metrology.reciprocity_coupler

Pressure calibration of laboratory standard microphones by reciprocity in a closed coupler (IEC 61094-2:2009).

Two microphones close the two ends of a small cavity. A current $i_1$ through the transmitter makes its diaphragm a source of short-circuit volume velocity $M_{\mathrm{p},1}{i}_1$, the gas in the cavity turns that into the pressure $p_2=Z_{\mathrm{a},12}{M}_{\mathrm{p},1}{i}_1$ on the receiver, and the receiver turns the pressure into its open-circuit voltage, so (Formula (2))

The electrical transfer impedance $U_2/i_1$ is measured; this module computes the acoustic transfer impedance $Z_{\mathrm{a},12}$ it is divided by, with every correction the standard gives, and solves the three products for the sensitivities with reciprocity_calibration.

Two couplers (5.4 and Annex C). A large-volume coupler, small against the wavelength, holds a pure compliance, and Formula (3) adds the admittances of the gas and of the two microphones,

with $V$ the coupler volume plus the two front cavities (7.3.3.1), and the bores that Figure C.2 draws between each microphone face and the cavity (dimension F of Table C.2), and $V_{\mathrm{e}}$ the complex equivalent volume of each microphone. A plane-wave coupler, of the diameter of the diaphragms, is a transmission line of length $l_0$ between them (Formula (4)):

Heat conduction (5.5 and Annex A). In the large-volume coupler the walls draw heat from the compressed gas and the volume looks larger, by the complex factor of Formula (A.1),

where $E_V$ is Gerber’s temperature transfer function of a finite cylinder: temperature_transfer_function computes it either by the approximation (A.2) or by the full solution of the reference [A.1], which A.2 requires below 20 Hz unless the uncertainty component is increased instead, and which reproduces every entry of Table A.1 to its stated 0,000 01. In the plane-wave coupler the propagation coefficient and the wave impedance of Formulas (A.3) and (A.4) carry the losses at the cylindrical wall, and the admittance of Formula (A.5) those at the two diaphragms.

Capillary tubes (5.6 and Annex B). Tubes that equalise the static pressure shunt the cavity, and Formula (6) divides the transfer impedance by

with $Z_{\mathrm{a},\mathrm{C}}$ the input impedance of an open tube of Formulas (B.1) to (B.3), which capillary_tube_impedance computes and Tables B.1 and B.2 test.

The microphone (7.3.3 and Annex E). Its acoustic impedance is a lumped compliance, mass and resistance, written as an equivalent volume, a resonance frequency and a loss factor (ReciprocityMicrophone); its front cavity adds volume, length and, through the excess of its measured volume over the cylinder of its depth, a further terminating admittance (7.3.3.1).

The wave-motion corrections of Table C.3 for the air-filled large-volume coupler of LS1P microphones are large_volume_wave_motion_correction, the coupler dimensions of Tables C.1 and C.2 are IEC61094_2_TABLE_C1 and IEC61094_2_TABLE_C2, and coupler_parameter_uncertainty finds the uncertainty each coupler and microphone parameter contributes, by the one-at-a-time recalculation 7.5 describes.

The properties of the gas, $\rho$, $c$, $\kappa$, $\eta$ and ${\alpha }_t$, are those of humid air by Annex F (air) at the conditions of the calibration, or of any Fluid passed as gas: 7.3.2.1 allows the coupler to be filled with hydrogen or helium.

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

capillary_tube_impedance(
    frequencies_hz: ArrayLike,
    *,
    length_m: float,
    radius_m: float,
    gas: Fluid,
) -> CapillaryTubeImpedance

The acoustic input impedance of an open capillary tube (IEC 61094-2:2009 B.1).

Formulas (B.2) and (B.3) give the product and the quotient of the propagation coefficient and the wave impedance of an infinite tube of radius $a_{\mathrm{t}}$,

with $k=(-\mathrm{j}\omega \rho /\eta {)}^{1/2}$ and $B=(\eta /\rho {\alpha }_t{)}^{1/2}$; each follows from their product and quotient on the branch with a positive real part, and Formula (B.1) gives $Z_{\mathrm{a},\mathrm{C}}=Z_{\mathrm{a},\mathrm{t}}\tanh \gamma l_{\mathrm{C}}$. A tube blocked along its length by a wire has ${\Delta }_{\mathrm{C}}=1$ instead (B.1), which a coupler without a capillary stands for.

