emission.sound_power

Sound power level of a noise source from sound pressure measurements over an enveloping measurement surface: ISO 3744:2010 (engineering, accuracy grade 2) and ISO 3746:2010 (survey, accuracy grade 3).

The source stands on one (or more) reflecting plane(s). Sound pressure levels are measured at an array of microphone positions on a hypothetical surface of area S enveloping the source (a hemisphere or a right parallelepiped). The sound power level follows from the energy-averaged pressure level, the background correction $K_{1}$ , the environmental correction $K_{2}$ and the surface area (ISO 3744:2010 clause 8.2, equations (12), (16)-(18)):

\overline{L_{p}} = 10 lo g_{10} [\frac{1}{N _{M}} i \sum 1 0^{0.1 L_{p i}}] (Eq. 12)

K_{1} = - 10 lo g_{10} (1 - 1 0^{- 0.1Δ L_{p}}) (Eq. 16)

K_{2} = 10 lo g_{10} (1 + \frac{4 S}{A}) (Eq. A.2)

L_{p} = \overline{L_{p}} - K_{1} - K_{2} (Eq. 17)

L_{W} = L_{p} + 10 lo g_{10} \frac{S}{S _{0}}, S_{0} = 1 m^{2} (Eq. 18)

The measurement surface area is a closed form of the source geometry: a full hemisphere $S = 2 π r^{2}$ (half $π r^{2}$ , quarter $π r^{2} /2$ ) for one, two or three reflecting planes (ISO 3744 clause 7.2.3); a parallelepiped $S = 4 (ab + b c + c a)$ with $a = 0.5 l_{1} + d$ , $b = 0.5 l_{2} + d$ , $c = l_{3} + d$ for one plane (clause 7.2.4, equations (9)-(11)).

The A-weighted sound power level is combined from band levels with the A-weighting band corrections $C_{k}$ of ISO 3744 Annex E (Tables E.1/E.2):

L_{W A} = 10 lo g_{10} [k \sum 1 0^{0.1 (L_{W k} + C_{k})}] (Eq. E.1)

ISO 3746:2010 shares the surfaces, the energy average and the LW/K1/K2 forms but is coarser: fewer microphone positions (clause 8.2.1), a background criterion of 3 dB instead of 6 dB (clause 8.4.1) and validity up to $K_{2 A} \leq 7$ dB instead of 4 dB (clause 4.3).

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background_noise_correction

background_noise_correction(
    source_levels: np.ndarray,
    background_levels: np.ndarray,
    grade: Grade = 'engineering',
) -> np.ndarray

Background-noise correction K1 per band (ISO 3744:2010 Eq. 16).

$K_{1} = - 10 lo g_{10} (1 - 1 0^{- 0.1Δ L_{p}})$ with $Δ L_{p} = L_{source} - L_{background}$ . For $Δ L_{p}$ strictly above the upper criterion (15 dB engineering, 10 dB survey) the background is negligible and $K_{1} = 0$ ; at the criterion itself Eq. (16) still applies (ISO 3744:2010, 8.2.3: $6 \leq Δ L_{p} \leq 15$ dB; ISO 3746:2010, 8.3.3: $3 \leq Δ L_{p} \leq 10$ dB). For $Δ L_{p}$ below the lower criterion (6 dB engineering, 3 dB survey) the accuracy is reduced: K1 is clamped to its value at that criterion and a SoundPowerWarning is emitted, the result then being an upper bound (clause 8.2.3).

Parameters

Name	Description
`source_levels`	Levels with the source operating, in decibels.
`background_levels`	Background-noise levels, in decibels.
`grade`	`'engineering'` (ISO 3744) or `'survey'` (ISO 3746).

Returns: K1 per band, in decibels.

environmental_correction

environmental_correction(
    surface_area: float,
    *,
    absorption_area: float | np.ndarray | None = None,
    reverberation_time: float | np.ndarray | None = None,
    volume: float | None = None,
    mean_absorption_coefficient: float | np.ndarray | None = None,
    room_surface: float | None = None,
) -> float | np.ndarray

Environmental correction K2 (ISO 3744:2010 Eq. A.2).

