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)):

The measurement surface area is a closed form of the source geometry: a full hemisphere $S=2\pi r^2$ (half $\pi r^2$, quarter $\pi r^2/2$) for one, two or three reflecting planes (ISO 3744 clause 7.2.3); a parallelepiped $S=4(ab+bc+ca)$ with $a=0.5l_1+d$, $b=0.5l_2+d$, $c=l_3+d$ 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):

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 $K_{2\mathrm{A}}\le 7$ dB instead of 4 dB (clause 4.3).

A noise burst or a transient emission has no steady power to report, and both standards describe it by the sound energy level $L_J=10{\log }_{10}(J/J_0)$ instead, $J=\int P(t)\mathrm{d}t$ in joules and $J_0=1$ pJ (ISO 3744:2010 clauses 3.22 and 3.23). Its determination (clause 8.3; ISO 3746:2010 clause 8.4) is the chain above with the single event time-integrated sound pressure level $L_E=10{\log }_{10}\left[\int p^2\mathrm{d}t/E_0\right]$, $E_0=(20\mu \mathrm{Pa}{)}^2\mathrm{s}$ (clause 3.4), in place of the time-averaged $L_p$: the $N_{\mathrm{e}}$ events at each position are combined into the level of one event (Eq. 19 or Eq. 20), the positions are averaged as in 8.2.2 (Eq. 12), the background and the environment are corrected by the same $K_1$ and $K_2$ (Eq. 21, 22) and the surface term closes it:

For a source that is steady over the whole interval $T$, clause 3.4 NOTE 1 gives $L_E=L_{p,T}+10{\log }_{10}(T/T_0)$ with $T_0=1$ s, so $L_J=L_W+10{\log }_{10}(T/T_0)$: the energy a steady source radiates in $T$ seconds. Annex E carries the band levels to the A-weighted $L_{J\mathrm{A}}$ with the same $C_k$ as $L_{W\mathrm{A}}$ (Eq. E.2), and Annex G refers either level to the reference atmosphere with the corrections $C_1+C_2$ (Eq. G.1, G.3), required above 500 m of altitude or below 10 degrees C (clauses 8.2.5 and 8.3.6).

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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).

$K_1=-10{\log }_{10}\left(1-10^{-0.1\Delta L_p}\right)$ with $\Delta L_p=L_{\text{source}}-L_{\text{background}}$. For $\Delta L_p$ 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: $6\le \Delta L_p\le 15$ dB; ISO 3746:2010, 8.3.3: $3\le \Delta L_p\le 10$ dB). For $\Delta L_p$ 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

Returns: K1 per band, in decibels.

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).

$K_2=10{\log }_{10}\left(1+4S/A\right)$ where A is the equivalent sound absorption area of the room. A is taken directly from absorption_area, or from the Sabine reverberation time $A=0.16V/T$ (Eq. A.3, reverberation_time + volume), or from the mean absorption coefficient $A=\alpha S_v$ (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

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

mean_single_event_level(
    levels: np.ndarray,
    *,
    events: int | None = None,
) -> np.ndarray

Mean single event time-integrated level of one event (ISO 3744 Eq. 19/20).

Two ways of measuring $N_{\mathrm{e}}$ sound emission events reach the same quantity, the single event time-integrated sound pressure level of one event at a microphone position. Measured one at a time (events=None), the first axis of levels holds one entry per event and the mean is their energy average, ISO 3744:2010 Eq. (19):

Measured as one level that encompasses $N_{\mathrm{e}}$ successive events (events $=N_{\mathrm{e}}$), the level of one event is the measurement less $10{\log }_{10}{N}_{\mathrm{e}}$, Eq. (20):

ISO 3746:2010 Eq. (16)/(17) and ISO 3741:2010 Eq. (22)/(23) print the same pair. Both modes require at least five events (clause 8.3.1); fewer are accepted with a SoundPowerWarning.

Parameters

Returns: The level of one event, in decibels: levels less its first axis for events=None, the shape of levels otherwise.

Raises

measurement_positions(
    surface: Surface,
    *,
    radius: float,
    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

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

plot_microphone_positions(
    positions: ArrayLike,
    ax: Axes3D | None = None,
    *,
    radius: float | None = None,
    language: str = 'en',
    **kwargs: Any,
) -> Axes3D

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

Returns: The 3-D axes.

reference_atmosphere_correction(
    temperature: float,
    static_pressure: float | None = None,
    *,
    altitude: float | None = None,
) -> ReferenceAtmosphereCorrection

Corrections to reference meteorological conditions (ISO 3744 Annex G).

A sound power or sound energy level determined by Eq. (18) or Eq. (23) holds for the meteorological conditions at the time and place of the test. Above 500 m of altitude or below 10 degrees C the standard requires it to be carried to the reference static pressure 101.325 kPa and air temperature 23.0 degrees C (clauses 8.2.5 and 8.3.6) by adding

with ${\theta }_0=314$ K and ${\theta }_1=296$ K, so that $L_{W\mathrm{ref},\mathrm{atm}}=L_W+C_1+C_2$ (Eq. G.1) and $L_{J\mathrm{ref},\mathrm{atm}}=L_J+C_1+C_2$ (Eq. G.3). $C_1$ accounts for the different reference quantities of the pressure and power decibels through the characteristic impedance of the air, and is omitted when $K_2$ came from the absolute comparison test of A.2; $C_2$ is the radiation-impedance correction of a monopole, a mean value for other sources. Where the static pressure was not measured it is estimated from the altitude of the site by Eq. (G.2), $p_{\mathrm{s}}=p_{\mathrm{s},0}(1-a{H}_{\mathrm{a}}{)}^b$, with $a=2.2560\times 10^{-5}$ m^-1 and $b=5.2553$.