Tables B.1 and B.2 tabulate $Z_{\mathrm{a},\mathrm{C}}$ at the reference conditions for tubes 50 mm and 100 mm long and 0,1667 mm, 0,20 mm and 0,25 mm in radius; the first radius is 1/6 mm, which is what the printed values were computed with.

Parameters

Returns: The CapillaryTubeImpedance.

Raises

CapillaryTube(length_m: float, radius_m: float, count: int = 1)

Identical open capillary tubes that equalise the static pressure of a coupler (IEC 61094-2:2009 5.6 and Annex B).

Attributes

CapillaryTubeImpedance(
    frequencies_hz: NDArray[np.float64],
    length_m: float,
    radius_m: float,
    propagation_coefficient_per_m: NDArray[np.complex128],
    wave_impedance_pa_s_m3: NDArray[np.complex128],
)

The acoustic input impedance of an open capillary tube (IEC 61094-2:2009 Formulas (B.1) to (B.3)).

Attributes

property

$Z_{\mathrm{a},\mathrm{C}}=Z_{\mathrm{a},\mathrm{t}}\tanh \gamma l_{\mathrm{C}}$ (Formula (B.1)), in Pa·s/m³.

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

Plot the real and imaginary parts of $Z_{\mathrm{a},\mathrm{C}}$ in GPa·s/m³, the unit of Tables B.1 and B.2.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

check_coupler(
    frequencies_hz: ArrayLike,
    coupler: PlaneWaveCoupler | LargeVolumeCoupler,
    microphones: Sequence[ReciprocityMicrophone],
    *,
    temperature_c: float,
    static_pressure_pa: float,
    relative_humidity_percent: float,
    gas: Fluid | None = None,
    heat_conduction_method: str = 'exact',
) -> CouplerCheck

Do the coupler formulas of IEC 61094-2:2009 hold for this calibration?

For a plane-wave coupler, Formulas (A.3) and (A.4) “are valid for the frequency range given by $\omega \rho a^2>100\eta$” (A.3), which is required at the lowest frequency; C.2 recommends a ratio of the distance between the diaphragms to the diameter of 0,5 to 0,75, reported but not required. For a large-volume coupler with the approximation (A.2), A.2 states its accuracy for $0,125<R<8$ and $X>5$, which is required; below 20 Hz A.2 asks for the full solution or a larger uncertainty component, which is reported but not required. In air, the conditions are checked against the domain Annex F states for its equations (15 °C to 27 °C, 60 kPa to 110 kPa, 10 % to 90 %).

Parameters

Returns: The CouplerCheck.

Raises

coupler_parameter_uncertainty(
    frequencies_hz: ArrayLike,
    coupler: PlaneWaveCoupler | LargeVolumeCoupler,
    microphones: Sequence[ReciprocityMicrophone],
    uncertainties: CouplerInputUncertainties,
    *,
    temperature_c: float,
    static_pressure_pa: float,
    relative_humidity_percent: float,
    microphone: int = 1,
    gas: Fluid | None = None,
    heat_conduction_method: str = 'exact',
) -> CouplerParameterUncertainty

The uncertainty components of the acoustic transfer impedance, one parameter at a time (IEC 61094-2:2009 7.5).

“Due to the complexity of the final expression for the pressure sensitivity in Equation (7) the uncertainty analysis of the acoustic transfer impedance is usually performed by repeating a calculation while the various components are changed one at a time by their associated uncertainty. The difference to the result derived by the unchanged components is then used to determine the standard uncertainty related to the various components.” This is that: each parameter with a non-zero standard uncertainty is moved by it, the three transfer impedances of the triad recomputed, and the change of the sensitivity level of microphone by Formula (7), with the measured electrical transfer impedances held, is its component. A microphone parameter is moved for each of the three microphones in turn, as three independent quantities, and their changes combined in quadrature into the one row of Table 1; so are the length and the radius of the capillary tubes.

