Source: https://jmrplens.github.io/phonometry/reference/conformance/ phonometry's key differentiator is not the feature list but the proof behind it: every metric is implemented from the governing standard's text, and a **numerical conformance report** pins each check to a standard, a clause or table, the normative expected value and the value the library actually computes, with the delta and a pass/fail verdict. The report is an auto-generated document, regenerated by CI on **every pull request** (the build fails if it drifts from the code), so it is always in sync with the released library. The whole of it is reproduced below, transplanted verbatim at build time from [`docs/CONFORMANCE.md`](https://github.com/jmrplens/phonometry/blob/main/docs/CONFORMANCE.md). ## How to read it - **Filter classes**: the IEC 61260-1:2014 class verdict per filter architecture, with the measured relative attenuation at the *governing* band, the class-1 limit it must clear and the margin in dB. - **Frequency weightings**: A/C (IEC 61672-1 Table 3) and G (ISO 7196 A.3) deviations from the nominal curves, judged at the governing frequency with the applicable tolerance band and headroom. - **One conformance table per domain** (levels, psychoacoustics, room and building acoustics, sound power, materials, vibration, uncertainty, ...): `Standard | Quantity | Expected | Computed | Delta | Status`, where the expected values come from the standards' own worked examples or from closed forms synthesized to a known result. Every domain section is collapsible and stays collapsed while all of its rows pass; a section with any failing row opens automatically. On narrow screens the wide tables scroll sideways inside their own box. ## How it is generated The registry of checks lives in [`scripts/conformance_report.py`](https://github.com/jmrplens/phonometry/blob/main/scripts/conformance_report.py) and is run locally with `make conformance`. Expected values are single-sourced from the same reference tables the test suite enforces, so the report and the tests cannot disagree silently. This page is filled in from that same document by `make site-reports`, and CI fails if either the report or this copy of it drifts. For the design philosophy behind this approach, and a worked case study on IEC 61672-1 time weighting, see [Why phonometry](/phonometry/reference/why-phonometry/). Re-deriving the standards this closely also turns up defects in the published documents themselves: worked examples that contradict their own normative clauses, misprinted constants, broken cross-references. Every confirmed case, with its evidence and what the library does about it, is recorded in the [errata registry](/phonometry/reference/errata/). ## Numerical conformance report ✅ **427/427 conformance checks pass** across 53 domains and 278 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% (10/10)

| 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 | ✅ | | ANSI S1.4-1983 Tables IV/V | B-weighting (historical) deviation vs Type 0 limits (fs=48 kHz) | deviation within limits @ 200 Hz | -0.049 dB in [-0.70, +0.70] dB | headroom +0.651 dB | ✅ | | IEC 61012:1990 Table 1 / 2.2 | AU-weighting deviation vs separate-unit tolerances (fs=96 kHz) | deviation within limits @ 10000 Hz | -0.072 dB in [-1.00, +1.00] dB | headroom +0.928 dB | ✅ | | IEC 537:1976 (withdrawn) via NASA CR-3406 Table SLD-I | D-weighting response vs the published tabulated curve (fs=48 kHz) | abs(response - table) <= 0.2 dB (0.45 dB at 1600/2500 Hz) | -0.131 dB @ 8000 Hz (bound 0.20 dB) | headroom +0.069 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% (10/10)

| 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 Annex M | Full-STI worked example: printed MTF + speech/noise spectra -> STI | STI 0.76 (MTI row of step 4c) | STI 0.758 (max MTI dev 0.00) | -0.002 | ✅ | | 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 | ✅ |

✅ System measurement (Golay / Kirkeby / Mueller-Massarani): 100% (5/5)

| Standard | Quantity | Expected (norm) | Computed | Δ | Status | |:---|:---|:---|:---|:---|:---:| | Havelock 2008 Part I Ch. 6 (Xiang), Eq. (2) | Golay pair: sum of periodic autocorrelations = 2L*delta (L = 4096) | 0 (algebraic identity, +/-1e-10) | 0 | 0 | ✅ | | Havelock 2008 Part I Ch. 6 (Xiang), Eq. (4) | Golay chain recovers a delay+gain system IR (noiseless, exact) | 0 (machine precision, +/-1e-13) | 0 | 0 | ✅ | | Kirkeby & Nelson 1999 Eq. (17) / Mueller-Massarani 2001 Sec. 3.1 | In-band equalization residue equals eps/(|H|^2 + eps) bin by bin | 0 (closed form, +/-1e-12) | 0 | 0 | ✅ | | Kirkeby & Nelson 1999 (max of x/(x^2+eps) = 1/(2*sqrt(eps))) | Out-of-band inverse-filter gain within the regularization cap | <= -6.021 dB (analytic cap) | -6.034 dB | headroom +0.013 dB | ✅ | | Mueller-Massarani 2001 Secs. 4.2-4.3 (group-delay synthesis) | Shaped sweep's Welch spectrum follows the pink target, in-band | 0 dB in-band deviation (+/-0.5 dB) | 0.0652 dB | 0.065 dB | ✅ |

