Computed Δ Status
IEC 61400-11:2012 Formula 30 Critical bandwidth about a 500 Hz tone, Hz 117.255 Hz (+/-0 Hz) 117.255 Hz 0 Hz
IEC 61400-11:2012 Formula 26 Apparent sound power level of a single band, dB re 1 pW 148.5139 dB (+/-0.0001 dB) 148.5139 dB 0 dB
IEC 61400-11:2012 Formulae 31-34 Tonal audibility of a synthetic clean tone, dB 16.38 dB (+/-0.06 dB) 16.38 dB -0.001 dB
Porous & multilayer absorbers (Mechel / Bies / Cox & D'Antonio): 100% (10/10)
Standard Quantity Expected (norm) Computed Δ Status
Bies 5e App. D Table D.1 / Mechel 2e G.11 (2) Delany-Bazley normalised Zc at X = 0.1, real part 1.3241 (+/-0) 1.3241 0
Bies 5e App. D Table D.1 / Mechel 2e G.11 (2) Delany-Bazley normalised Zc at X = 0.1, imaginary part -0.4694 (+/-0) -0.4694 0
Miki 1990 Eqs. (30)-(34) Miki normalised wavenumber at f/sigma = 0.1, real part 1.4523 (+/-0) 1.4523 0
Johnson et al. 1987 / Cox & D'Antonio 3e Eq. (6.19) JCA static viscous limit j w rho_e -> sigma, Pa s/m2 20000 Pa s/m2 (+/-0.01%) 20000 Pa s/m2 0 Pa s/m2
Mechel 2e Sect. D.3 Eq. (1) Hard-backed layer: TMM vs -j Zc cot(kd), max rel deviation 0 (+/-0) 0 0
Lossless-layer limit (Mechel 2e Sect. D.3-D.4) Air cavity over a rigid wall at lambda/4: alpha 0 (+/-0) 0 0
Mechel 2e Sect. D.5 Maximum statistical absorption of a locally reacting plane 0.951 (+/-0.001) 0.951 0
Cox & D'Antonio 3e Eq. (7.9) Membrane resonance 60/sqrt(m d), m = 5 kg/m2, d = 5 cm, Hz 120 Hz (+/-2%) 119.85 Hz -0.15 Hz
Maa 1998 Fig. 5 / Cox & D'Antonio 3e Fig. 7.28 Microperforated panel (d=t=0.2 mm, b=2.5 mm, D=6 cm): peak alpha 0.95 (+/-0.05) 0.956 0.006
Maa 1998 Eqs. (5a)/(10) MPP peak absorption vs 4r/(1+r)^2 with Maa's printed resistance 4r/(1+r)^2 = 0.949 0.956 0.007
Program loudness (ITU-R BS.1770 / EBU R 128): 100% (8/8)
Standard Quantity Expected (norm) Computed Δ Status
ITU-R BS.1770-5 Annex 1 997 Hz sine at 0 dB FS on the left channel, LKFS -3.01 LKFS (+/-0.01 LKFS) -3.01 LKFS 0 LKFS
EBU Tech 3341:2023 Table 1 case 1 Integrated loudness of the -23 dBFS stereo sine, LUFS -23 LUFS (+/-0.1 LUFS) -22.99 LUFS 0.007 LUFS
EBU Tech 3341:2023 Table 1 case 5 Gated integrated loudness of the -26/-20/-26 dBFS steps, LUFS -23 LUFS (+/-0.1 LUFS) -22.98 LUFS 0.021 LUFS
EBU Tech 3341:2023 Table 1 case 6 Integrated loudness of the 5.0-channel sine (Table 3 weights), LUFS -23 LUFS (+/-0.1 LUFS) -23.02 LUFS -0.016 LUFS
EBU Tech 3341:2023 Table 1 case 15 True-peak level of the fs/4 sine at 0.5 FFS, dBTP -6 dBTP (+0.2/-0.4 dB) -6.02 dBTP -0.015 dBTP
EBU Tech 3341:2023 Table 1 case 19 True-peak level of the fs/4 sine at 1.41 FFS, dBTP 3 dBTP (+0.2/-0.4 dB) 3 dBTP 0.001 dBTP
EBU Tech 3342:2023 Table 1 case 1 Loudness range of the -20/-30 dBFS tone steps, LU 10 LU (+/-1 LU) 10 LU 0 LU
EBU Tech 3342:2023 Table 1 case 3 Loudness range of the -40/-20 dBFS tone steps, LU 20 LU (+/-1 LU) 20 LU 0 LU
2D FDTD wave simulation (Attenborough & Van Renterghem 2021, Ch. 4): 100% (2/2)
Standard Quantity Expected (norm) Computed Δ Status
Rigid rectangular box eigenfrequency Mode (1,1) of a 1.0 x 0.7 m rigid box, f = (c/2)*sqrt(1/lx^2 + 1/ly^2), Hz 299.06 Hz (+/-1.5 Hz) 298.91 Hz -0.153 Hz
Free-field pulse arrival delay Probe-to-probe delay of a pulse over 0.6 m of air, (r2 - r1)/c, ms 1.749 ms (+/-0.05 ms) 1.756 ms 0.007 ms
Swept-sine distortion & phase utilities (Farina / Novak): 100% (7/7)
Standard Quantity Expected (norm) Computed Δ Status
Farina 2000 / Novak et al. 2015 (Chebyshev identity) 3rd-harmonic response H3 magnitude of a cubic polynomial, re a3/4 0.05 (+/-0.0005) 0.05001 0
Novak et al. 2015, JAES 63(10), Eqs. 18/49 Synchronized-sweep phase of H3 (Chebyshev: -sin(3wt)), rad 3.1416 rad (+/-0.005 rad) 3.1411 rad 0 rad
Farina 2000, AES 108th Conv. (THD from one sweep) THD(1 kHz) of the polynomial vs sqrt((a2/2)^2+(a3/4)^2)/(1+3a3/4) 0.06149 (+/-0.001) 0.06159 0
Farina 2000 (distortion rejected from the linear IR) THD floor of a purely linear path (gain 0.5), max over 100-2000 Hz 0 (+/-0.001) 0.00033 0
Bendat & Piersol, Random Data 4e Sec. 13.1.4 (Hilbert relation) Min-phase reconstruction of a strictly min-phase biquad, max err, rad 0 rad (+/-0 rad) 0 rad 0 rad
First-order allpass closed form (1-a^2)/(1+2a cos w+a^2) Group delay of the a = 0.5 allpass at w = pi/2, samples 0.6 (+/-0.00001) 0.6 0
All-pass decomposition of a pure latency (B&P Sec. 13.1.4) Excess group delay of a biquad delayed 7.25 samples, samples 7.25 (+/-0) 7.25 0
Spherical ground & barriers (Attenborough / Salomons / Bies): 100% (6/6)
Standard Quantity Expected (norm) Computed Δ Status
Attenborough 2e Eq. (2.40c) (spherical Q, hard-ground limit) abs(Q) as Z grows large (Rp -> 1 so (1 - Rp) -> 0 and Q -> 1) 1 (+/-0.000001) 1 0
Salomons 2001 Sec. 3.4 (two-ray field over a rigid ground) dL enhancement at small path difference (constructive, +6 dB) 6.0206 dB (+/-0.1 dB) 6.0205 dB 0 dB
Salomons 2001 Eq. (D.59) (plane-wave Rp, grazing incidence) Re(Rp) at grazing (hs, hr -> 0, cos(theta) -> 0 so Rp -> -1) -1 (+/-0.001) -1 0
Bies 5e Eq. (5.138) (Kurze-Anderson, N -> 0) Barrier attenuation at the shadow boundary N = 0 5 dB (+/-0 dB) 5 dB 0 dB
Bies 5e Eq. (5.138) (Kurze-Anderson, large-N slope) Delta(N=10) - Delta(N=1) vs the 10 lg(10) = 10 dB decade growth 10 dB (+/-0.5 dB) 9.8845 dB -0.116 dB
Attenborough 2e Eqs. (9.19)-(9.20) (rigid half-plane, shadow boundary) Exact thin-screen insertion loss at grazing (field halved, 6 dB) 6.0206 dB (+/-0.6 dB) 5.7932 dB -0.227 dB
Atmospheric refraction (Salomons rays / GFPE): 100% (3/3)
Standard Quantity Expected (norm) Computed Δ Status
Salomons Sec. 4.4 (ray turning height, linear profile) Turning height of a 10 deg ray vs Rc(1 - cos theta0) (circular arc), m 26.457 m (+/-0.1 m) 26.457 m 0 m
Salomons Eq. (3.4) (GFPE vs spherical-wave ground effect, homogeneous) PE relative level at 500 m over grassland vs Weyl-Van der Pol, dB -13.919 dB (+/-0.5 dB) -13.842 dB 0.077 dB
Salomons Eq. (3.4) (GFPE hard ground vs two-ray, homogeneous) PE relative level at 500 m over a rigid ground vs the coherent two-ray, dB 5.997 dB (+/-0.6 dB) 5.593 dB -0.405 dB

