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ISO/TR 25417:2007

ISO/TR 25417:2007 specifies definitions of acoustical quantities and terms used in noise measurement documents prepared by ISO Technical Committee TC 43, Acoustics, Subcommittee SC 1, Noise, together with their symbols and units, with the principal aim of harmonizing the terminology used in ISO/TR 25417.

Attributes

REFERENCE_PRESSURE module-attribute 

REFERENCE_PRESSURE = 2e-05

Reference value of the sound pressure \(p_0\) is \(2 \cdot 10^{-5}\) Pa.

REFERENCE_SOUND_EXPOSURE module-attribute 

REFERENCE_SOUND_EXPOSURE = 4e-10

Reference value of the sound exposure \(E_0\) is \(4 \cdot 10^{-12} \mathrm{Pa}^2\mathrm{s}\).

REFERENCE_POWER module-attribute 

REFERENCE_POWER = 1e-12

Reference value of the sound power \(P_0\) is 1 pW.

REFERENCE_ENERGY module-attribute 

REFERENCE_ENERGY = 1e-12

Reference value of the sound energy \(J_0\) is 1 pJ.

REFERENCE_INTENSITY module-attribute 

REFERENCE_INTENSITY = 1e-12

Reference value of the sound intensity \(I_0\) is \(\mathrm{1 pW/m^2}\).

Functions

sound_pressure_level 

sound_pressure_level(
    pressure, reference_pressure=REFERENCE_PRESSURE
) -> float | ndarray

Sound pressure level \(L_p\) in dB.

The sound pressure level is calculated as: $$ L_p = 10 \log_{10}{ \left( \frac{p^2}{p_0^2} \right)} $$

See section 2.2 of the standard.

PARAMETER DESCRIPTION
pressure

Instantaneous sound pressure \(p\).
reference_pressure

Reference value \(p_0\).

DEFAULT: REFERENCE_PRESSURE

RETURNS DESCRIPTION
float | ndarray

Sound pressure level
Source code in acoustic_toolbox/standards/iso_tr_25417_2007.py 
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def sound_pressure_level(
    pressure, reference_pressure=REFERENCE_PRESSURE
) -> float | np.ndarray:
    r"""Sound pressure level $L_p$ in dB.

    The sound pressure level is calculated as:
    $$
    L_p = 10 \log_{10}{ \left( \frac{p^2}{p_0^2} \right)}
    $$

    See section 2.2 of the standard.

    Args:
        pressure: Instantaneous sound pressure $p$.
        reference_pressure: Reference value $p_0$.

    Returns:
        Sound pressure level
    """
    return 10.0 * np.log10(pressure**2.0 / reference_pressure**2.0)

equivalent_sound_pressure_level 

equivalent_sound_pressure_level(
    pressure, reference_pressure=REFERENCE_PRESSURE, axis=-1
) -> float | ndarray

Time-averaged sound pressure level \(L_{p,T}\) or equivalent-continious sound pressure level \(L_{p,eqT}\) in dB.

The time-averaged sound pressure level is calculated as: $$ L_{p,T} = L_{p,eqT} = 10.0 \log_{10}{ \left( \frac{\frac{1}{T} \int_{t_1}^{t_2} p^2 (t) \mathrm{d} t }{p_0^2} \right)} $$

See section 2.3 of the standard.

PARAMETER DESCRIPTION
pressure

Instantaneous sound pressure \(p\).
reference_pressure

Reference value \(p_0\).

DEFAULT: REFERENCE_PRESSURE

axis

Axis

DEFAULT: -1

RETURNS DESCRIPTION
float | ndarray

Time-averaged sound pressure level
Source code in acoustic_toolbox/standards/iso_tr_25417_2007.py 
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def equivalent_sound_pressure_level(
    pressure, reference_pressure=REFERENCE_PRESSURE, axis=-1
) -> float | np.ndarray:
    r"""Time-averaged sound pressure level $L_{p,T}$ or equivalent-continious sound pressure level $L_{p,eqT}$ in dB.