✅ Intensity & sound power: 100% (6/6)

| 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 4871:1996 clause 3.15 / Annex B | Declared L_WAd = L_WA + K_WA (Annex B, L_WA=88, K_WA=2) | 90 dB (+/-0 dB) | 90 dB | 0 dB | ✅ | | ISO 4871:1996 clause 6.2 | Single-machine verification boundary L_1 <= L_WAd | L_1=90 verified, L_1=91 rejected (L_WAd=90) | 90->True, 91->False | boundary L_1 = L_WAd | ✅ | | ISO 3741:2010 Eq. 20 | Reverberation-room method inverts to a known LW | 0 dB error | 0 dB | 0 dB | ✅ |

✅ Room & building acoustics: 100% (52/52)

| 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 21 printed rows; (B.1) reduces to (B.2) | max abs(Kc - Table B.1) <= 0,05 dB (1 dp print) | 0.047 dB (B.1 vs B.2: 4.33e-04 dB) | 0.047 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 16251-1 / ISO 717-2 (Foret et al. 2011, carpet) | Measured textile-carpet improvement rates to ΔLw = 29 dB | ΔLw = 29 dB (paper, ISO 16251-1) | ΔLw = 29 dB | +0 dB | ✅ | | 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 | ✅ | | ISO 12354-1:2017 Formula (20) vs Hopkins Eq. 2.201 (6 mm glass) | Flanking critical frequency (c0²/1,8·cL·h) vs plate coincidence (c0²/2π · sqrt(m''/B')) | 2107.4 Hz (+/-1%) | 2123.5 Hz | 16.156 Hz | ✅ | | 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) | 120 dB (+/-0 dB) | 120 dB | 0 dB | ✅ | | 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 | 0 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% (14/14)

| 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) | Directional diffusion coefficient (QRD, model arc) | 0.1099 (+/-0) | 0.1099 | 0 | ✅ | | ISO 17497-2:2012 Formula (5) | Directional diffusion coefficient (flat reference) | 0.0049 (+/-0) | 0.0049 | 0 | ✅ | | ISO 17497-2:2012 Formula (7) | Normalised diffusion coefficient (QRD, model arc) | 0.1055 (+/-0) | 0.1055 | 0 | ✅ | | Cox & D'Antonio 3e App. B (2D BEM) | Normalised diffusion d_n, N=7 QRD x 6 periods, 200 Hz band (low-band anchor) | 0 (+/-0.015) | 0 | 0 | ✅ | | Cox & D'Antonio 3e App. B (2D BEM) | Normalised diffusion d_n, N=7 QRD x 6 periods, 250 Hz band (low-band anchor) | 0.01 (+/-0.015) | 0.001 | -0.009 | ✅ | | Cox & D'Antonio 3e App. B (2D BEM) | Normalised diffusion d_n, N=7 QRD x 6 periods, 315 Hz band (low-band anchor) | 0.01 (+/-0.015) | 0.002 | -0.008 | ✅ | | Cox & D'Antonio 3e App. B (2D BEM) | Normalised diffusion d_n, N=7 QRD x 6 periods, 400 Hz band (low-band anchor) | 0.01 (+/-0.015) | 0.008 | -0.002 | ✅ | | ISO 17497-2:2012 Formula (8) | Zenith area factor (radians convention) | 1.57105 (+/-0) | 1.57105 | 0 | ✅ | | Cox & D'Antonio Eq (10.3) | QRD deepest well depth (N=7, f0=500 Hz) | 0.196 m (+/-0 m) | 0.196 m | 0 m | ✅ | | Cox & D'Antonio Eq (5.8) + ISO 17497-2 Formula (7) | Flat-panel predicted normalised diffusion (self-reference zero) | 0 (+/-0) | 0 | 0 | ✅ | | Cox & D'Antonio Eq (5.8) + ISO 17497-2 Formula (7) | QRD predicted normalised diffusion at 2 kHz (above flat panel) | 0.208 (+/-0) | 0.208 | 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 | ✅ |

