hearing.real_ear_attenuation

Real-ear attenuation of a hearing protector and its uncertainty (ISO 4869-1:2018).

ISO 4869-2 starts from a grid of attenuations, one per subject per octave band, and this is where that grid comes from. ISO 4869-1 measures it subjectively: each of sixteen test subjects finds their threshold of hearing twice for every test signal, once with open ears and once with the protector in place, and the attenuation of that subject in that band is the difference (4.6.2):

The test signals are one-third-octave bands of pink noise centred on the octave frequencies 125 Hz to 8 kHz, with 63 Hz optional (4.1). The method measures at threshold, so it describes a passive protector at any level but underestimates one whose attenuation depends on level (Clause 1).

What is reported (4.6.3, Clause 6). The individual attenuations, and per test signal their mean $m$ and standard deviation $s$, together with the expanded uncertainty of the mean. The uncertainty is the subject of the normative Annex A, which models the attenuation as the measured value plus three zero-mean input quantities (Formula (A.1)): the method (subject group, fitting, threshold determination, tester, specimen), the test equipment and the environment, each normal with a sensitivity coefficient of 1. Within one laboratory the combined standard uncertainty of a given measurement is the standard deviation of the mean (A.2),

which is what real_ear_attenuation returns. Table A.2 prints typical values of the three components within a laboratory and Table B.2 between laboratories, for earplugs and earmuffs in three frequency ranges; REAT_WITHIN_LABORATORY_UNCERTAINTY and REAT_BETWEEN_LABORATORY_UNCERTAINTY carry the components, and the combined and expanded values are derived from them rather than copied, which reproduces every cell the two tables print.

Are two measurements different? (Annex B). Two mean attenuations differ significantly at the 5 % level when their difference exceeds the root sum of squares of their expanded uncertainties (B.1.2),

which for two equal uncertainties is $\sqrt{2}{U}_{95}$, the minimum difference of B.1.1 and B.2. assess_attenuation_difference applies it band by band and minimum_significant_difference gives the second form. B.1.1 and B.2 evaluate it on the rounded $U_{95}$ their tables print, and say so: “the expanded measurement uncertainty … is 2,3 dB. The minimum difference is thus $\sqrt{2}$ × 2,3 dB = 3,3 dB”. From the unrounded 2,27 dB it is 3,21 dB, and from the unrounded 6,62 dB of Table B.2 it is 9,37 dB rather than 9,3 dB; both are the same rule, fed a different precision.

The sound field (4.2.2). The test room is qualified with the subject absent: the level 15 cm from the reference point along the three axes stays within ±2,5 dB of the level at it, the two ear-side positions within 3 dB of each other, and from 500 Hz up a directional microphone rotated through 360° sees a variation no larger than Table 1 allows for its free-field rejection. check_reat_sound_field judges those three conditions, and its verdict only passes a room whose directionality was measured: without the rotation, b) is not judged and the room is not shown to qualify.

Clause, formula and table numbers refer to ISO 4869-1:2018(E).

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

allowable_field_variation(free_field_rejection_db: float) -> float

How much a rotated directional microphone may see vary (Table 1).

Parameters

Returns: The allowable variation of the sound-field level, in dB.

Raises

assess_attenuation_difference(
    first: ArrayLike | RealEarAttenuationResult,
    second: ArrayLike | RealEarAttenuationResult,
    *,
    first_expanded_uncertainty_db: ArrayLike | None = None,
    second_expanded_uncertainty_db: ArrayLike | None = None,
    frequencies: ArrayLike | None = None,
) -> AttenuationDifferenceResult

Do two attenuation measurements differ significantly? (Annex B).

Annex B asks it of two tests of the same earmuff in two configurations (B.1.2), of two earplugs in one laboratory (B.1.1) and of one earplug in two laboratories (B.2), and answers band by band the same way: the means differ significantly at the 5 % level when

Each measurement is either a RealEarAttenuationResult, which carries its own $U_{95}$ from its own data (B.1.2), or its mean attenuations with an uncertainty given alongside, such as the typical one reat_expanded_uncertainty reads from Table A.2 or B.2 (B.1.1, B.2).

Parameters

Returns: AttenuationDifferenceResult.

Raises

AttenuationDifferenceResult(
    difference_db: np.ndarray,
    criterion_db: np.ndarray,
    significant: np.ndarray,
    first_mean_db: np.ndarray,
    second_mean_db: np.ndarray,
    first_expanded_uncertainty_db: np.ndarray,
    second_expanded_uncertainty_db: np.ndarray,
    frequencies: np.ndarray,
)

Whether two mean attenuations differ significantly, band by band (B.1.2).