    The time-averaged sound pressure level is calculated as:
    $$
    L_{p,T} = L_{p,eqT} = 10.0 \log_{10}{ \left( \frac{\frac{1}{T} \int_{t_1}^{t_2} p^2 (t) \mathrm{d} t  }{p_0^2} \right)}
    $$

    See section 2.3 of the standard.

    Args:
        pressure: Instantaneous sound pressure $p$.
        reference_pressure: Reference value $p_0$.
        axis: Axis

    Returns:
        Time-averaged sound pressure level
    """
    return 10.0 * np.log10((pressure**2.0).mean(axis=axis) / reference_pressure**2.0)

max_sound_pressure_level 

max_sound_pressure_level(
    pressure, reference_pressure=REFERENCE_PRESSURE, axis=-1
) -> float | ndarray

Maximum time-averaged sound pressure level \(L_{F,max}\) in dB.

PARAMETER DESCRIPTION
pressure

Instantaneous sound pressure \(p\).
reference_pressure

Reference value \(p_0\).

DEFAULT: REFERENCE_PRESSURE

axis

Axis

DEFAULT: -1

RETURNS DESCRIPTION
float | ndarray

Maximum sound pressure level \(\mathrm{max}{(L_{p})}\)
Source code in acoustic_toolbox/standards/iso_tr_25417_2007.py 
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def max_sound_pressure_level(
    pressure, reference_pressure=REFERENCE_PRESSURE, axis=-1
) -> float | np.ndarray:
    r"""Maximum time-averaged sound pressure level $L_{F,max}$ in dB.

    Args:
        pressure: Instantaneous sound pressure $p$.
        reference_pressure: Reference value $p_0$.
        axis: Axis

    Returns:
        Maximum sound pressure level $\mathrm{max}{(L_{p})}$
    """
    return sound_pressure_level(pressure, reference_pressure=reference_pressure).max(
        axis=axis
    )

peak_sound_pressure 

peak_sound_pressure(pressure, axis=-1) -> float | ndarray

Peak sound pressure \(p_{peak}\) is the greatest absolute sound pressure during a certain time interval.

PARAMETER DESCRIPTION
pressure

Instantaneous sound pressure \(p\).
axis

Axis

DEFAULT: -1

RETURNS DESCRIPTION
float | ndarray

Peak sound pressure \(p_{peak} = \mathrm{max}(|p|)\)
Source code in acoustic_toolbox/standards/iso_tr_25417_2007.py 
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def peak_sound_pressure(pressure, axis=-1) -> float | np.ndarray:
    r"""Peak sound pressure $p_{peak}$ is the greatest absolute sound pressure during a certain time interval.

    Args:
        pressure: Instantaneous sound pressure $p$.
        axis: Axis

    Returns:
        Peak sound pressure $p_{peak} = \mathrm{max}(|p|)$
    """
    return np.abs(pressure).max(axis=axis)

peak_sound_pressure_level 

peak_sound_pressure_level(
    pressure, reference_pressure=REFERENCE_PRESSURE, axis=-1
) -> float | ndarray

Peak sound pressure level \(L_{p,peak}\) in dB.

PARAMETER DESCRIPTION
pressure

Instantaneous sound pressure \(p\).
reference_pressure

Reference value \(p_0\).

DEFAULT: REFERENCE_PRESSURE

axis

Axis

DEFAULT: -1

RETURNS DESCRIPTION
float | ndarray

Peak sound pressure level $$ L_{p,peak} = 10.0 \log \frac{p_{peak}^2.0}{p_0^2} $$
Source code in acoustic_toolbox/standards/iso_tr_25417_2007.py 
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def peak_sound_pressure_level(
    pressure, reference_pressure=REFERENCE_PRESSURE, axis=-1
) -> float | np.ndarray:
    r"""Peak sound pressure level $L_{p,peak}$ in dB.