✅ Impulsive-sound prominence (ISO/PAS 1996-3): 100% (2/2)

| Standard | Quantity | Expected (norm) | Computed | Δ | Status | |:---|:---|:---|:---|:---|:---:| | ISO/PAS 1996-3:2022 3.5 | Onset rate of a 30 dB ramp over 0.30 s | 100 dB/s (+/-0 dB/s) | 100 dB/s | 0 dB/s | ✅ | | ISO/PAS 1996-3:2022 Formula 3 | Adjustment KI of the ramp onset | 7.1176 dB (+/-0 dB) | 7.1176 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% (6/6)

| 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 | ✅ | | ISO 1999:2013 Annex C, Formulae (C.6) to (C.8) | NIPTS at 1/2/4 kHz, 90 dB, 30 yr, Q = 10 % (annex inputs) | 0, 9, 19 dB | 0, 9, 19 dB | 0 dB | ✅ | | ISO 1999:2013 Annex C, Formula (C.5) | Compressed 4 kHz shift, Formula (1) with the annex's H = 36 dB | 13.3 dB (+/-0.1 dB) | 13.3 dB | 0 dB | ✅ | | ISO 1999:2013 Annex C, Formula (C.11) | Hearing threshold level with age and noise, 1/2/4 kHz mean, Q = 10 % | 31.1 dB (+/-0.1 dB) | 31.1 dB | 0 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% (20/20)

| 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 60268-5:2003 (20.3/20.4) | Characteristic sensitivity level, 1 W into 8 ohm at 1 m (flat 90 dB) | 90 dB (+/-0.000001 dB) | 90 dB | 0 dB | ✅ | | IEC 60268-5:2003 (21.2) | Effective frequency range = -10 dB crossings (50 Hz / 18 kHz) | 50 Hz / 18000 Hz (ref -10 dB crossings) | 50.000 Hz / 18000.0 Hz | -0.000 / -0.000 Hz | ✅ | | IEC 60268-3:2013 (14.12.5) | 2nd-order harmonic distortion d2 (rel. total) | 0.099361 (+/-0.0001) | 0.099361 | 0 | ✅ | | IEC 60268-4:2014 (11.1/11.3) | Microphone sensitivity level, 12.5 mV/Pa -> 20 lg 0.0125 dB re 1 V/Pa | -38.0618 dB (+/-0.00001 dB) | -38.0618 dB | 0 dB | ✅ | | IEC 60268-4:2014 (12.2) | Effective frequency range = +/-3 dB tolerance crossings (40 Hz / 18 kHz) | 40 Hz / 18000 Hz (+/-3 dB tolerance crossings) | 40.000 Hz / 18000.0 Hz | 0.000 / -0.000 Hz | ✅ | | IEC 60268-4:2014 (13.2.2) | Directivity index of the ideal cardioid, 10 lg 3 dB (11.2.2 a integral) | 4.771213 dB (+/-0.005 dB) | 4.771214 dB | 0 dB | ✅ | | IEC 60268-4:2014 (17.2) | Equivalent noise level, 2.5 uV over 12.5 mV/Pa -> 200 uPa = 20 dB SPL | 20 dB SPL (+/-0 dB SPL) | 20 dB SPL | 0 dB SPL | ✅ | | 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% (12/12)

