emission.reference_sound_source

Reference sound sources: the performance requirements and the calibration of ISO 6926:2016.

A reference sound source is the yardstick of every comparison method of the ISO 3740 family: ISO 3741 in a reverberation room, ISO 3747 in situ, ISO 9295 in the 16 kHz octave band. ISO 6926 says what a source must do to serve (clause 5) and how its sound power levels are calibrated (clauses 8 to 10).

Requirements (clause 5). The sound power output is steady: the standard deviation under repeatability conditions of three repeated sound power levels or five repeated sound pressure levels,

with $\overline{L_X}$ the energy average of the $N$ repetitions, does not exceed Table 1 (0,8 dB from 50 Hz to 80 Hz, 0,4 dB from 100 Hz to 160 Hz, 0,2 dB from 200 Hz to 20 kHz), and over the declared range of its electrical or mechanical supply (the line voltage, say) no one-third octave band varies by more than 0,3 dB either way. The spectrum is broadband: from 100 Hz to 10 000 Hz every one-third octave band lies within a range of 12 dB and within 3 dB of its neighbours, and 16 dB and 4 dB over a range extended beyond it (5.4). The directivity index $D_{\mathrm{I}i}=L_{pi}-\overline{L_p}$ (3.9) does not exceed +6 dB in any band from 100 Hz to 10 000 Hz (5.5), unless the source is labelled for reverberation rooms only. Recalibration is due when a band has moved by more than 2,83 times Table 1 between two checks (5.6).

Calibration in a hemi-anechoic room (clause 8). The room meets the broadband qualification of ISO 3745 Annex A (8.1), the source stands on the reflecting plane and the levels are measured over a hemisphere of radius 2 m (8.2.1). The sound power level under the reference meteorological conditions of clause 4 (23,0 degC, 101,325 kPa) is

with $C_1=-10\lg (p_{\mathrm{s}}/p_{\mathrm{s},0})+5\lg (\theta /{\theta }_0)$, ${\theta }_0$ = 314 K, the radiation impedance correction $C_2$ from the manufacturer or from Annex A, and the air absorption $C_3=A_0(1,0053-0,0012A_0{)}^{1,6}$ with $A_0=a(f)r$. Annex A gives $C_2=-10\lg (p_{\mathrm{s}}/p_{\mathrm{s},0})+n\lg (\theta /{\theta }_1)$, ${\theta }_1$ = 296 K, with $n$ = 15 for a monopole below the knee frequency $f_{\mathrm{k}}=c/(2\pi d_0)$, 5 for a monopole at or above it, 25 for an aerodynamic dipole at or above it and 7,5 when the radiation is unknown. Annex B replaces the 50 Hz, 63 Hz and 80 Hz bands by sound intensity levels when those agree with the pressure levels within Table B.1 from 50 Hz to 315 Hz. Table 2 gives the reproducibility standard deviation from which clause 11 builds the expanded uncertainty.

The calibration is consumed where a comparison method asks for $L_{W(\mathrm{RSS})}$: sound_power_comparison, sound_energy_comparison, sound_power_in_situ, sound_energy_in_situ and high_frequency_sound_power_comparison accept a ReferenceSourceCalibration where they accept the levels, and read the bands they need from it. The calibration holds $L_W$ under the reference meteorological conditions, where $C_2$ carried the power the source radiated during the calibration (8.4). ISO 3741 wants $L_{W(\mathrm{RSS})}$ “corrected to the meteorological conditions at the time of test” (Formulae (21) and (31)), and ISO 9295 carries its levels to the reference conditions as ISO 3741 does (10.1), so for those methods the calibration is read as $L_W-C_2$, with $C_2$ evaluated at the test by the same formula the calibration used, as 8.4 asks (ReferenceSourceCalibration.sound_power_level_at with the test’s temperature and pressure). ISO 3747 instead corrects the reference source’s measured pressure levels “for speed, temperature and static pressure according to the manufacturer’s specifications” (Equation (9)), which puts the source back at its calibration, and reads the calibrated levels as they are.