    Args:
        pressure: Instantaneous sound pressure $p$.
        reference_pressure: Reference value $p_0$.
        axis: Axis

    Returns:
        Peak sound pressure level
            $$
            L_{p,peak} = 10.0 \log \frac{p_{peak}^2.0}{p_0^2}
            $$
    """
    return 10.0 * np.log10(
        peak_sound_pressure(pressure, axis=axis) ** 2.0 / reference_pressure**2.0
    )

sound_exposure 

sound_exposure(pressure, fs, axis=-1) -> float | ndarray

Calculate sound exposure \(E_T\).

PARAMETER DESCRIPTION
pressure

Instantaneous sound pressure \(p\).
fs

Sample frequency \(f_s\).
axis

Axis

DEFAULT: -1

RETURNS DESCRIPTION
float | ndarray

Sound exposure $$ E_T = \int_{t_1}^{t_2} p^2(t) \mathrm{d}t $$
Source code in acoustic_toolbox/standards/iso_tr_25417_2007.py 
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def sound_exposure(pressure, fs, axis=-1) -> float | np.ndarray:
    r"""Calculate sound exposure $E_T$.

    Args:
        pressure: Instantaneous sound pressure $p$.
        fs: Sample frequency $f_s$.
        axis: Axis

    Returns:
        Sound exposure
            $$
            E_T = \int_{t_1}^{t_2} p^2(t) \mathrm{d}t
            $$
    """
    return (pressure**2.0 / fs).sum(axis=axis)

sound_exposure_level 

sound_exposure_level(
    pressure,
    fs,
    reference_sound_exposure=REFERENCE_SOUND_EXPOSURE,
    axis=-1,
) -> float | ndarray

Sound exposure level \(L_{E,T}\) in dB.

PARAMETER DESCRIPTION
pressure

Instantaneous sound pressure \(p\).
fs

Sample frequency \(f_s\).
reference_sound_exposure

Reference sound exposure \(E_T\).

DEFAULT: REFERENCE_SOUND_EXPOSURE

axis

Axis

DEFAULT: -1

RETURNS DESCRIPTION
float | ndarray

Sound exposure level $$ L_{E,T} = 10 \log_{10}{ \frac{E_T}{E_0} } $$
Source code in acoustic_toolbox/standards/iso_tr_25417_2007.py 
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def sound_exposure_level(
    pressure, fs, reference_sound_exposure=REFERENCE_SOUND_EXPOSURE, axis=-1
) -> float | np.ndarray:
    r"""Sound exposure level $L_{E,T}$ in dB.

    Args:
        pressure: Instantaneous sound pressure $p$.
        fs: Sample frequency $f_s$.
        reference_sound_exposure: Reference sound exposure $E_T$.
        axis: Axis

    Returns:
        Sound exposure level
            $$
            L_{E,T} = 10 \log_{10}{ \frac{E_T}{E_0}  }
            $$
    """
    return 10.0 * np.log10(
        sound_exposure(pressure, fs, axis=axis) / reference_sound_exposure
    )

sound_power_level 

sound_power_level(
    power, reference_power=REFERENCE_POWER
) -> float | ndarray

Sound power level \(L_W\).

PARAMETER DESCRIPTION
power

Sound power \(P\).
reference_power

Reference sound power \(P_0\).

DEFAULT: REFERENCE_POWER

RETURNS DESCRIPTION
float | ndarray

Sound power level calculated as: $$ 10 \log_{10}{ \frac{P}{P_0} } $$
Source code in acoustic_toolbox/standards/iso_tr_25417_2007.py 
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def sound_power_level(power, reference_power=REFERENCE_POWER) -> float | np.ndarray:
    r"""Sound power level $L_W$.

    Args:
        power: Sound power $P$.
        reference_power: Reference sound power $P_0$.

    Returns:
        Sound power level calculated as:
            $$
            10 \log_{10}{ \frac{P}{P_0}  }
            $$
    """
    return 10.0 * np.log10(power / reference_power)

sound_energy 

sound_energy(power, axis=-1) -> float | ndarray

Sound energy \(J\).