$K_{2} = 10 lo g_{10} (1 + 4 S / A)$ where A is the equivalent sound absorption area of the room. A is taken directly from absorption_area, or from the Sabine reverberation time $A = 0.16 V / T$ (Eq. A.3, reverberation_time + volume), or from the mean absorption coefficient $A = α S_{v}$ (Eq. A.7, mean_absorption_coefficient + room_surface). With no room data the field is treated as free and $K_{2} = 0$ ; supplying only one member of a pair raises ValueError rather than silently falling back to the free-field result.

The room absorption is frequency dependent (T, alpha and hence A vary with the band). Passing absorption_area, reverberation_time or mean_absorption_coefficient as a per-band array returns K2 per band with that shape; scalar inputs return a scalar, unchanged.

Parameters

Name	Description
`surface_area`	Measurement surface area `S`, in square metres.
`absorption_area`	Equivalent absorption area `A` (m^2), scalar or per band.
`reverberation_time`	Sabine `T` (s), scalar or per band, with `volume` (Eq. A.3).
`volume`	Room volume `V` (m^3), with `reverberation_time`.
`mean_absorption_coefficient`	`alpha` in (0, 1], scalar or per band, with `room_surface` (Eq. A.7).
`room_surface`	Room boundary area `Sv` (m^2), with `alpha`.

Returns: K2 in decibels; a scalar for scalar inputs, otherwise an array per band.

measurement_positions

measurement_positions(
    surface: Surface,
    *,
    radius: float | None = None,
    reflecting_planes: int = 1,
    tones: bool = True,
    grade: Grade = 'engineering',
) -> np.ndarray

Normative microphone coordinates on the measurement surface.

For a 'hemisphere' the coordinates come from ISO 3744:2010 Annex B: Table B.1 for sources that may emit discrete tones (tones=True) and Table B.2 for broadband sources. The engineering grade uses the 10 key positions for one reflecting plane (5 for two, 3 for three); the survey grade uses the reduced arrays of ISO 3746:2010 clause 8.2.1 (positions 4, 5, 6, 10 for one plane). Coordinates are scaled by radius and returned as an (N, 3) array of Cartesian (x, y, z) in metres.

Parameters

Name	Description
`surface`	`'hemisphere'` (only shape with a coordinate table).
`radius`	Hemisphere radius `r`, in metres.
`reflecting_planes`	Number of reflecting planes (1, 2 or 3).
`tones`	If True use Table B.1, else Table B.2.
`grade`	`'engineering'` or `'survey'`.

Returns: (N, 3) microphone coordinates, in metres.

plot_microphone_positions

plot_microphone_positions(
    positions: ArrayLike,
    ax: Any | None = None,
    *,
    radius: float | None = None,
    language: str = 'en',
    **kwargs: Any,
) -> Any

Draw a microphone position array on its measurement surface, in 3-D.

Numbered microphone points with a wireframe of the hemisphere (or full sphere when positions dip below the reflecting plane) of the given radius; pairs with measurement_positions and precision_positions, whose (N, 3) arrays it accepts directly.

Parameters

Name	Description
`positions`	Cartesian microphone positions, shape `(N, 3)`, in metres.
`ax`	Existing 3-D axes (`projection="3d"`), or `None` to create a figure.
`radius`	Surface radius for the wireframe, in metres; `None` uses the largest position norm.
`language`	Label language, `"en"` (default) or `"es"`.
`kwargs`	Forwarded to the microphone `scatter`.

Returns: The 3-D axes.

RoomEnvironment

RoomEnvironment(
    absorption_area: float | np.ndarray | None = None,
    reverberation_time: float | np.ndarray | None = None,
    volume: float | None = None,
    mean_absorption_coefficient: float | np.ndarray | None = None,
    room_surface: float | None = None,
)

Room data behind the environmental correction K2 (ISO 3744 Annex A).

The three routes the standard offers to the equivalent sound absorption area A of the test room, in the order environmental_correction tries them: A itself, the Sabine reverberation time with the room volume ( $A = 0.16 V / T$ , Eq. A.3) and the mean absorption coefficient with the area of the room boundaries ( $A = α S_{v}$ , Eq. A.7). Each route is a pair that must be given whole; the empty environment carries no room data at all, which is the free field ( $K_{2} = 0$ ).

Every field may also be a per-band array, in which case K2 comes out per band with that shape.