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

CalibrationConditions(
    *,
    temperature_c: float = 23.0,
    static_pressure_kpa: float = 101.325,
    air_absorption_db_per_m: ArrayLike | None = None,
)

The air of a calibration on the 2 m hemisphere (ISO 6926 8.4).

The three travel together because Formula (2) reads them from the same air: $C_1$ and the Annex A $C_2$ read its temperature and its static pressure, and $C_3$ reads the attenuation coefficient $a(f)$ that ISO 9613-1 gives for it. The defaults are the reference meteorological conditions of clause 4, 23,0 degC and 101,325 kPa, with no air absorption.

Parameters

Raises

knee_frequency(d0_m: float, *, speed_of_sound: float = 343.0) -> float

Knee frequency of the radiation efficiency (ISO 6926 Formula (A.1)).

$f_{\mathrm{k}}=c/(2\pi d_0)$: the frequency at which the radiation efficiency has dropped 3 dB from its high-frequency value. ISO 6926:2016 describes $d_0$ as “half the characteristic source dimension (see ISO 3745)”, while ISO 3745:2012 3.14 defines the characteristic source dimension, with the same symbol, as the distance from the origin to the farthest corner of the reference box, already a half dimension (see docs/ERRATA.md). The value passed here is the $d_0$ that enters the formula, a radius-like length; the choice of which length that is stays with the caller.

Parameters

Returns: $f_{\mathrm{k}}$, in hertz.

radiation_impedance_correction(
    *,
    temperature_c: float = 23.0,
    static_pressure_kpa: float = 101.325,
    radiation: RadiationCharacter = 'unknown',
    frequencies_hz: ArrayLike | None = None,
    knee_frequency_hz: float | None = None,
) -> np.ndarray

The radiation impedance correction $C_2$ of ISO 6926 Annex A.

$C_2=-10\lg (p_{\mathrm{s}}/p_{\mathrm{s},0})+n\lg (\theta /{\theta }_1)$, ${\theta }_1$ = 296 K and $\theta$ the air temperature in kelvin, with $n$ = 7,5 for a source whose radiation is unknown (A.5), 15 below and 5 at or above the knee frequency for a monopole (A.2, A.3), and 25 at or above it for an aerodynamic dipole (A.4). Annex A is informative: 8.4 prefers the manufacturer’s value, and the formula the calibration used should be the one the user applies.

Parameters

Returns: $C_2$ per band, in dB (one value without frequencies).

Raises

reference_source_calibration(
    levels_db: ArrayLike,
    *,
    frequencies_hz: ArrayLike,
    arrangement: MicrophoneArrangement,
    background_levels_db: ArrayLike | None = None,
    maximum_levels_db: ArrayLike | None = None,
    conditions: CalibrationConditions | None = None,
    radiation: RadiationCharacter = 'unknown',
    knee_frequency_hz: float | None = None,
    c2_db: ArrayLike | None = None,
    intensity_sound_power_level_db: ArrayLike | None = None,
    room_qualification: FreeFieldCheck | None = None,
    coverage_factor: float = 1.96,
) -> ReferenceSourceCalibration

Calibrate a reference sound source in a hemi-anechoic room (ISO 6926 clause 8).

The one-third octave band levels over the 2 m hemisphere are corrected for background position by position and energy-averaged as ISO 3745 prescribes (sound_power_anechoic), then Formula (2) carries them to the sound power level under the reference meteorological conditions with the $C_1$, $C_2$ and $C_3$ of 8.4. The directivity index of each position (3.9) is its level less the surface level; for traversing microphones 8.3.2 takes the highest level seen on the traverse instead, which maximum_levels_db carries. Annex B, the alternative at low frequencies, replaces the 50 Hz to 80 Hz bands by the intensity levels when both agree within Table B.1 from 50 Hz to 315 Hz. B.2 asks for the directivity index of those three bands from the intensity measurements too; the result keeps the one from sound pressure, and ReferenceSourceCalibration.intensity_bands marks the bands whose level was replaced, as B.2 asks the report to.

Parameters

Returns: ReferenceSourceCalibration.

