materials.absorption_uncertainty

Measurement uncertainty for sound absorption (ISO 12999-2:2020).

Companion of the sound-insulation uncertainty of phonometry.building_uncertainty (ISO 12999-1). This part gives the standard uncertainty u of the quantities produced by a reverberation-room absorption measurement and its ratings:

• the sound absorption coefficient αs and the equivalent sound absorption area AT measured according to ISO 354, in one-third-octave bands (Clause 5, Table 1);
• the practical sound absorption coefficient αp determined according to ISO 11654, in octave bands (Clause 6, Table 2);
• the single-number weighted sound absorption coefficient αw (ISO 11654) and single-number rating DLα,NRD (EN 1793-1) (Clause 7).

The standard uncertainty is estimated by the reproducibility standard deviation σR (different laboratories) or the repeatability standard deviation σr (same location, operator and equipment), both derived from inter-laboratory tests to ISO 5725. Where specimen-specific uncertainty data exist they take precedence (Clause 4).

Band formulae (Clause 5-6). For the absorption coefficient σR = m·α + n (Formula (1)/(4)); for the equivalent area σR = m·AT + n·S with S = 10 m² (Formula (2)); the repeatability value is σr = 0,6·σR (Formula (3)/(5)). m and n are the frequency-dependent constants of Table 1 (one-third-octave, 63-5000 Hz) and Table 2 (octave, 250-4000 Hz).

Single numbers (Clause 7). αw: σR = 0,035 (Formula (6)), σr = 0,020 (Formula (7)). DLα,NRD: σR = 0,10·DLα,NRD (Formula (8)), σr = 0,02·DLα,NRD (Formula (9)).

Reporting (Clause 8). The expanded uncertainty is U = k·u (Formula (10)) with the coverage factor k of Table 3 (Gaussian assumption). The reported U is rounded to two decimal digits for absorption coefficients and one decimal digit for the equivalent area and DLα,NRD; the code keeps the exact U and exposes the rounded view through AbsorptionUncertaintyResult.reported_expanded_uncertainty.

Auto-generated from the source docstrings by scripts/generate_api_docs.py (make api-docs). Do not edit by hand.

absorption_coverage_factor

absorption_coverage_factor(confidence: float = 0.95) -> float

Return the coverage factor k for a confidence level (Table 3).

Parameters

Name	Description
confidence	Confidence level as a fraction; one of 0.68, 0.80, 0.90, 0.95, 0.99, 0.999 (Table 3, Gaussian measurand).

Raises

Exception	When
ValueError	Confidence level not tabulated in Table 3.

AbsorptionUncertaintyResult

AbsorptionUncertaintyResult(
    quantity: str,
    condition: str,
    frequencies: np.ndarray,
    values: np.ndarray,
    standard_uncertainty: np.ndarray,
    coverage_factor: float,
    expanded_uncertainty: np.ndarray,
)

Standard and expanded uncertainty of an absorption quantity (ISO 12999-2).

For the single-number quantities (αw, DLα,NRD) the frequency and value arrays are empty and the uncertainty arrays hold a single element.

Attributes

Name	Description
quantity	"absorption_coefficient", "equivalent_area", "practical_coefficient", "weighted_coefficient" or "single_number_rating".
condition	"reproducibility" (σR) or "repeatability" (σr).
frequencies	Band centre frequencies, in Hz (empty for single numbers).
values	The input quantity per band (empty for single numbers).
standard_uncertainty	Standard uncertainty u (σR/σr), one per band.
coverage_factor	Coverage factor k (Table 3).
expanded_uncertainty	Exact U = k·u (Formula (10)), one per band.

AbsorptionUncertaintyResult.lower

property

Lower interval bound value − U (exact U).

AbsorptionUncertaintyResult.plot()

AbsorptionUncertaintyResult.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the quantity with its ±U uncertainty ribbon (band quantities).

Requires matplotlib (pip install phonometry[plot]); returns the Axes.

AbsorptionUncertaintyResult.reported_expanded_uncertainty

property

U rounded for reporting (Clause 8): two decimals for absorption coefficients, one decimal for the equivalent area and DLα,NRD.