Parameters

Returns: The CouplerParameterUncertainty, with a component for each parameter given a non-zero uncertainty.

Raises

coupler_transfer_impedance(
    frequencies_hz: ArrayLike,
    coupler: PlaneWaveCoupler | LargeVolumeCoupler,
    transmitter: ReciprocityMicrophone,
    receiver: ReciprocityMicrophone,
    *,
    temperature_c: float,
    static_pressure_pa: float,
    relative_humidity_percent: float,
    gas: Fluid | None = None,
    heat_conduction_method: str = 'exact',
) -> CouplerTransferImpedance

The acoustic transfer impedance $Z_{\mathrm{a},12}$ of a coupler closed by two microphones (IEC 61094-2:2009 5.4 to 5.6).

A LargeVolumeCoupler takes Formula (3): the gas of the coupler, the two bores of Figure C.2 and the two front cavities (7.3.3.1) as one compliance, its volume multiplied by ${\Delta }_{\mathrm{H}}$ of Formula (A.1) for the heat conduction, in parallel with the equivalent volumes of the two microphones. The surface the heat conduction sees is that of the coupler plus the wall of each bore and front cavity and any thread in it (7.3.2.2): the diaphragm takes the place of the port it closes (LargeVolumeCoupler.closed_volume_m3, LargeVolumeCoupler.closed_surface_m2).

A PlaneWaveCoupler takes Formula (4): a line of length $l_0$, the coupler plus the two front-cavity depths, terminated at each end by the microphone’s acoustic impedance in parallel with the excess volume of its front cavity (7.3.3.1); the losses of Formulas (A.3) to (A.5) give $Z_{\mathrm{a},12}^{\prime \prime }$, and the same line without them $Z_{\mathrm{a},12}^{\prime }$.

Both are then divided by ${\Delta }_{\mathrm{C}}$ of Formula (6) for the capillary tubes. The pair is reciprocal, so which microphone transmits does not change the result.

Parameters

Returns: The CouplerTransferImpedance.

Raises

CouplerCheck(
    coupler: str,
    length_to_diameter_ratio: float,
    broadband_margin: float | None,
    lowest_x: float | None,
    lowest_frequency_hz: float,
    *,
    heat_conduction_method: str,
    temperature_c: float,
    static_pressure_pa: float,
    relative_humidity_percent: float,
    in_air: bool,
)

Whether the formulas of IEC 61094-2:2009 apply to a coupler at the frequencies and conditions of a calibration.

Built by check_coupler. The verdicts are read from the figures and the conditions the check holds, against the ranges the standard prints, so they are not fields.

Attributes

property

For a large-volume coupler computed with Formula (A.2), whether A.2 states its accuracy.

$0,125<R<8$ and $X>5$; None with the full solution or for a plane-wave coupler.

property

Whether Formulas (A.3) and (A.4) hold at every frequency.

property

For air, whether the conditions are within the domain Annex F states for its equations.

15 °C to 27 °C, 60 kPa to 110 kPa and 10 % to 90 %, ends included; None for another gas.

property

For a large-volume coupler computed with Formula (A.2), whether a frequency is below 20 Hz.

A.2 then asks for the full solution “or the corresponding uncertainty component shall be increased accordingly”; None with the full solution or for a plane-wave coupler. Advisory: it does not enter passes, because the larger uncertainty is the caller’s to state.

property

The verdict: the formulas the calibration uses hold where it uses them.

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

Plot each condition as its margin to the limit it is held to.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

property

For a plane-wave coupler, whether $R$ is within the 0,5 to 0,75 C.2 recommends.

None for a large-volume one. Advisory: it does not enter passes.

CouplerDimensions(
    microphone_diameter_mm: float,
    front_cavity_diameter_mm: float,
    coupler_diameter_mm: float,
    front_cavity_depth_mm: float,
    coupler_length_mm: float | None = None,
    coupler_length_range_mm: tuple[float, float] | None = None,
    port_length_mm: float | None = None,
    tolerance_mm: float | None = None,
)

One column of IEC 61094-2:2009 Table C.1 or Table C.2, the nominal dimensions of a coupler for one type of laboratory standard microphone, in millimetres as printed.