Raises

reference_source_reproducibility_db(
    frequencies_hz: ArrayLike,
    *,
    environment: CalibrationEnvironment,
    arrangement: MicrophoneArrangement | None = None,
    bandwidth: BandWidth = 'one-third-octave',
) -> np.ndarray

Standard deviation of reproducibility of a calibration (ISO 6926 Table 2).

The one-third octave and octave columns of Table 2 are read separately, as printed: the 3 150 Hz one-third octave band sits in the 200 Hz to 3 150 Hz row while the 4 000 Hz octave row begins at 4 000 Hz.

Parameters

Returns: ${\sigma }_R$ per band, in dB.

Raises

ReferenceSoundSourceVerdict(
    frequencies_hz: np.ndarray,
    sound_power_level_db: np.ndarray,
    repeatability_db: np.ndarray | None,
    supply_variation_db: np.ndarray | None,
    directivity_index_db: np.ndarray | None,
    reverberation_rooms_only: bool,
)

Whether a source meets the performance requirements of ISO 6926 clause 5.

Only what was measured is a field. The limits of clause 5 (Table 1, the 0,3 dB of the supply, the 12 dB and 16 dB ranges, the 3 dB and 4 dB steps, the +6 dB of the directivity) are read from the bands as properties, and so are the spectrum figures they are compared with, so a verdict cannot be built against another limit.

Attributes

property

The step each band is held to (5.4), in dB.

Returns: 3 dB from 100 Hz to 10 000 Hz, 4 dB where a neighbour lies in an extended range; per band, the pair that comes closest to its limit.

property

The largest difference from a neighbouring band, per band (5.4), in dB.

property

The spread of $L_W$ from 100 Hz to 10 000 Hz, in dB.

property

The 12 dB of 5.4, in dB.

property

The +6 dB of 5.5, in dB.

property

5.5: the directivity index at most +6 dB from 100 Hz to 10 000 Hz.

Returns: The verdict, True for a source labelled for reverberation rooms only, or None when not judged.

property

The spread over every band when the range is extended, else nan.

property

The 16 dB of 5.4, in dB.

property

Whether every band from 100 Hz to 10 000 Hz is present (5.4).

property

The requirements without data, by name.

property

Whether every requirement of clause 5 is judged and met (5.1).

Returns: True when the source may be declared in compliance.

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

Draw each requirement as a share of its limit, per band.

Parameters

Returns: The axes.

property

The Table 1 limit on ${\sigma }_r$ per band, in dB (5.2).

Returns: 0,8 dB up to 80 Hz, 0,4 dB up to 160 Hz, 0,2 dB above.

property

5.4: the 12 dB range and 3 dB steps, 16 dB and 4 dB when extended.

Returns: The verdict.

property

5.2: ${\sigma }_r$ within Table 1 in every band.

Returns: The verdict, or None when not judged.

property

The 0,3 dB either way of 5.2, in dB.

property

5.2: no band moves by more than 0,3 dB over the declared supply range.

Returns: The verdict, or None when not judged.

ReferenceSourceCalibration(
    frequencies_hz: np.ndarray,
    surface_pressure_level_db: np.ndarray,
    directivity_index_db: np.ndarray,
    c1_db: float,
    c2_db: np.ndarray,
    c3_db: np.ndarray,
    expanded_uncertainty_db: np.ndarray,
    coverage_factor: float,
    arrangement: str,
    radiation: str | None,
    knee_frequency_hz: float | None,
    intensity_sound_power_level_db: np.ndarray | None = None,
    room_qualification: FreeFieldCheck | None = None,
)

Calibrated sound power levels of a reference sound source (ISO 6926 8.4).

The levels, the Annex B comparison and the room verdict are read from the surface levels, the corrections, the intensity levels and the room qualification the calibration holds, so they are not fields: a calibration cannot be built to take its low bands from an intensity measurement Table B.1 refuses.

Attributes

property

The expanded uncertainty of sound_power_level_a_db (Table 2).

Returns: $k{\sigma }_R$ of the A-weighted row, in dB.

property

The bands the A-weighted total covers: those of ISO 3744 Annex E.

Returns: (lowest, highest) nominal frequency, in hertz.

property

Whether the pressure and intensity levels agree within Table B.1 from 50 Hz to 315 Hz.

