materials.surfaces.road_absorption

In-situ sound absorption of road surfaces (ISO 13472-1 / ISO 13472-2).

Two complementary standardised in-situ methods are supported here. They target opposite ends of the absorption scale and are not interchangeable:

BS ISO 13472-1:2002 - extended surface method. A free-field impulse response is measured over the road, the direct (incident) and surface (reflected) components are separated in the time domain by the subtraction technique and an Adrienne-type temporal window (Clause 6.4), transformed to frequency, and ratioed. The normal-incidence sound absorption coefficient is (Clause 4.1):
$α (f) = 1 - Q_{W} (f) = 1 - \frac{1}{K _{r}^{2}} \frac{H _{r} ( f )}{H _{i} ( f )}^{2}$
with Hi/Hr the incident/reflected transfer functions and Kr the geometrical-spreading factor $K_{r} = (d_{s} - d_{m}) / (d_{s} + d_{m})$ for the mandatory geometry $d_{s} = 1.25$ m (source-to-plane) and $d_{m} = 0.25$ m (mic-to-plane), giving $K_{r} = 2/3$ (Clause 4.2 / Annex C). The complex pressure reflection factor $Q_{p} = (1/ K_{r}) (H_{r} / H_{i}) e^{+ j 2 π f Δ τ}$ with $Δ τ = 2 d_{m} / c$ (Annex C) is available for theory comparison. A highly reflective reference surface removes the electro-acoustic chain error and the geometry factor by a ratio (Annex B), and non-normal incidence uses $K_{r, θ}$ (Annex F).
BS ISO 13472-2:2010 - spot method. This is an in-situ application of the ISO 10534-2 two-microphone impedance tube for reflective surfaces (measured alpha below ~0.15). Part 2 does not restate the transfer-function / reflection-factor / absorption mathematics; Clauses 4, 5.7 and 6.6 defer it to ISO 10534-2. The core computation therefore lives in two_microphone_impedance and is not reimplemented here. This module contributes only the Part-2 tube geometry/validity helpers (upper usable frequency, microphone-spacing bounds, the 250-1600 Hz one-third-octave working range) and the Annex A internal-loss system correction $α \approx α_{measured} - α_{system}$ .

Sign / normalisation convention (ISO 13472-1): the forward transform is NumPy’s rfft with kernel $e^{- j 2 π f t}$ (unnormalised); every quantity here is a ratio of two transforms from the same processing chain, so the transform normalisation cancels (Clause 6.1). A pure time delay tau of the reflected path scales its spectrum by $e^{- j 2 π f τ}$ ; the optional phase restoration multiplies by $e^{+ j 2 π f τ}$ to recover Qp (Annex C / Annex G, resolving the Clause 4.1 NOTE shorthand to the frequency-dependent form).

The window durations of the Adrienne window are not fixed by the standard: Clause 6.4 mandates only a sharp leading edge, a 5 ms flat portion and a cosine-squared or Blackman-Harris trailing edge, with the shape and lengths reported per measurement. They are therefore configurable here and default to a short leading edge, a 5 ms flat top and a Blackman-Harris trailing edge (the Annex E example report); the historical fixed edge timings are not hard-coded as if normative.

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

absorption_reference_corrected

absorption_reference_corrected(
    road_reflection: ArrayLike,
    reference_reflection: ArrayLike,
) -> Real

Reference-corrected road absorption (ISO 13472-1:2002, Annex B).

Dividing the road and reference measured pressure reflection factors removes both the electro-acoustic chain error e(f) and, because the geometry is identical, the Kr factor:

Q_{p, road} (f) = \frac{Q _{p, road,meas} ( f )}{Q _{p, ref,meas} ( f )}

α_{road} (f) = 1 - \frac{Q _{p, road,meas} ( f )}{Q _{p, ref,meas} ( f )}^{2}

The reference surface is assumed totally reflecting ( $∣ Q_{p, ref} ∣ = 1$ , checked in an impedance tube to have absorption < 0.05, Annex B).