Attributes

property

Whether the two measurements differ significantly in any band.

Returns: True when at least one band’s difference exceeds its criterion.

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

Draw each band’s difference against the criterion it has to beat.

Parameters

Returns: The axes.

property

The test signals at which the two measurements differ, in hertz.

Returns: The centre frequencies of the significant bands.

check_reat_sound_field(
    position_levels_db: Mapping[str, ArrayLike],
    reference_levels_db: ArrayLike,
    *,
    rotation_levels_db: ArrayLike | None = None,
    free_field_rejection_db: float | None = None,
    frequencies: ArrayLike | None = None,
) -> ReatSoundFieldCheck

Is the sound field of the test site diffuse enough? (4.2.2).

Measured with the subject and the chair absent (4.2.1):

• a) the level at each of the six positions 15 cm from the reference point, front and back, left and right, up and down, stays within ±2,5 dB of the level at the reference point, and the right and left positions within 3 dB of each other;
• b) from the 500 Hz test signal up, a directional microphone rotated through 360° in the horizontal plane at the reference point sees the level vary by no more than Table 1 allows for its free-field rejection (allowable_field_variation).

The reverberation time of 4.2.3 and the ambient noise of 4.2.4 are separate requirements of the test site and are not judged here.

Parameters

Returns: ReatSoundFieldCheck.

Raises

minimum_significant_difference(
    expanded_uncertainty_db: ArrayLike,
) -> float | np.ndarray

The smallest difference between two means that is significant (B.1.1).

For two measurements with the same expanded uncertainty the criterion of B.1.2 reduces to

and two means that differ by more than that differ significantly at the 95 % confidence level. B.1.1 and B.2 evaluate it on the uncertainty their tables print rounded to one decimal, and say so: with the 2,3 dB of Table A.2 it is 3,3 dB, where the unrounded 2,27 dB gives 3,21 dB. Feed this the value the comparison should rest on.

Parameters

Returns: $\sqrt{2}{U}_{95}$, in dB, a float for a scalar input and an array otherwise.

Raises

ProtectorUncertaintyBudget(
    method_db: float,
    equipment_db: float,
    environment_db: float,
)

The three standard uncertainties of a hearing protector measurement.

The budget of Table A.1: each component is normally distributed with a mean of zero and a sensitivity coefficient of 1, so the combined standard uncertainty is their root sum of squares (Formula (A.2)) and the expanded one is twice that. ISO 4869-6:2019 Annex A uses the same model for the active insertion loss of an active noise reduction earmuff.

Attributes

property

$u=\sqrt{u_{\mathrm{meth}}^2+u_{\mathrm{eq}}^2+u_{\mathrm{env}}^2}$, in dB.

Returns: The combined standard uncertainty, unrounded.

property

$U_{95}=2u$, in dB.

Returns: The expanded uncertainty for a 95 % coverage, unrounded.

real_ear_attenuation(
    attenuation_db: ArrayLike | None = None,
    *,
    open_threshold_db: ArrayLike | None = None,
    occluded_threshold_db: ArrayLike | None = None,
    frequencies: ArrayLike | None = None,
) -> RealEarAttenuationResult

The attenuation of a protector, its spread and its uncertainty (4.6, A.2).

Give the individual attenuations, or the two thresholds they come from (4.6.2):

and this returns, per test signal, the mean, the standard deviation over the subjects, the standard uncertainty of the mean and the expanded uncertainty of Annex A:

Everything is computed at full precision; Tables A.3 and B.1 round to one decimal afterwards, and so should a report. The two thresholds only need to share a reference: a threshold in sound pressure level and one in hearing level give the same difference.

Parameters

Returns: RealEarAttenuationResult.

Raises

RealEarAttenuationResult(
    attenuation_db: np.ndarray,
    mean_db: np.ndarray,
    standard_deviation_db: np.ndarray,
    standard_uncertainty_db: np.ndarray,
    expanded_uncertainty_db: np.ndarray,
    frequencies: np.ndarray,
    subjects: int,
)

The attenuation of a hearing protector on a panel of subjects (4.6).

Attributes

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

Draw the mean attenuation the way Clause 6 l) asks for it.

Increasing attenuation points downwards and, on a figure this creates, 50 dB on the vertical axis spans one decade on the horizontal one (IEC 60263). The individual attenuations are drawn faint behind the mean, and the expanded uncertainty as bars on it.