Parameters

Returns: ReferenceAtmosphereCorrection with c1, c2, their total and the static pressure used.

Raises

ReferenceAtmosphereCorrection(
    c1: float,
    c2: float,
    static_pressure: float,
    temperature: float,
)

The two Annex G corrections to reference meteorological conditions.

c1 is the reference-quantity correction and c2 the radiation-impedance correction of ISO 3744:2010 Annex G, both in decibels; total is their sum, the whole of what Eq. (G.1) adds to $L_W$ and Eq. (G.3) to $L_J$. static_pressure is the $p_{\mathrm{s}}$ the corrections were evaluated at, in kilopascals, whether it was measured or estimated from the altitude by Eq. (G.2), and temperature the air temperature $\theta$, in degrees Celsius.

property

c1 + c2, in decibels: the correction Eq. (G.1)/(G.3) applies.

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 ($A=0.16V/T$, Eq. A.3) and the mean absorption coefficient with the area of the room boundaries ($A=\alpha S_v$, 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

sound_energy_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,
    events: int | None = None,
    background_levels: np.ndarray | None = None,
    integration_time: float | None = None,
    frequencies: np.ndarray | None = None,
    room: RoomEnvironment | None = None,
    grade: Grade = 'engineering',
    omc_uncertainty: float = 0.0,
) -> SoundEnergyResult

Sound energy level of a noise burst from surface single event levels (ISO 3744:2010 clause 8.3, ISO 3746:2010 clause 8.4).

The single event time-integrated sound pressure levels $L_{Ei(\mathrm{ST})}^{\prime }$ are measured simultaneously at every microphone position through a period that encompasses the full burst (clause 8.3.1; a traversing microphone is not permitted). levels_positions is either the (NM, NB) mean single event level of one event at each position, a (Ne, NM, NB) array of the $N_{\mathrm{e}}$ events measured one at a time (reduced by Eq. 19), or the (NM, NB) level of one measurement encompassing events successive events (reduced by Eq. 20). The positions are then energy-averaged as in 8.2.2 (clause 8.3.3), the surface level is corrected for background noise and for the test environment and the surface term added:

$K_1$ follows Eq. (21) with the same criteria as the time-averaged path (background_noise_correction: 6 dB to 15 dB engineering, 3 dB to 10 dB survey, clamped below the lower criterion with a SoundPowerWarning), and $K_2$ the room data in room (Annex A). The background is the time-averaged level the standard has measured over the same integration time $T$ as the events, and it is compared as its exposure over that $T$, $L_{p(\mathrm{B})}+10{\log }_{10}(T/T_0)$ (clause 3.4 NOTE 1), so that the energies Eq. (21) subtracts share one reference; this is why integration_time is required whenever background_levels is given. The surface area S comes from the geometry exactly as in sound_power_pressure, and so do the minimum number of positions, the A-weighted total (Annex E, Eq. E.2) and the expanded uncertainty, which clause 9.1 Eq. (24) makes the same for $L_J$ as for $L_W$.

The level holds for the meteorological conditions of the test; above 500 m of altitude or below 10 degrees C add the Annex G correction of reference_atmosphere_correction (Eq. G.3).

Parameters

Returns: SoundEnergyResult.

Raises

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:

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

Returns: SoundPowerResult.

SoundEnergyResult(
    frequencies: np.ndarray | None,
    sound_energy_level: np.ndarray,
    surface_event_level: np.ndarray,
    mean_event_level: np.ndarray,
    background_correction: np.ndarray,
    environmental_correction: np.ndarray,
    directivity_index: np.ndarray,
    surface_area: float,
    sound_energy_level_a: float,
    uncertainty: float,
    grade: str,
    events: int | None,
    integration_time: float | None,
)

Result of a sound energy level determination from surface single event levels (ISO 3744:2010 clause 8.3, ISO 3746:2010 clause 8.4).

sound_energy_level is the per-band LJ (ISO 3744 Eq. 23); surface_event_level the surface single event time-integrated sound pressure level $\overline{L_E}$ after the K1/K2 corrections (Eq. 22); mean_event_level the raw energy-averaged level $\overline{L_E^{\prime }}(\mathrm{ST})$ over the positions (clause 8.3.3, as Eq. 12). background_correction (K1, Eq. 21) and environmental_correction (K2) are per band. sound_energy_level_a is the A-weighted total LJA (Eq. E.2), computed only when frequencies are supplied; for a single band it equals LJ, and for several bands without frequencies it is NaN (A-weighting needs the band centres). directivity_index is the apparent directivity index per microphone position and band, shape (NM, NB), formed from the single event levels exactly as clause 3.24 allows. uncertainty is the expanded uncertainty $U=2\sqrt{{\sigma }_{\mathrm{R}0}^2+{\sigma }_{\mathrm{omc}}^2}$ (95 %), which clause 9.1 Eq. (24) makes the same for LJ as for LW. events is the number of single sound emission events $N_{\mathrm{e}}$ the levels were reduced from, or None when the caller supplied the per-position mean single event levels directly; integration_time is the interval $T$ of the single event levels, in seconds, or None when no background correction needed it.

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

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

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

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 $U=2\sqrt{{\sigma }_{\mathrm{R}0}^2+{\sigma }_{\mathrm{omc}}^2}$ (95 %, ISO 3744 clause 9.5).

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 $L_{W\mathrm{Ad}}=L_{W\mathrm{A}}+K_{W\mathrm{A}}$ (ISO 4871 clause 3.15).

Parameters

Returns: A single-mode NoiseEmissionDeclaration.

Raises

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(
    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

Returns: The written path as a str.

Raises

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.