Parameters

Name	Description
`road_reflection`	Measured road pressure reflection factor `Qp,road,meas` (complex; the `1 / Kr` scaling need not be removed as it cancels).
`reference_reflection`	Measured reference pressure reflection factor `Qp,ref,meas` (complex, same geometry and chain).

Returns: Reference-corrected road absorption coefficient alpha_road(f).

adrienne_window

adrienne_window(
    fs: float | None = None,
    *,
    flat_duration: float = 0.005,
    leading_duration: float = 0.0005,
    trailing_duration: float = 0.005,
    leading_edge: str = 'blackman-harris',
    trailing_edge: str = 'blackman-harris',
) -> Real

Adrienne-type temporal window (ISO 13472-1:2002, Clause 6.4).

Clause 6.4 mandates a sharp leading edge, a 5 ms flat portion and a cosine-squared or Blackman-Harris trailing edge so as to suppress frequency-domain oscillations (Figure 4); the shape and the durations are reported per measurement rather than fixed by the standard. All three durations are therefore configurable. The window is the concatenation of a rising leading half-taper, a unit-valued flat portion and a falling trailing half-taper:

w = [ rising_edge (0 -> 1) | flat (== 1) | trailing_edge (1 -> 0) ]

The defaults (short 0.5 ms leading edge, 5 ms flat top, 5 ms Blackman-Harris trailing edge) follow the Annex E example report; they are not a normative fixed set of timings. The lower usable frequency scales as ~ 1 / T_window (Clause 6.4), so report the durations used.

Parameters

Name	Description
`fs`	Sampling frequency, in hertz (ISO 13472-1 Clause 6.2 requires `fs > 40 kHz` in practice).
`flat_duration`	Flat-portion duration, in seconds (default 5 ms).
`leading_duration`	Leading-edge (rise) duration, in seconds; 0 gives a sharp step onset.
`trailing_duration`	Trailing-edge (fall) duration, in seconds.
`leading_edge`	Leading-edge shape, `"blackman-harris"` or `"cosine-squared"`.
`trailing_edge`	Trailing-edge shape, `"blackman-harris"` or `"cosine-squared"`.

Returns: The time-domain window, one sample per 1 / fs (length round((leading + flat + trailing) * fs) samples).

Raises

Exception	When
ValueError	If `fs` is missing or not positive, a duration is negative, the flat duration is not positive, or an edge shape is unknown.

check_spot_frequency_range

check_spot_frequency_range(frequency: ArrayLike) -> None

Advise when a spot-method frequency is out of range (ISO 13472-2, Scope).

The spot method is valid over the one-third-octave bands 250-1600 Hz (narrow-band 220-1800 Hz). Frequencies outside SPOT_FREQUENCY_RANGE raise a RoadAbsorptionWarning; results there are advisory.

Parameters

Name	Description
`frequency`	Frequencies to check, in hertz.

Raises

Exception	When
ValueError	If any frequency is negative.

DEFAULT_MIC_HEIGHT

Constant (float).

DEFAULT_MIC_HEIGHT = 0.25

DEFAULT_SOURCE_HEIGHT

Constant (float).

DEFAULT_SOURCE_HEIGHT = 1.25

DEFAULT_SPEED_OF_SOUND

Constant (float).

DEFAULT_SPEED_OF_SOUND = 340.0

geometric_spreading_factor

geometric_spreading_factor(
    source_height: float = 1.25,
    mic_height: float = 0.25,
) -> float

Geometrical-spreading factor Kr (ISO 13472-1:2002, Clause 4.1).

$K_{r} = (d_{s} - d_{m}) / (d_{s} + d_{m})$ . It corrects the reflected path for the extra spherical spreading over the image-source distance $d_{s} + d_{m}$ relative to the direct distance $d_{s} - d_{m}$ (Annex C). The mandatory geometry $d_{s} = 1.25$ m, $d_{m} = 0.25$ m gives $K_{r} = 2/3$ (Clause 4.2).