Parameters

Returns: The axes.

Constant (mapping).

REAT_BETWEEN_LABORATORY_UNCERTAINTY = {'earplug': {'below 250 Hz': ProtectorUncertaintyBudget(method_db=4.0, equipment_db=0.3, environment_db=0.8), '250 Hz up to 4 kHz': ProtectorUncertaintyBudget(method_db=3.2, equipment_db=0.3, environment_db=0.8), 'above 4 kHz': ProtectorUncertaintyBudget(method_db=3.2, equipment_db=0.3, environment_db=0.8)}, 'earmuff': {'below 250 Hz': ProtectorUncertaintyBudget(method_db=1.8, equipment_db=0.3, environment_db=0.8), '250 Hz up to 4 kHz': ProtectorUncertaintyBudget(method_db=2.3, equipment_db=0.3, environment_db=0.8), 'above 4 kHz': ProtectorUncertaintyBudget(method_db=3.2, equipment_db=0.3, environment_db=0.8)}}

reat_expanded_uncertainty(
    frequencies: ArrayLike,
    *,
    protector: str,
    between_laboratories: bool = False,
) -> np.ndarray

The typical $U_{95}$ of a mean attenuation, band by band (A.2, B.2).

Reads the budget of Table A.2 (within one laboratory) or Table B.2 (between laboratories) for the protector type and the frequency range each test signal falls in, and returns its expanded uncertainty at full precision. These are the typical values B.1.1 and B.2 draw on when no data of a specific measurement are at hand; the text of both uses them rounded to one decimal, as the tables print them (see minimum_significant_difference).

Parameters

Returns: $U_{95}$ per band, in dB.

Raises

Constant (tuple).

REAT_FIELD_VARIATION_LIMITS = ((25.0, 20.0), (20.0, 15.0), (15.0, 10.0), (10.0, 5.0))

Constant (tuple).

REAT_FREQUENCY_RANGES = ('below 250 Hz', '250 Hz up to 4 kHz', 'above 4 kHz')

Constant (mapping).

REAT_WITHIN_LABORATORY_UNCERTAINTY = {'earplug': {'below 250 Hz': ProtectorUncertaintyBudget(method_db=1.5, equipment_db=0.2, environment_db=0.5), '250 Hz up to 4 kHz': ProtectorUncertaintyBudget(method_db=1.0, equipment_db=0.2, environment_db=0.5), 'above 4 kHz': ProtectorUncertaintyBudget(method_db=1.5, equipment_db=0.2, environment_db=0.5)}, 'earmuff': {'below 250 Hz': ProtectorUncertaintyBudget(method_db=1.0, equipment_db=0.2, environment_db=0.5), '250 Hz up to 4 kHz': ProtectorUncertaintyBudget(method_db=0.6, equipment_db=0.2, environment_db=0.5), 'above 4 kHz': ProtectorUncertaintyBudget(method_db=1.0, equipment_db=0.2, environment_db=0.5)}}

ReatSoundFieldCheck(
    frequencies: np.ndarray,
    position_deviation_db: np.ndarray,
    left_right_difference_db: np.ndarray,
    rotation_variation_db: np.ndarray,
    allowable_variation_db: float | None,
    positions: tuple[str, ...] = ('front', 'back', 'left', 'right', 'up', 'down'),
)

Whether the test site’s sound field qualifies for ISO 4869-1 (4.2.2).

Attributes

4.2.2 b) is a requirement of the clause, not an option: a check made without the rotation leaves it unjudged whenever a band reaches 500 Hz, directionality_judged says so, and passes is False until it is judged. uniform and balanced still give the verdict of a) on its own.

property

Per band, whether right and left differ by 3 dB at most (4.2.2 a)).

Returns: One boolean per band.

property

Per band, whether the rotation stays within Table 1 (4.2.2 b)).

Bands the clause does not reach, below 500 Hz, count as meeting it. With no rotation given nothing was measured, every band reads True here and directionality_judged is False.

Returns: One boolean per band.

property

Whether 4.2.2 b) was judged.

Returns: True when a rotation was given, or when no test signal reaches the 500 Hz from which b) applies.

property

Whether the sound field qualifies for 4.2.2, a) and b) both judged.

Returns: True when every band meets a) and b); False when a band fails either, or when b) was not judged.

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

Draw each condition of 4.2.2 against its limit, band by band.

Parameters

Returns: The axes.

property

Per band, whether all six positions stay within ±2,5 dB (4.2.2 a)).

Returns: One boolean per band.