AbsorptionUncertaintyResult.upper

property

Upper interval bound value + U (exact U).

equivalent_area_uncertainty

equivalent_area_uncertainty(
    area: float | Sequence[float] | np.ndarray,
    frequencies: float | Sequence[float] | np.ndarray,
    *,
    condition: str = 'reproducibility',
    confidence: float = 0.95,
) -> AbsorptionUncertaintyResult

Uncertainty of the ISO 354 equivalent sound absorption area AT (Clause 5).

σR = m·AT + n·S with S = 10 m² (Formula (2)) per one-third-octave band; σr = 0,6·σR (Formula (3)).

Parameters

Name	Description
area	Equivalent sound absorption area AT per band, in m².
frequencies	One-third-octave midband frequencies in Hz (Table 1), aligned with area.
condition	"reproducibility" (default) or "repeatability".
confidence	Confidence level for the coverage factor k (Table 3).

Raises

Exception	When
ValueError	Mismatched shapes, an untabulated frequency, an unknown condition or an untabulated confidence.

practical_coefficient_uncertainty

practical_coefficient_uncertainty(
    alpha_p: float | Sequence[float] | np.ndarray,
    frequencies: float | Sequence[float] | np.ndarray,
    *,
    condition: str = 'reproducibility',
    confidence: float = 0.95,
) -> AbsorptionUncertaintyResult

Uncertainty of the ISO 11654 practical absorption coefficient αp (Clause 6).

σR = m·αp + n (Formula (4)) per octave band; σr = 0,6·σR (Formula (5)).

Parameters

Name	Description
alpha_p	Practical sound absorption coefficient αp per band.
frequencies	Octave midband frequencies in Hz (Table 2, 250-4000), aligned with alpha_p.
condition	"reproducibility" (default) or "repeatability".
confidence	Confidence level for the coverage factor k (Table 3).

Raises

Exception	When
ValueError	Mismatched shapes, an untabulated frequency, an unknown condition or an untabulated confidence.

single_number_rating_uncertainty

single_number_rating_uncertainty(
    dl_alpha: float,
    *,
    condition: str = 'reproducibility',
    confidence: float = 0.95,
) -> AbsorptionUncertaintyResult

Uncertainty of the EN 1793-1 single-number rating DLα,NRD (Clause 7).

σR = 0,10·DLα,NRD (Formula (8)), σr = 0,02·DLα,NRD (Formula (9)).

Parameters

Name	Description
dl_alpha	Single-number rating DLα,NRD, in dB (non-negative).
condition	"reproducibility" (default) or "repeatability".
confidence	Confidence level for the coverage factor k (Table 3).

Raises

Exception	When
ValueError	Negative dl_alpha, unknown condition or an untabulated confidence.

sound_absorption_coefficient_uncertainty

sound_absorption_coefficient_uncertainty(
    alpha: float | Sequence[float] | np.ndarray,
    frequencies: float | Sequence[float] | np.ndarray,
    *,
    condition: str = 'reproducibility',
    confidence: float = 0.95,
) -> AbsorptionUncertaintyResult

Uncertainty of the ISO 354 sound absorption coefficient αs (Clause 5).

σR = m·αs + n (Formula (1)) per one-third-octave band; σr = 0,6·σR (Formula (3)).

Parameters

Name	Description
alpha	Sound absorption coefficient αs per band.
frequencies	One-third-octave midband frequencies in Hz (Table 1, 63-5000), aligned with alpha.
condition	"reproducibility" (default) or "repeatability".
confidence	Confidence level for the coverage factor k (Table 3).

Raises

Exception	When
ValueError	Mismatched shapes, an untabulated frequency, an unknown condition or an untabulated confidence.

weighted_coefficient_uncertainty

weighted_coefficient_uncertainty(
    alpha_w: float = 0.0,
    *,
    condition: str = 'reproducibility',
    confidence: float = 0.95,
) -> AbsorptionUncertaintyResult

Uncertainty of the ISO 11654 weighted absorption coefficient αw (Clause 7).

The standard uncertainty is a constant: σR = 0,035 (Formula (6)), σr = 0,020 (Formula (7)), independent of the value.

Parameters

Name	Description
alpha_w	Weighted sound absorption coefficient αw (carried through for the reported interval; does not affect u).
condition	"reproducibility" (default) or "repeatability".
confidence	Confidence level for the coverage factor k (Table 3).

Raises

Exception	When
ValueError	Unknown condition or an untabulated confidence.