Parameters

Name	Description
`source_height`	Source-to-reference-plane distance `ds`, in metres.
`mic_height`	Microphone-to-reference-plane distance `dm`, in metres.

Returns: Geometrical-spreading factor Kr (dimensionless, $0 < K_{r} < 1$ ).

Raises

Exception	When
ValueError	If `ds` or `dm` is not positive or $d_{s} \leq d_{m}$ .

geometric_spreading_factor_angle

geometric_spreading_factor_angle(
    incidence_angle: float,
    source_height: float = 1.25,
    mic_height: float = 0.25,
) -> float

Oblique geometrical-spreading factor (ISO 13472-1, Annex F).

$K_{r, θ}^{2} = 1 - cos^{2} (θ) (1 - K_{r}^{2})$ with Kr the normal-incidence factor of geometric_spreading_factor. At $θ = 0$ the cosine is unity and Kr,theta collapses to Kr (Clause 4.1).

Parameters

Name	Description
`incidence_angle`	Incidence angle `theta`, in radians.
`source_height`	Source-to-reference-plane distance `ds`, in metres.
`mic_height`	Microphone-to-reference-plane distance `dm`, in metres.

Returns: Oblique factor Kr,theta (positive root, dimensionless).

insitu_absorption_coefficient

insitu_absorption_coefficient(
    incident_ir: ArrayLike,
    reflected_ir: ArrayLike,
    *,
    source_height: float = 1.25,
    mic_height: float = 0.25,
    incidence_angle: float = 0.0,
    n: int | None = None,
) -> Real

Normal-incidence absorption coefficient alpha(f) (ISO 13472-1, 4.1).

$α (f) = 1 - Q_{W} (f) = 1 - (1/ K_{r}^{2}) ∣ H_{r} (f) / H_{i} (f) ∣^{2}$ (the direct energy route via power_reflection_coefficient; for oblique incidence Kr is replaced by Kr,theta, Annex F). Non-specularly reflected energy is treated as absorbed, so alpha may be slightly overestimated (Clause 4.1).

Parameters

Name	Description
`incident_ir`	Windowed incident impulse response `hi(t)`, real.
`reflected_ir`	Windowed reflected impulse response `hr(t)`, real.
`source_height`	Source-to-plane distance `ds`, in metres.
`mic_height`	Microphone-to-plane distance `dm`, in metres.
`incidence_angle`	Incidence angle `theta`, in radians (0 = normal).
`n`	FFT length; defaults to the longer input.

Returns: Absorption coefficient alpha(f) at the rfft frequency bins.

insitu_absorption_from_reflection

insitu_absorption_from_reflection(reflection: ArrayLike) -> Real

Absorption coefficient from the reflection factor (ISO 13472-1, 4.1).

$α = 1 - ∣ r ∣^{2}$ . With r already carrying the $1/ K_{r}$ factor (see insitu_reflection_factor) this is the reflection-factor route to alpha and equals the direct energy route of insitu_absorption_coefficient.

Parameters

Name	Description
`reflection`	Complex reflection factor `r`.

Returns: Absorption coefficient alpha (real).

insitu_absorption_spectrum

insitu_absorption_spectrum(
    incident_ir: ArrayLike,
    reflected_ir: ArrayLike,
    fs: float | None = None,
    *,
    source_height: float = 1.25,
    mic_height: float = 0.25,
    incidence_angle: float = 0.0,
    n: int | None = None,
    f_min: float = 250.0,
    f_max: float = 4000.0,
    clip_negative: bool = True,
) -> InsituAbsorptionResult

In-situ one-third-octave absorption spectrum (ISO 13472-1, Clause 4.1).

End-to-end convenience: the windowed incident and reflected impulse responses give the narrow-band absorption via insitu_absorption_coefficient, which is then reduced to one-third-octave bands with one_third_octave_absorption and wrapped in a plottable InsituAbsorptionResult.