| 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 | ✅ | | IEC 60268-1:1985 Clause A2.1 / Table AII | 5 ms burst of 5 kHz tone at 48 kHz: gate RMS = A/sqrt(2) (integral periods) | 0.707107 (+/-0) | 0.707107 | 0 | ✅ | | Harris 1978 closed form (DFT-even Hann) | Hann window ENBW = n*sum(w^2)/sum(w)^2 = 3/2 exactly | 1.5 (+/-0) | 1.5 | 0 | ✅ | | Constant-power 1/n-octave kernel (closed form) | 1/3-octave smoothed line level = P*df/(f0*(2^(1/6)-2^(-1/6))) | 0.021592 (+/-1e-07%) | 0.021592 | 0 | ✅ | | Percival & Walden 1993, Table 382 | Slepian taper concentration lambda_14(31, 8/31), quadruple-precision table | 0.92943822082 (+/-0.000000000001) | 0.92943822082 | 0 | ✅ | | Percival & Walden 1993, Section 7.2 / Eq. (333) | Multitaper white-noise density = sigma^2/(fs/2), NW=4, K=7 tapers | 0.000977 (+/-3%) | 0.000963 | 0 | ✅ | | Percival & Walden 1993, Eq. (369a) tone calibration | Multitaper 'spectrum' scaling reads a sinusoid peak at A^2/2 | 4.5 (+/-0.01%) | 4.500003 | 0 | ✅ | | Percival & Walden 1993, Eq. (370b) | Adaptive multitaper dof -> 2K on white noise (weights -> uniform) | 14 (+/-2%) | 13.9847 | -0.015 | ✅ |

✅ Multiple-input coherence (Bendat & Piersol): 100% (5/5)

| Standard | Quantity | Expected (norm) | Computed | Δ | Status | |:---|:---|:---|:---|:---|:---:| | Bendat & Piersol, Random Data 4e Problem 7.2 / Eqs. (7.86)/(7.94) | Conditioned coherent output of the 2nd input abs(G2y.1)^2/G22.1 = 4/3 exactly | 1.333333333 (+/-0) | 1.333333333 | 0 | ✅ | | Bendat & Piersol, Random Data 4e Problem 7.2 / Eqs. (7.87)/(7.116) | Partial coherence gamma^2_2y.1 = 2/15 and multiple coherence = 0.7 | 0.7 (+/-0) | 0.7 | 0 | ✅ | | Bendat & Piersol, Random Data 4e Eq. (7.35) with Eqs. (6.40)/(6.41) | Multiple coherence of a known-SNR system: gamma^2_{y:x} = SNR/(1+SNR) | 0.8889 (+/-0.03) | 0.8913 | 0.002 | ✅ | | Bendat & Piersol, Random Data 4e Eq. (7.117) | Uncorrelated inputs: multiple coherence = sum of ordinary coherences | 0 (+/-0.02) | -0.0098 | -0.01 | ✅ | | Bendat & Piersol, Random Data 4e Eqs. (7.88)/(7.121) | Output-power decomposition Gyy = sum of Gvi + Gnn (exact) | 0 (+/-0.000000000001) | 0 | 0 | ✅ |

✅ Time-frequency analysis (Bendat & Piersol): 100% (3/3)

| Standard | Quantity | Expected (norm) | Computed | Δ | Status | |:---|:---|:---|:---|:---|:---:| | Bendat & Piersol, Random Data 4e Eq. (12.173) | Spectrogram of an on-bin tone reads its mean square A^2/2 in every column | 2 (+/-1e-07%) | 2 | 0 | ✅ | | Parseval + COLA identity (Hann taper, 75% overlap) | Time-integrated STFT power = time-domain energy of an interior burst | 0.236151 (+/-1e-10%) | 0.236151 | 0 | ✅ | | Bendat & Piersol, Random Data 4e Eqs. (11.128)-(11.130) | Zoom FFT tone amplitude = demodulate-decimate-DFT chain, machine precision | 0.7 (+/-1e-10%) | 0.7 | 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 + m*cos(2pi*fm*t) exactly | 0 (+/-0) | 0 | 0 | ✅ |

✅ Cepstrum, liftering and envelope spectrum (Havelock / B&P): 100% (3/3)

| Standard | Quantity | Expected (norm) | Computed | Δ | Status | |:---|:---|:---|:---|:---|:---:| | Havelock 2008 Ch. 27 Fig. 21 + Mercator series of ln(1+a*e^{-j*theta}) | Power-cepstrum height at the echo delay = reflection coefficient a | 0.4 (+/-0) | 0.4 | 0 | ✅ | | Havelock 2008 Ch. 87 Eq. (14): complex cepstrum, series term n = 2 | Second rahmonic of a reflection a = 0.4 equals -a^2/2 | -0.08 (+/-0) | -0.08 | 0 | ✅ | | Bendat & Piersol, Random Data 4e Sec. 13.3 (Fig. 13.11) | Envelope-spectrum line of an AM tone (A0 = 2, m = 0.35) at fm | 0.7 (+/-0.002) | 0.7 | 0 | ✅ |