Attributes

CouplerInputUncertainties(
    *,
    u_coupler_length_m: float = 0.0,
    u_coupler_diameter_m: float = 0.0,
    u_coupler_volume_m3: float = 0.0,
    u_coupler_surface_area_m2: float = 0.0,
    u_capillary_length_m: float = 0.0,
    u_capillary_radius_m: float = 0.0,
    u_static_pressure_pa: float = 0.0,
    u_temperature_k: float = 0.0,
    u_relative_humidity_percent: float = 0.0,
    u_front_cavity_depth_m: float = 0.0,
    u_front_cavity_volume_m3: float = 0.0,
    u_equivalent_volume_m3: float = 0.0,
    u_resonance_frequency_hz: float = 0.0,
    u_loss_factor: float = 0.0,
)

The standard uncertainty of each input quantity of the acoustic transfer impedance in a coupler: those Table 1 of IEC 61094-2:2009 lists under “Coupler properties” (7.3.2) and “Microphone parameters” (7.3.3) that coupler_parameter_uncertainty can move.

Each one left at zero contributes no component. A microphone parameter is the uncertainty of that parameter on each of the three microphones.

Parameters

Raises

CouplerParameterUncertainty(
    frequencies_hz: NDArray[np.float64],
    components_db: Mapping[str, NDArray[np.float64]],
    microphone: int,
)

The standard uncertainty of a sensitivity level that each parameter of the acoustic transfer impedance contributes (IEC 61094-2:2009 7.5).

Built by coupler_parameter_uncertainty; ready to pass to reciprocity_uncertainty_budget.

Attributes

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

Plot each component against frequency.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

CouplerTransferImpedance(
    frequencies_hz: NDArray[np.float64],
    coupler: str,
    adiabatic_impedance_pa_s_m3: NDArray[np.complex128],
    heat_conducting_impedance_pa_s_m3: NDArray[np.complex128],
    capillary_correction: NDArray[np.complex128],
    heat_conduction: HeatConductionCorrection | None = None,
)

The acoustic transfer impedance of a coupler closed by two microphones, with its corrections (IEC 61094-2:2009 5.4 to 5.6).

Attributes

property

$-20\lg |{\Delta }_{\mathrm{C}}|$, the change of $|Z_{\mathrm{a},12}|$ the tubes cause, in dB.

property

$20\lg |Z_{\mathrm{a},12}^{\prime \prime }/Z_{\mathrm{a},12}^{\prime }|$, in dB.

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

Plot the heat-conduction and capillary corrections of the transfer impedance, in dB, against frequency.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

property

$Z_{\mathrm{a},12}=Z_{\mathrm{a},12}^{\prime \prime }/{\Delta }_{\mathrm{C}}$, the impedance the electrical transfer impedance is divided by, in Pa·s/m³.

heat_conduction_correction(
    frequencies_hz: ArrayLike,
    *,
    volume_m3: float,
    surface_area_m2: float,
    length_to_diameter_ratio: float,
    gas: Fluid,
    method: str = 'exact',
) -> HeatConductionCorrection

The heat-conduction correction ${\Delta }_{\mathrm{H}}$ of a closed cavity (IEC 61094-2:2009 5.5, A.2).

${\Delta }_{\mathrm{H}}$ multiplies the geometrical volume $V$ in Formula (3). For a coupler closed by microphones, $V$ and the surface are those of the coupler together with the front cavities (7.3.2.2), which coupler_transfer_impedance assembles; $R$ is that of the coupler.

Parameters

Returns: The HeatConductionCorrection.

Raises

HeatConductionCorrection(
    frequencies_hz: NDArray[np.float64],
    length_to_diameter_ratio: float,
    volume_to_surface_m: float,
    x: NDArray[np.float64],
    transfer_function: NDArray[np.complex128],
    heat_capacity_ratio: float,
    method: str,
)

The heat-conduction correction of a closed cavity at low frequencies (IEC 61094-2:2009 5.5 and A.2, Formula (A.1)).

Attributes

property

$20\lg |{\Delta }_{\mathrm{H}}|$, the apparent increase of the volume, in dB.