None without intensity levels.

property

Per band, whether the level came from the sound intensity of Annex B.

property

The highest directivity index over the positions, per band (5.5).

Returns: One value per band, in dB.

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

Draw the calibrated spectrum with its expanded uncertainty.

Parameters

Returns: The axes.

property

Whether the room qualification meets 8.1 for the pressure bands at 2 m.

None when none was given.

property

A-weighted sound power level over a_weighted_range_hz (5.3).

Returns: $L_{WA}$, in dB re 1 pW.

ReferenceSourceCalibration.sound_power_level_at(
    frequencies_hz: ArrayLike,
    *,
    bandwidth: BandWidth = 'one-third-octave',
    temperature_c: float | None = None,
    static_pressure_kpa: float | None = None,
) -> np.ndarray

The calibrated level in the bands a comparison method asks for.

Without meteorological conditions, $L_W$ under the reference conditions, as calibrated. With the temperature and the static pressure of a test, the power the source radiates there, $L_W-C_2$, with $C_2$ evaluated at the test by the Annex A formula the calibration used (8.4: the formula of the calibration laboratory “should be the same as the one used by the user”); ISO 3741 Formulae (21) and (31) ask for that level. An octave band is the energy sum of its three one-third octave bands, all of which must have been calibrated.

Parameters

Returns: The level per requested band, in dB re 1 pW.

Raises

property

$L_W$ under the reference meteorological conditions, per band, in dB re 1 pW.

Formula (2) from the surface levels and the three corrections; the 50 Hz to 80 Hz bands come from sound intensity where Annex B validated them.

ReferenceSourceDriftResult(
    frequencies_hz: np.ndarray,
    change_db: np.ndarray,
)

Whether a reference sound source has drifted enough to be recalibrated.

The limit is the clause’s, 2,83 times Table 1, read from the bands as limit_db, so a result cannot be built against another one.

Attributes

property

2,83 times the Table 1 value of each band (5.6), in dB.

property

Whether every band stays within 2,83 times Table 1.

Returns: True when no recalibration is called for.

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

Draw the change of each band against its limit.

Parameters

Returns: The axes.

property

5.6.3: a band moved by more than 2,83 times Table 1.

Returns: The opposite of passes.

repeatability_standard_deviation(levels_db: ArrayLike) -> np.ndarray

Standard deviation under repeatability conditions (ISO 6926 Formula (1)).

${\sigma }_r=\sqrt{{\sum }_j(L_{X,j}-\overline{L_X}{)}^2/(N-1)}$ with $\overline{L_X}$ the energy average of the repetitions, as clause 8.4 defines it, not their arithmetic mean.

Parameters

Returns: ${\sigma }_r$ per band, in dB.

Raises

verify_reference_sound_source(
    calibration: ReferenceSourceCalibration | ArrayLike,
    *,
    frequencies_hz: ArrayLike | None = None,
    repeated_levels_db: ArrayLike | None = None,
    supply_variation_db: ArrayLike | None = None,
    directivity_index_db: ArrayLike | None = None,
    reverberation_rooms_only: bool = False,
) -> ReferenceSoundSourceVerdict

May this source be declared a reference sound source? (ISO 6926 clause 5).

Judges the temporal steadiness (5.2, Table 1), the variation over the declared range of the supply (5.2), the spectrum (5.4) and the directivity (5.5). A calibration made here brings its bands, levels and directivity indices; a source calibrated elsewhere, for instance in a reverberation room by clause 9, passes its one-third octave levels and frequencies.

Parameters

Returns: ReferenceSoundSourceVerdict.

Raises

verify_reference_source_drift(
    reference_levels_db: ArrayLike,
    latest_levels_db: ArrayLike,
    *,
    frequencies_hz: ArrayLike,
) -> ReferenceSourceDriftResult

Has the source drifted beyond what ISO 6926 5.6 allows?

The same check serves 5.6.2 (two calibrations), 5.6.3 (the regular one-third octave band levels at fixed reference points) and 5.6.4 (the surface levels of a source kept in one place): a change larger than 2,83 times Table 1 in any band calls for recalibration.

Parameters

Returns: ReferenceSourceDriftResult.

Raises