✅ Time synchronous averaging (McFadden 1987): 100% (5/5)

| Standard | Quantity | Expected (norm) | Computed | Δ | Status | |:---|:---|:---|:---|:---|:---:| | McFadden 1987 Eq. 8 / Eq. 9: comb filter \|C(f)\| at a harmonic k/T | Comb-filter tooth height at a harmonic equals unity (any N) | 1 (+/-0) | 1 | 0 | ✅ | | McFadden 1987 Eq. 8: comb filter one quarter-order from a tooth, N = 2 | Comb-filter magnitude = 1/sqrt(2) at order 0.25 | 0.70710678 (+/-0) | 0.70710678 | 0 | ✅ | | McFadden 1987 Sec. 4 (Fig. 5): node selection, tone at 32.05 orders | N = 20 places a comb node on 32.05 orders (\|C\| = 0), not the power-of-2 N = 32 | 0 (+/-0.0000000001) | 0 | 0 | ✅ | | McFadden 1987 Eq. 5: exact recovery, integer samples per period | Noiseless periodic waveform (M = 256) recovered to machine precision | 0 (+/-0.0000000001) | 0 | 0 | ✅ | | McFadden 1987 Sec. 1: asynchronous-noise variance reduced by 1/N | Residual noise std of the average falls as sigma/sqrt(N), N = 64 | 0.125 (+/-15%) | 0.12414 | -0.001 | ✅ |

✅ Data qualification and Rice statistics (Bendat & Piersol): 100% (8/8)

| Standard | Quantity | Expected (norm) | Computed | Δ | Status | |:---|:---|:---|:---|:---|:---:| | Bendat & Piersol, Random Data 4e Example 4.4 | Reverse arrangements of the 20-observation sequence | 86 (+/-0) | 86 | 0 | ✅ | | Bendat & Piersol, Random Data 4e Table A.6 | Lower percentage point A(20; 0.975) at alpha = 0.05 | 64 (+/-0) | 64 | 0 | ✅ | | Bendat & Piersol, Random Data 4e Table A.6 | Upper percentage point A(20; 0.025) at alpha = 0.05 | 125 (+/-0) | 125 | 0 | ✅ | | Wald & Wolfowitz 1940 exact run distribution | Runs acceptance region for n1 = n2 = 10, alpha = 0.05: lower point | 6 (+/-0) | 6 | 0 | ✅ | | Wald & Wolfowitz 1940 exact run distribution | Runs acceptance region for n1 = n2 = 10, alpha = 0.05: upper point | 15 (+/-0) | 15 | 0 | ✅ | | Bendat & Piersol, Random Data 4e Example 5.13 / Eq. (5.195) | Zero-crossing rate of bandlimited noise (fc = 1 kHz, B = 400 Hz) | 2013 (+/-1%) | 2013 | -0.551 | ✅ | | Bendat & Piersol, Random Data 4e Example 5.12 | Apparent frequency of low-pass noise (B = 2 kHz) = 0.577 B | 1155 (+/-1%) | 1159 | 3.911 | ✅ | | Bendat & Piersol, Random Data 4e Example 5.14 / Eq. (5.206) | Prob[positive peak > 4 sigma] of a narrow bandwidth record | 0.000335 (+/-0.00001) | 0.000334 | 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% (15/15)

| 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 | ✅ | | EASA ANP database round-trip | Interpolated NPD level at a tabulated node vs the published ANP value, dB | 98.8 dB (+/-0 dB) | 98.8 dB | 0 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 | ✅ |

✅ Slow-sound perfect absorbers (Jimenez et al. Appl. Sci. 2017): 100% (3/3)

| Standard | Quantity | Expected (norm) | Computed | Δ | Status | |:---|:---|:---|:---|:---|:---:| | Jimenez et al. Appl. Sci. 2017 Eq. (9) | Critical coupling: alpha at the design frequency (300 Hz, normal) | 1 (+/-0.001) | 1 | 0 | ✅ | | Poiseuille limit (Stinson 1991) | Slit: j w rho_s -> 12 eta / h^2 as w -> 0 (h = 1.2 mm) | 153.3 Pa s/m2 (+/-0.1%) | 153.3 Pa s/m2 | 0 Pa s/m2 | ✅ | | Poiseuille limit (Stinson 1991) | Square duct: j w rho -> 28.454 eta / w^2 as w -> 0 (w = 3 mm) | 58.2 Pa s/m2 (+/-0.2%) | 58.2 Pa s/m2 | 0 Pa s/m2 | ✅ |