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

Plot $|{\Delta }_{\mathrm{H}}|$ in dB and its phase against frequency.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

property

${\Delta }_{\mathrm{H}}=\kappa /(1+(\kappa -1)E_V)$, the complex factor on the geometrical volume (Formula (A.1)).

Constant (mapping).

IEC61094_2_TABLE_C1 = {'LS1P': CouplerDimensions(microphone_diameter_mm=23.77, front_cavity_diameter_mm=18.6, coupler_diameter_mm=18.6, front_cavity_depth_mm=1.95, coupler_length_mm=None, coupler_length_range_mm=(3.5, 9.5), port_length_mm=None, tolerance_mm=None), 'LS2aP': CouplerDimensions(microphone_diameter_mm=13.2, front_cavity_diameter_mm=9.3, coupler_diameter_mm=9.3, front_cavity_depth_mm=0.5, coupler_length_mm=None, coupler_length_range_mm=(3.0, 7.0), port_length_mm=None, tolerance_mm=None), 'LS2bP': CouplerDimensions(microphone_diameter_mm=12.15, front_cavity_diameter_mm=9.8, coupler_diameter_mm=9.8, front_cavity_depth_mm=0.7, coupler_length_mm=None, coupler_length_range_mm=(3.5, 6.0), port_length_mm=None, tolerance_mm=None)}

Constant (mapping).

IEC61094_2_TABLE_C2 = {'LS1P': CouplerDimensions(microphone_diameter_mm=23.77, front_cavity_diameter_mm=18.6, coupler_diameter_mm=42.88, front_cavity_depth_mm=1.95, coupler_length_mm=12.55, coupler_length_range_mm=None, port_length_mm=0.8, tolerance_mm=0.03), 'LS2aP': CouplerDimensions(microphone_diameter_mm=13.2, front_cavity_diameter_mm=9.3, coupler_diameter_mm=18.3, front_cavity_depth_mm=0.5, coupler_length_mm=3.5, coupler_length_range_mm=None, port_length_mm=0.4, tolerance_mm=0.03), 'LS2bP': CouplerDimensions(microphone_diameter_mm=12.15, front_cavity_diameter_mm=9.8, coupler_diameter_mm=18.3, front_cavity_depth_mm=0.7, coupler_length_mm=3.5, coupler_length_range_mm=None, port_length_mm=0.4, tolerance_mm=0.03)}

Constant (mapping).

IEC61094_2_TABLE_C3 = {800.0: 0.0, 1000.0: -0.002, 1250.0: -0.013, 1600.0: -0.034, 2000.0: -0.06, 2500.0: -0.087}

large_volume_wave_motion_correction(
    frequencies_hz: ArrayLike,
    *,
    speed_of_sound_ratio: float = 1.0,
) -> WaveMotionCorrection

The wave-motion correction of the large-volume coupler used with LS1P microphones (IEC 61094-2:2009 C.3, Table C.3).

The correction is to be added to the pressure sensitivity level determined in the air-filled coupler of Table C.2, when it is not practical to determine it for the individual coupler and microphones. It is nil up to 800 Hz and printed at five frequencies from 1 kHz to 2,5 kHz, where C.3 sets the upper limit of the coupler for LS1P microphones. A frequency within 2 % of a printed one takes its value; one between two rows is interpolated linearly in lg f, and flagged.

For a coupler filled with hydrogen, C.3 allows the same corrections “provided the frequency scale is multiplied by a factor equal to the ratio of the speed of sound”: speed_of_sound_ratio is that factor, and each frequency is read at its value divided by it.

Parameters

Returns: The WaveMotionCorrection.

Raises

LargeVolumeCoupler(
    length_m: float,
    diameter_m: float,
    port_length_m: float,
    capillary: CapillaryTube | None = None,
    volume_m3: float | None = None,
    surface_area_m2: float | None = None,
)

A large-volume coupler: a cylinder much larger than the front cavities and the equivalent volumes (IEC 61094-2:2009 C.3, Table C.2 and Figure C.2).