Parameters

Name	Description
`absorption_area`	Equivalent absorption area `A` (m^2), scalar or per band.
`reverberation_time`	Sabine `T` (s), scalar or per band, with `volume` (Eq. A.3).
`volume`	Room volume `V` (m^3), with `reverberation_time`.
`mean_absorption_coefficient`	`alpha` in (0, 1], scalar or per band, with `room_surface` (Eq. A.7).
`room_surface`	Room boundary area `Sv` (m^2), with `alpha`.

sound_power_pressure

sound_power_pressure(
    levels_positions: np.ndarray,
    surface: Surface,
    *,
    radius: float | None = None,
    dimensions: tuple[float, float, float] | None = None,
    distance: float | None = None,
    reflecting_planes: int = 1,
    background_levels: np.ndarray | None = None,
    frequencies: np.ndarray | None = None,
    room: RoomEnvironment | None = None,
    grade: Grade = 'engineering',
    omc_uncertainty: float = 0.0,
) -> SoundPowerResult

Sound power level from surface pressure levels (ISO 3744/3746:2010).

levels_positions is an (NM, NB) array of time-averaged sound pressure levels: one row per microphone position, one column per frequency band (or a single column for a directly measured A-weighted level). The surface-averaged level is corrected for background noise (K1, from background_levels) and for the test environment (K2, from the room absorption data) and combined with the measurement surface area:

L_{W} = 10 lo g_{10} [\frac{1}{N _{M}} i \sum 1 0^{0.1 L_{p i}}] - K_{1} - K_{2} + 10 lo g_{10} \frac{S}{S _{0}}

The surface area S is computed from the geometry: radius for a 'hemisphere' (clause 7.2.3) or dimensions + distance for a 'box' (clause 7.2.4). When frequencies are given the A-weighted sound power level is combined via ISO 3744 Annex E.

Parameters

Name	Description
`levels_positions`	`(NM, NB)` sound pressure levels, in decibels.
`surface`	`'hemisphere'` or `'box'`.
`radius`	Hemisphere radius `r` (metres), for `surface='hemisphere'`.
`dimensions`	Reference box `(l1, l2, l3)` (metres), for `'box'`.
`distance`	Measurement distance `d` (metres), for `'box'`.
`reflecting_planes`	Number of reflecting planes (1, 2 or 3).
`background_levels`	`(NM, NB)` background levels for `K1`, or a single spectrum `(NB,)` / `(1, NB)` broadcast to every position.
`frequencies`	Band mid-band frequencies (Hz) for the A-weighted total.
`room`	Room absorption data behind `K2` (`RoomEnvironment`); `None` is a room with no data at all, i.e. a free field ( $K_{2} = 0$ ).
`grade`	`'engineering'` (ISO 3744) or `'survey'` (ISO 3746).
`omc_uncertainty`	`sigma_omc` (dB), operating/mounting instability.

Returns: SoundPowerResult.

SoundPowerResult

SoundPowerResult(
    frequencies: np.ndarray | None,
    sound_power_level: np.ndarray,
    surface_pressure_level: np.ndarray,
    mean_pressure_level: np.ndarray,
    background_correction: np.ndarray,
    environmental_correction: np.ndarray,
    directivity_index: np.ndarray,
    surface_area: float,
    sound_power_level_a: float,
    uncertainty: float,
    grade: str,
)

Result of a sound power determination from surface pressure levels.

sound_power_level is the per-band LW (ISO 3744 Eq. 18); surface_pressure_level the surface SPL Lp after the K1/K2 corrections (Eq. 17); mean_pressure_level the raw energy-averaged level Lp'(ST) (Eq. 12). background_correction (K1) and environmental_correction (K2) are per band. sound_power_level_a is the A-weighted total LWA (Eq. E.1), computed only when frequencies are supplied; for a single band it equals LW, and for several bands without frequencies it is NaN (A-weighting needs the band centres). directivity_index is the apparent directivity index DIi* per microphone position and frequency band, shape (NM, NB) (Eq. 7, evaluated per band per clause 8.4). uncertainty is the expanded uncertainty $U = 2 σ_{R 0}^{2} + σ_{o m c}^{2}$ (95 %, ISO 3744 clause 9.5).