PARAMETER DESCRIPTION
power

Sound power \(P\).
axis

Axis

DEFAULT: -1

RETURNS DESCRIPTION
float | ndarray

Sound energy $$ J = \int_{t_1}^{t_2} P(t) \mathrm{d} t $$
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def sound_energy(power, axis=-1) -> float | np.ndarray:
    r"""Sound energy $J$.

    Args:
        power: Sound power $P$.
        axis: Axis

    Returns:
        Sound energy
            $$
            J = \int_{t_1}^{t_2} P(t) \mathrm{d} t
            $$
    """
    return power.sum(axis=axis)

sound_energy_level 

sound_energy_level(
    energy, reference_energy=REFERENCE_ENERGY
) -> ndarray

Sound energy level \(L_J\) in dB.

PARAMETER DESCRIPTION
energy

Sound energy \(J\).
reference_energy

Reference sound energy \(J_0\).

DEFAULT: REFERENCE_ENERGY

RETURNS DESCRIPTION
ndarray

Sound energy level $$ L_{J} = 10 \log_{10}{ \frac{J}{J_0} } $$
Source code in acoustic_toolbox/standards/iso_tr_25417_2007.py 
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def sound_energy_level(energy, reference_energy=REFERENCE_ENERGY) -> np.ndarray:
    r"""Sound energy level $L_J$ in dB.

    Args:
        energy: Sound energy $J$.
        reference_energy: Reference sound energy $J_0$.

    Returns:
        Sound energy level
            $$
            L_{J} = 10 \log_{10}{ \frac{J}{J_0} }
            $$
    """
    return np.log10(energy / reference_energy)

sound_intensity 

sound_intensity(pressure, velocity) -> ndarray

Sound intensity \(\mathbf{i}\).

PARAMETER DESCRIPTION
pressure

Sound pressure \(p(t)\).
velocity

Particle velocity \(\mathbf{u}(t)\).
RETURNS DESCRIPTION
ndarray

Sound intensity $$ \mathbf{i} = p(t) \cdot \mathbf{u}(t) $$
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def sound_intensity(pressure, velocity) -> np.ndarray:
    r"""Sound intensity $\mathbf{i}$.

    Args:
        pressure: Sound pressure $p(t)$.
        velocity: Particle velocity $\mathbf{u}(t)$.

    Returns:
        Sound intensity
            $$
            \mathbf{i} = p(t) \cdot \mathbf{u}(t)
            $$
    """
    return pressure * velocity

time_averaged_sound_intensity 

time_averaged_sound_intensity(intensity, axis=-1) -> float

Time-averaged sound intensity \(\mathbf{I}_T\).

PARAMETER DESCRIPTION
intensity

Sound intensity \(\mathbf{i}\).
axis

Axis

DEFAULT: -1

RETURNS DESCRIPTION
float

Time-averaged sound intensity $$ I_T = \frac{1}{T} \int_{t_1}^{t_2} \mathbf{i}(t) $$
Source code in acoustic_toolbox/standards/iso_tr_25417_2007.py 
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def time_averaged_sound_intensity(intensity, axis=-1) -> float:
    r"""Time-averaged sound intensity $\mathbf{I}_T$.

    Args:
        intensity: Sound intensity $\mathbf{i}$.
        axis: Axis

    Returns:
        Time-averaged sound intensity
            $$
            I_T = \frac{1}{T} \int_{t_1}^{t_2} \mathbf{i}(t)
            $$
    """
    return intensity.mean(axis=axis)

time_averaged_sound_intensity_level 

time_averaged_sound_intensity_level(
    time_averaged_sound_intensity,
    reference_intensity=REFERENCE_INTENSITY,
    axis=-1,
) -> float

Time-averaged sound intensity level \(L_{I,T}\).

PARAMETER DESCRIPTION
time_averaged_sound_intensity

Time-averaged sound intensity \(\mathbf{I}_T\).
reference_intensity

Reference sound intensity \(I_0\).

DEFAULT: REFERENCE_INTENSITY

axis

Axis along which to calculate norm.