✅ 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% (7/7)

| 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 | ✅ | | Salomons 2001 Fig. D.3 (grassland ground dip, sigma = 200 kPa s/m2) | Minimum dL for hs = hr = 2 m, r = 100 m (dip near 395 Hz), dB | -12.7 dB (+/-0.3 dB) | -12.72 dB | -0.022 dB | ✅ | | 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 | ✅ |

✅ Panel & aperture sound insulation (Bies / Hopkins / Cremer): 100% (11/11)

| Standard | Quantity | Expected (norm) | Computed | Δ | Status | |:---|:---|:---|:---|:---|:---:| | Bies 5e Eq. 7.40 (mass law) | 6 dB per octave (500 -> 1000 Hz) | 6.0206 dB (+/-0.01 dB) | 6.02 dB | -0.001 dB | ✅ | | Bies 5e Eq. 7.40 (mass law) | 6 dB per doubling of mass | 6.0206 dB (+/-0.01 dB) | 6.02 dB | -0.001 dB | ✅ | | Bies 5e Eq. 7.42 (field incidence) | One-third-octave correction 5.5 dB | 5.5 dB (+/-0.001 dB) | 5.5 dB | 0 dB | ✅ | | Hopkins Eq. 2.201 / Bies Eq. 7.3 | Coincidence frequency, 6 mm glass | 2079 Hz (+/-3%) | 2107.3639 Hz | 28.364 Hz | ✅ | | Cremer Table 5.1 | Thin-plate point impedance Z = 8 sqrt(B' m'') | 2529.8221 N.s/m (+/-0 N.s/m) | 2529.8221 N.s/m | 0 N.s/m | ✅ | | Cremer Table 5.1 | Infinite-beam mobility phase -45 deg | -45 deg (+/-0 deg) | -45 deg | 0 deg | ✅ | | Hopkins Eq. 2.229 (Leppington/Maidanik) | Radiation efficiency at f = 2 fc | 1.4142 (+/-0) | 1.4142 | 0 | ✅ | | Bies Eq. 7.62 / Hopkins Eq. 4.73 | Mass-air-mass resonance f0, empty cavity | 76.9484 Hz (+/-0.5%) | 76.8521 Hz | -0.096 Hz | ✅ | | Bies Eq. 7.64 (double wall) | Below f0 = mass law of the combined mass | 11.6144 dB (+/-0 dB) | 11.6144 dB | 0 dB | ✅ | | Hopkins Eq. 4.92 (composite) | 1 % open area caps R at 10 lg(S/Sa) | 20 dB (+/-0.05 dB) | 19.9996 dB | 0 dB | ✅ | | Hopkins Eq. 4.99/4.101 (Gomperts slit) | Transmission maximum at first resonance | 1544.9615 Hz (+/-15 Hz) | 1542.9615 Hz | -2 Hz | ✅ |

✅ Bending-wave plate-junction transmission (Cremer / Craik / Hopkins): 100% (6/6)

| Standard | Quantity | Expected (norm) | Computed | Δ | Status | |:---|:---|:---|:---|:---|:---:| | Hopkins Eq. 5.12 (identical plates) | X-junction corner tau12(0 deg) = 1/8 | 0.125 (+/-0) | 0.125 | 0 | ✅ | | Hopkins Eqs 5.12 + 5.6 (identical plates) | X-junction corner angular average = 1/12 | 0.0833 (+/-0) | 0.0833 | 0 | ✅ | | Hopkins Eqs 5.12 + 5.6 (identical plates) | L-junction corner angular average = 1/3 | 0.3333 (+/-0) | 0.3333 | 0 | ✅ | | Hopkins Eq. 5.14 (identical plates) | In-line junction tau12(0 deg) = 1 | 1 (+/-0) | 1 | 0 | ✅ | | Hopkins Eq. 5.7 (SEA consistency) | X-junction reciprocity tau_bar_12 / tau_bar_21 = chi | 1.5 (+/-0) | 1.5 | 0 | ✅ | | Hopkins Eq. 5.116 (identical plates, fc_j = f_ref) | X-junction vibration reduction index = 10 lg(12) | 10.7918 dB (+/-0 dB) | 10.7918 dB | 0 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 | -16.368 dB (+/-0.5 dB) | -16.402 dB | -0.035 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 | ✅ |