SoundPowerResult.declare()

SoundPowerResult.declare(
    *,
    uncertainty: float | None = None,
    mode: str = 'Operating mode 1',
    emission_pressure_level: float | None = None,
    emission_pressure_uncertainty: float | None = None,
    verification_level: float | None = None,
    machine: str | None = None,
    operating_conditions: str | None = None,
    noise_test_code: str | None = None,
    basic_standards: str | Sequence[str] = (),
    form: DeclarationForm = 'dual-number',
) -> NoiseEmissionDeclaration

Build an ISO 4871:1996 noise-emission declaration from this result.

Wraps the A-weighted sound power level LWA of this measurement as the declared measured value L_WA of a single operating mode, with the uncertainty K_WA defaulting to the result’s own expanded uncertainty U (ISO 3744/3746 clause 9.5). The declared single-number value is $L_{W A d} = L_{W A} + K_{W A}$ (ISO 4871 clause 3.15).

Parameters

Name	Description
`uncertainty`	`K_WA` in decibels; defaults to this result’s expanded uncertainty `uncertainty`.
`mode`	Operating-mode label for the declaration column.
`emission_pressure_level`	Optional A-weighted emission sound pressure level `L_pA` at a work station, in decibels re 20 uPa.
`emission_pressure_uncertainty`	`K_pA` in decibels; required with `emission_pressure_level`.
`verification_level`	Optional verification measurement `L_1` of the A-weighted sound power level (ISO 4871 clause 6).
`machine`	Machine identification (clause 5 a).
`operating_conditions`	Operating/mounting conditions (clause 5 c).
`noise_test_code`	Noise test code the values were determined to (clause 5 b).
`basic_standards`	Basic emission standard(s) used (clause 5 b).
`form`	`"dual-number"` (default) or `"single-number"`.

Returns: A single-mode NoiseEmissionDeclaration.

Raises

Exception	When
ValueError	If the A-weighted sound power level is not finite (several bands were combined without `frequencies`).

SoundPowerResult.plot()

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

Plot the LW spectrum with the A-weighted total annotated.

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

SoundPowerResult.report()

SoundPowerResult.report(
    path: str,
    *,
    metadata: ReportMetadata | None = None,
    engine: str = 'reportlab',
    verbose: bool = False,
    language: str = 'en',
) -> str

Render an ISO 3744/3746 sound-power determination fiche to a PDF.

Writes a one-page sound-power test sheet: the standard-basis line naming the applied method and accuracy grade (ISO 3744:2010 engineering grade 2 or ISO 3746:2010 survey grade 3), an optional metadata header (client, noise source, test environment, instrumentation, climate, date), a per-band table (nominal octave/one-third-octave frequency, the surface sound-pressure level Lp and the band sound-power level LW), the sound-power spectrum LW(f), the boxed A-weighted sound power level LWA (dB re 1 pW) with the total LW, the expanded uncertainty U and the measurement surface area S, an optional verdict row against a declared limit, and a measurement-basis strip stating the applied background (K1) and environmental (K2) corrections.

Parameters

Name	Description
`path`	Destination path of the PDF file.
`metadata`	Optional `ReportMetadata` supplying the header (`client`, `specimen` the noise source, `test_room` the test environment, `instrumentation`, `temperature`, `relative_humidity`, `pressure`, `test_date`), the footer identity (`laboratory`, `operator`, `report_id`, `notes`) and, via `requirement`, a declared A-weighted sound-power limit the fiche checks the result against (lower is better).
`engine`	Rendering back end; only `"reportlab"` is supported.
`verbose`	When `True` the per-band table adds the energy-averaged level `Lp'` and the background (`K1`) and environmental (`K2`) corrections.
`language`	Fiche language: `"en"` (default) or `"es"`.

Returns: The written path as a str.

Raises

Exception	When
ValueError	If `engine` is not `"reportlab"` or `language` is unknown.
ImportError	If reportlab (or, for the figure, matplotlib) is not installed (`pip install phonometry[report]`).

SoundPowerWarning

Non-fatal qualification issue in any of the sound-power methods.

Emitted for ISO 3744/3746 background margin below the criterion and for K2 beyond the method’s validity limit (8.2.3, 4.3.2); for ISO 3741 reverberation-room qualification (room volume vs Table 1, mean absorption) and microphone/source-position sampling; and for ISO 9614-2 negative total partial power and unmet field-indicator criteria. Where a lower criterion is only just met the returned levels represent upper bounds and must be reported as such.

Created and maintained by José Manuel Requena Plens ORCID All projects