Figure C.2 draws each microphone with its face port_length_m back from the cavity: the front cavity, of diameter B, continues through the wall of the coupler as a bore of length F to the cavity. Each bore adds $\pi B^{2}F/4$ to the volume of Formula (3) and $\pi BF$ to the surface the heat conduction sees, with B the front-cavity diameter of the microphone in it (coupler_transfer_impedance). For the coupler of Table C.2 the two bores of LS1P microphones are 2,4 % of the cavity, about 0,1 dB on each sensitivity.

Attributes

property

The surface of the cavity of length E, in m²: the measured one, or the closed cylinder’s.

property

The volume of the cavity of length E, in m³: the measured one, or the cylinder’s.

LargeVolumeCoupler.closed_surface_m2(
    microphones: Sequence[ReciprocityMicrophone],
) -> float

The surface the heat conduction sees with the coupler closed by two microphones, in m²: the closed cylinder, the wall of each bore and of each front cavity, and any thread in it (7.3.2.2); each diaphragm takes the place of the port it closes.

Parameters

Returns: The surface, in m².

Raises

LargeVolumeCoupler.closed_volume_m3(
    microphones: Sequence[ReciprocityMicrophone],
) -> float

The volume $V$ of Formula (3) with the coupler closed by two microphones, in m³: the cavity, the two bores and the two front cavities (7.3.3.1, Figure C.2).

Parameters

Returns: $V$, in m³.

Raises

microphone_acoustic_impedance(
    electrical_admittance_s: ArrayLike,
    blocked_impedance_ohm: ArrayLike,
    pressure_sensitivity_v_per_pa: ArrayLike,
) -> NDArray[np.complex128]

The acoustic impedance of a microphone from its electrical admittance (IEC 61094-2:2009 E.4, Formula (E.1)).

with the admittance $Y$ measured while the diaphragm is terminated by a closed quarter-wavelength tube ($p=0$), and the blocked impedance $Z_{\mathrm{e},0}$ at 100 kHz to 200 kHz, where the diaphragm cannot move. E.4 calculates it “by iteration”, because the pressure sensitivity is itself the result of a calibration that used $Z_{\mathrm{a}}$: alternate this with pressure_reciprocity until both stop changing.

Parameters

Returns: $Z_{\mathrm{a}}$, complex, in Pa·s/m³.

Raises

PlaneWaveCoupler(
    length_m: float,
    diameter_m: float,
    capillary: CapillaryTube | None = None,
)

A plane-wave coupler: a cylinder of the diameter of the front cavities (IEC 61094-2:2009 C.2, Table C.1 and Figure C.1).

Attributes

pressure_reciprocity(
    frequencies_hz: ArrayLike,
    electrical_transfer_impedances_ohm: Sequence[ArrayLike],
    acoustic_transfer_impedances: Sequence[ArrayLike | CouplerTransferImpedance],
    *,
    corrections_db: Mapping[str, ArrayLike] | None = None,
    expanded_uncertainty_db: ArrayLike | None = None,
) -> ReciprocityCalibration

The pressure sensitivities of three microphones calibrated in pairs in a coupler (IEC 61094-2:2009 5.7.1, Formula (7)).

Each pair gives the product $M_{\mathrm{p},i}{M}_{\mathrm{p},j}=Z_{\mathrm{e},ij}/Z_{\mathrm{a},ij}$ (Formula (2)), and Formula (7) solves the three:

with similar expressions for the other two, and the phase “by a similar procedure from the phase angle of each term”. The library solves the complex products together, on the branch described in reciprocity_calibration.

Parameters

Returns: The ReciprocityCalibration.

Raises

pressure_reciprocity_pair(
    frequencies_hz: ArrayLike,
    electrical_transfer_impedance_ohm: ArrayLike,
    acoustic_transfer_impedance: ArrayLike | CouplerTransferImpedance,
    sensitivity_ratio: ArrayLike,
    *,
    corrections_db: Mapping[str, ArrayLike] | None = None,
    expanded_uncertainty_db: ArrayLike | None = None,
) -> ReciprocityCalibration

The pressure sensitivities of two microphones and an auxiliary sound source (IEC 61094-2:2009 5.1.3 and 5.7.2, Formula (8)).

with the ratio of the two sensitivities measured by exposing both to the same pressure of the auxiliary source; only microphone (1) needs to be reciprocal (5.1.1).