Tests & coverage — 23490 tests, 0 failures (✅ all green)
Python Version Tests Failures Coverage Status
macos-latest-3.13 3915 0 96.1% ✅ Passed
macos-latest-3.14 3915 0 96.1% ✅ Passed
ubuntu-latest-3.13 3915 0 96.1% ✅ Passed
ubuntu-latest-3.14 3915 0 96.1% ✅ Passed
windows-latest-3.13 3915 0 96.1% ✅ Passed
windows-latest-3.14 3915 0 96.1% ✅ Passed

Conformance harness: scripts/conformance_report.py · full CI artifacts

…ction

- ray_curvature_radius: reject a zero/non-finite gradient with abs(g) > 0
  instead of a float equality test (Sonar S1244); physics unchanged.
- _plot/environmental: hoist the duplicated 'Height [m]'/'Range [m]' axis
  labels into module constants (Sonar S1192).
- atmospheric_ray_paths: evaluate the travel-time sound speed at the folded
  (true, non-negative) ray height after the ground reflection, dropping the
  np.clip and improving the reflection-step travel time.
- atmospheric_parabolic_equation: store NaN (not +inf) in the singular
  source-range column so reductions and colormap autoscaling stay well-behaved.
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@jmrplens
jmrplens merged commit 80ba580 into main Jul 19, 2026
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@jmrplens
jmrplens deleted the feat/atmospheric-refraction branch July 19, 2026 17:12
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