Parameters

Name	Description
`incident_ir`	Windowed incident (direct-path) impulse response `hi`.
`reflected_ir`	Windowed reflected-path impulse response `hr`.
`fs`	Sampling frequency, in hertz.
`source_height`	Source-to-plane distance `ds`, in metres.
`mic_height`	Microphone-to-plane distance `dm`, in metres.
`incidence_angle`	Incidence angle `theta`, in radians (0 = normal).
`n`	FFT length; defaults to the longer of the two impulse responses.
`f_min`	Lowest band centre to report, in hertz (default 250 Hz).
`f_max`	Highest band centre to report, in hertz (default 4000 Hz).
`clip_negative`	Clip negative band results to zero (default `True`).

Returns: An InsituAbsorptionResult with .plot().

Raises

Exception	When
ValueError	On empty inputs, invalid geometry, or a missing or non-positive `fs`.

insitu_reflection_factor

insitu_reflection_factor(
    incident_ir: ArrayLike,
    reflected_ir: ArrayLike,
    *,
    source_height: float = 1.25,
    mic_height: float = 0.25,
    incidence_angle: float = 0.0,
    fs: float | None = None,
    delay: float | None = None,
    n: int | None = None,
) -> Complex

Complex pressure reflection factor r(f) (ISO 13472-1, Clause 4.1).

$r (f) = (1/ K_{r}) H_{r} (f) / H_{i} (f)$ from the windowed reflected and incident impulse responses, with Hr/Hi their real FFTs and Kr the geometrical-spreading factor (or Kr,theta when incidence_angle is given, Annex F). When both fs and delay are supplied the reflected-path time offset is undone by $exp (+ j 2 π f delay)$ , yielding the complex Qp of the Clause 4.1 NOTE (with delay set to $Δ τ = 2 d_{m} / c$ , Annex C; the frequency-dependent form of Annex G).

Parameters

Name	Description
`incident_ir`	Windowed incident (direct-path) impulse response `hi(t)`, real, one sample per `1 / fs`.
`reflected_ir`	Windowed reflected-path impulse response `hr(t)`, real, same sampling as `incident_ir`.
`source_height`	Source-to-plane distance `ds`, in metres.
`mic_height`	Microphone-to-plane distance `dm`, in metres.
`incidence_angle`	Incidence angle `theta`, in radians (0 = normal).
`fs`	Sampling frequency, in hertz; required with `delay` for phase restoration.
`delay`	Reflected-path delay `dtau` to undo, in seconds; `None` returns the raw spectral ratio.
`n`	FFT length; defaults to the longer of the two impulse responses.

Returns: Complex reflection factor r(f) at the rfft frequency bins.

Raises

Exception	When
ValueError	On empty inputs, invalid geometry, or `delay` given without `fs`.

InsituAbsorptionResult

InsituAbsorptionResult(
    frequencies: Real,
    absorption: Real,
    source_height: float | None = None,
    mic_height: float | None = None,
)

An in-situ one-third-octave absorption spectrum (ISO 13472-1).

Attributes

Name	Description
`frequencies`	One-third-octave band centre frequencies, in hertz.
`absorption`	Sound-absorption coefficient `alpha` per band (a band with no contributing narrow-band samples is `nan`).
`source_height`	Source height the spectrum was reduced with, in metres, retained (with `mic_height`) so `plot_geometry` can draw the set-up; `None` for hand-built results.
`mic_height`	Microphone height, in metres, or `None`.

InsituAbsorptionResult.plot()

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

Plot the in-situ absorption spectrum alpha(f).

Requires matplotlib (pip install phonometry[plot]); returns the Axes and never calls plt.show.

InsituAbsorptionResult.plot_geometry()

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

Draw the measurement set-up to scale.

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

Raises

Exception	When
ValueError	If the result does not retain its geometry.

max_sampled_area_radius

max_sampled_area_radius(
    window_width: float,
    *,
    source_height: float = 1.25,
    mic_height: float = 0.25,
    speed_of_sound: float = 340.0,
) -> float

Radius of the maximum sampled area (ISO 13472-1:2002, Annex A).