Parameters

Returns: The ReciprocityCalibration, of two microphones.

Raises

ReciprocityMicrophone(
    equivalent_volume_m3: float,
    resonance_frequency_hz: float,
    loss_factor: float,
    front_cavity_volume_m3: float,
    front_cavity_depth_m: float,
    front_cavity_diameter_m: float,
    thread_area_m2: float = 0.0,
)

The parameters of a laboratory standard microphone that enter the acoustic transfer impedance (IEC 61094-2:2009 7.3.3 and Annex E).

The acoustic impedance is the lumped series compliance, mass and resistance of E.4, written as the equivalent volume at low frequencies, the resonance frequency and the loss factor:

E.4 states this representation is generally sufficient up to about 1,3 times the resonance frequency.

Attributes

ReciprocityMicrophone.acoustic_impedance_pa_s_m3(
    frequencies_hz: ArrayLike,
) -> NDArray[np.complex128]

$Z_{\mathrm{a}}=r_{\mathrm{a}}+\mathrm{j}\omega m_{\mathrm{a}}+1/(\mathrm{j}\omega c_{\mathrm{a}})$, in Pa·s/m³.

Parameters

Returns: $Z_{\mathrm{a}}$ at each frequency, in Pa·s/m³.

ReciprocityMicrophone.complex_equivalent_volume_m3(
    frequencies_hz: ArrayLike,
) -> NDArray[np.complex128]

The complex equivalent volume $V_{\mathrm{e}}$ of Formula (3), in m³, which tends to equivalent_volume_m3 at low frequencies:

Parameters

Returns: $V_{\mathrm{e}}$ at each frequency, in m³.

property

$c_{\mathrm{a}}=V_{\mathrm{eq}}/({\kappa }_{\mathrm{r}}{p}_{\mathrm{s},\mathrm{r}})$, in m³/Pa.

property

$m_{\mathrm{a}}=1/((2\pi f_0{)}^2{c}_{\mathrm{a}})$, in kg/m⁴.

property

$r_{\mathrm{a}}=d/(2\pi f_0{c}_{\mathrm{a}})$, in Pa·s/m³.

temperature_transfer_function(
    length_to_diameter_ratio: float,
    x: ArrayLike,
    *,
    method: str = 'exact',
) -> NDArray[np.complex128]

Gerber’s complex temperature transfer function $E_V$ of a cylindrical cavity (IEC 61094-2:2009 A.2, Formula (A.2) and Table A.1).

$E_V$ is “the ratio of the space average of the sinusoidal temperature variation associated with the sound pressure to the sinusoidal temperature variation that would be generated if the walls of the coupler were perfectly non-conducting”, a function of the length-to-diameter ratio $R$ of the cylinder and of

with $l$ its volume to surface ratio and ${\alpha }_t$ the thermal diffusivity of the gas.

method="exact" (default) sums the full solution of the annex’s reference [A.1], which A.2 requires below 20 Hz unless the uncertainty component is increased instead, and which reproduces all 96 entries of Table A.1 to the 0,000 01 the annex states for them. method="approximation" is Formula (A.2), whose modulus the annex states accurate to 0,01 % for $0,125<R<8$ and $X>5$; its first two terms are the approximation the annex allows for a coupler that is not a right circular cylinder.

Parameters

Returns: $E_V$, complex, with the shape of x.

Raises

WaveMotionCorrection(
    frequencies_hz: NDArray[np.float64],
    correction_db: NDArray[np.float64],
    speed_of_sound_ratio: float,
)

The wave-motion correction of the large-volume coupler for LS1P microphones (IEC 61094-2:2009 C.3, Table C.3).

Attributes

Whether each value was interpolated between rows of the table (interpolated) is read from the frequencies and the ratio, so it is not a field.

property

Whether each value was interpolated between rows of Table C.3.

A frequency whose air equivalent lies within 2 % of a printed row takes that row, and one below the first row takes its nil correction; any other is interpolated between two rows.

Returns: One boolean per frequency.

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

Plot the correction against frequency, with the rows of Table C.3.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).