✅ Electroacoustics: 100% (6/6)

| Standard | Quantity | Expected (norm) | Computed | Δ | Status | |:---|:---|:---|:---|:---|:---:| | Beranek & Mellow 2e Eq. (13.117) | Piston resistance R1(x) = 1 - 2 J1(x)/x at x = 2ka = 2 | 0.423275 (+/-0.00001) | 0.423275 | 0 | ✅ | | Beranek & Mellow 2e Eq. (13.118) | Piston reactance X1(x) = 2 H1(x)/x at x = 2ka = 2 | 0.646764 (+/-0.00001) | 0.646764 | 0 | ✅ | | Beranek & Mellow 2e Eq. (13.117) (low-frequency limit) | R1 -> (ka)^2/2 as ka -> 0 (x = 0.02, ka = 0.01) | 0.00005 (+/-0.01%) | 0.00005 | 0 | ✅ | | Beranek & Mellow 2e Eq. (4.151) | Radiation mass M = 8 rho a^3 / 3 (a = 0.1 m, rho = 1.206) | 0.003216 kg (+/-0 kg) | 0.003216 kg | 0 kg | ✅ | | Beranek & Mellow 2e Eq. (13.102), Table 14.1 | First directivity null at ka sin(theta) = 3.8317 (first zero of J1) | 0 (+/-0.000001) | 0 | 0 | ✅ | | Beranek & Mellow 2e §4.19 (half-space baffle) | Directivity index DI -> 10 lg 2 = 3.01 dB as ka -> 0 | 3.0103 dB (+/-0.001 dB) | 3.0103 dB | 0 dB | ✅ |

✅ Industrial noise control: 100% (9/9)

| Standard | Quantity | Expected (norm) | Computed | Δ | Status | |:---|:---|:---|:---|:---|:---:| | Bies 5e Eq. (8.111) | Expansion-chamber peak TL = 10 lg[1 + (1/4)(m - 1/m)^2], m = 4 at kL = pi/2 | 6.5472 dB (+/-0 dB) | 6.5472 dB | 0 dB | ✅ | | Bies 5e Eq. (8.111) | Expansion-chamber trough TL = 0 at kL = pi (chamber transparent) | 0 dB (+/-0 dB) | 0 dB | 0 dB | ✅ | | Bies 5e Eq. (8.44) / Example 8.1 | Quarter-wave tube tuning f = c/(4 l_e), l_e = 1.516 m -> 56.6 Hz | 56.6 Hz (+/-0.1 Hz) | 56.6 Hz | 0.003 Hz | ✅ | | Bies 5e Eq. (8.46) | Helmholtz resonance f0 = (c/2pi) sqrt(S/(l_e V)) (S=1e-4, l_e=0.02, V=1e-3) | 122.067 Hz (+/-0 Hz) | 122.067 Hz | 0 Hz | ✅ | | Bies 5e Eq. (8.73) | Side-branch TL = 20 lg abs(1 + rho c/(2 Sd Zb)) (QWT branch, closed form) | 0.1638 dB (+/-0 dB) | 0.1638 dB | 0 dB | ✅ | | Bies 5e Eqs. (8.141)/(8.148) (four-pole insertion loss) | Insertion loss = transmission loss for the anechoic reference Zs=Zr=rho c/S | 6.2498 dB (= TL) | 6.2498 dB | 0 dB | ✅ | | Bies 5e Eq. (8.275) (Wells' plenum method) | Plenum TL = -10 lg[S_out(cos0/pi r^2 + (1-a)/(Sw a))] (S_out=.1,r=1,Sw=20,a=.2) | 12.8541 dB (+/-0 dB) | 12.8541 dB | 0 dB | ✅ | | Bies 5e Table 8.14 (ASHRAE end reflection, flush) | Duct end reflection D = 200 mm at 125 Hz = 10 dB (table node) | 10 dB (+/-0 dB) | 10 dB | 0 dB | ✅ | | Bies 5e Eqs. (7.103), (7.111) (enclosure, fully absorbing limit) | Enclosure correction C -> 10 lg 0.3 = -5.23 dB as alpha_i -> 1 | -5.2288 dB (+/-0.001 dB) | -5.2288 dB | 0 dB | ✅ |