DEFAULT: -1

RETURNS DESCRIPTION
float

Time-averaged sound intensity level calculated as: $$ L_{I,T} = 10 \log_{10} { \frac{|\mathbf{I}_T|}{I_0} } $$
Source code in acoustic_toolbox/standards/iso_tr_25417_2007.py 
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def time_averaged_sound_intensity_level(
    time_averaged_sound_intensity, reference_intensity=REFERENCE_INTENSITY, axis=-1
) -> float:
    r"""Time-averaged sound intensity level $L_{I,T}$.

    Args:
        time_averaged_sound_intensity: Time-averaged sound intensity $\mathbf{I}_T$.
        reference_intensity: Reference sound intensity $I_0$.
        axis: Axis along which to calculate norm.

    Returns:
        Time-averaged sound intensity level calculated as:
            $$
            L_{I,T} = 10 \log_{10} { \frac{|\mathbf{I}_T|}{I_0} }
            $$
    """
    return 10.0 * np.log10(
        np.linalg.norm(time_averaged_sound_intensity, axis=axis) / reference_intensity
    )

normal_time_averaged_sound_intensity 

normal_time_averaged_sound_intensity(
    time_averaged_sound_intensity, unit_normal_vector
) -> float

Normal time-averaged sound intensity \(\mathbf{I}_{n,T}\).

PARAMETER DESCRIPTION
time_averaged_sound_intensity

Time-averaged sound intensity \(\mathbf{I}_T\).
unit_normal_vector

Unit normal vector \(\mathbf{n}\).
RETURNS DESCRIPTION
float

Normal time-averaged sound intensity $$ I_{n,T} = \mathbf{I}_T \cdot \mathbf{n} $$
Source code in acoustic_toolbox/standards/iso_tr_25417_2007.py 
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def normal_time_averaged_sound_intensity(
    time_averaged_sound_intensity, unit_normal_vector
) -> float:
    r"""Normal time-averaged sound intensity $\mathbf{I}_{n,T}$.

    Args:
        time_averaged_sound_intensity: Time-averaged sound intensity $\mathbf{I}_T$.
        unit_normal_vector: Unit normal vector $\mathbf{n}$.

    Returns:
        Normal time-averaged sound intensity
            $$
            I_{n,T} = \mathbf{I}_T \cdot \mathbf{n}
            $$
    """
    return time_averaged_sound_intensity.dot(unit_normal_vector)

normal_time_averaged_sound_intensity_level 

normal_time_averaged_sound_intensity_level(
    normal_time_averaged_sound_intensity,
    reference_intensity=REFERENCE_INTENSITY,
) -> float

Normal time-averaged sound intensity level \(L_{I_{n,T}}\) in dB.

PARAMETER DESCRIPTION
normal_time_averaged_sound_intensity

Normal time-averaged sound intensity \(I_{n,T}\).
reference_intensity

Reference sound intensity \(I_0\).

DEFAULT: REFERENCE_INTENSITY

RETURNS DESCRIPTION
float

Normal time-averaged sound intensity level calculated as: $$ I_{n,T} = 10 \log_{10} { \frac{|I_{n,T}|}{I_0}} $$
Source code in acoustic_toolbox/standards/iso_tr_25417_2007.py 
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def normal_time_averaged_sound_intensity_level(
    normal_time_averaged_sound_intensity, reference_intensity=REFERENCE_INTENSITY
) -> float:
    r"""Normal time-averaged sound intensity level $L_{I_{n,T}}$ in dB.

    Args:
        normal_time_averaged_sound_intensity: Normal time-averaged sound intensity $I_{n,T}$.
        reference_intensity: Reference sound intensity $I_0$.

    Returns:
        Normal time-averaged sound intensity level calculated as:
            $$
            I_{n,T} = 10 \log_{10} { \frac{|I_{n,T}|}{I_0}}
            $$
    """
    return 10.0 * np.log10(
        np.abs(normal_time_averaged_sound_intensity / reference_intensity)
    )

:::