For normal incidence the maximum sampled area is a circle of radius (m):

r = \frac{1}{d _{s} + d _{m} + c T _{w}} (d_{s} + d_{m} + c T_{w} /2) (d_{s} + c T_{w} /2) (2 d_{m} + c T_{w}) (c T_{w})

with Tw the width of the temporal window isolating the reflected wave. The Annex A worked example ( $d_{s} = 1.25$ , $d_{m} = 0.25$ , $c = 340$ m/s, and the 5 ms flat window) gives $r \approx 1.34$ m.

Parameters

Name	Description
`window_width`	Temporal-window width `Tw` (reflected wave), seconds.
`source_height`	Source-to-plane distance `ds`, in metres.
`mic_height`	Microphone-to-plane distance `dm`, in metres.
`speed_of_sound`	Speed of sound `c`, in metres per second.

Returns: Maximum-sampled-area radius r, in metres.

Raises

Exception	When
ValueError	On non-positive geometry or window width.

msa_major_axis

msa_major_axis(
    window_width: float,
    projected_distance: float,
    *,
    source_height: float = 1.25,
    mic_height: float = 0.25,
    speed_of_sound: float = 340.0,
) -> float

Major axis of the oblique sampled-area ellipsoid (ISO 13472-1, Annex F).

$a = c T_{w} + (d_{s} + d_{m})^{2} + d_{p}^{2}$ for the ellipsoid of revolution with the source and microphone at its foci; dp is the source-to-microphone distance projected on the reference plane.

Parameters

Name	Description
`window_width`	Temporal-window width `Tw`, in seconds.
`projected_distance`	Projected source-to-mic distance `dp`, in metres.
`source_height`	Source-to-plane distance `ds`, in metres.
`mic_height`	Microphone-to-plane distance `dm`, in metres.
`speed_of_sound`	Speed of sound `c`, in metres per second.

Returns: Major axis a, in metres.

Raises

Exception	When
ValueError	On non-positive window width, speed, or negative `dp`.

one_third_octave_absorption

one_third_octave_absorption(
    frequency: ArrayLike,
    absorption: ArrayLike,
    *,
    f_min: float = 250.0,
    f_max: float = 4000.0,
    clip_negative: bool = True,
) -> tuple[Real, Real]

Aggregate narrow-band absorption into one-third-octave bands.

Both parts require a linear average of the narrow-band absorption over each one-third-octave band (ISO 13472-1 Clause 4.1; ISO 13472-2 Clause 6.6), keeping negative narrow-band values during the averaging. The band edges are the IEC base-two limits $f_{c} \cdot 2^{\pm 1/6}$ . Negative one-third-octave results are set to zero when clip_negative is true (ISO 13472-2 Clause 6.6 step 5); Part 1 does not mandate clipping, so pass clip_negative=False to reproduce its raw output.

Parameters

Name	Description
`frequency`	Narrow-band frequencies, in hertz.
`absorption`	Narrow-band absorption values aligned with `frequency`.
`f_min`	Lowest band centre to report, in hertz (default 250 Hz).
`f_max`	Highest band centre to report, in hertz (4000 Hz for Part 1; pass 1600 Hz for the Part-2 range).
`clip_negative`	Set negative band results to zero (default `True`).

Returns: Tuple (band_centres, band_absorption); a band with no narrow-band samples yields nan.

Raises

Exception	When
ValueError	If `frequency` and `absorption` differ in length or are empty.

PART1_FREQUENCY_RANGE

Constant (tuple).

PART1_FREQUENCY_RANGE = (250.0, 4000.0)

plot_insitu_geometry

plot_insitu_geometry(
    ax: Axes | None = None,
    *,
    source_height: float = 1.25,
    mic_height: float = 0.25,
    sampled_radius: float | None = 1.34,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Draw the in-situ surface-absorption set-up to scale.

Loudspeaker on its mast above the surface, microphone below it, direct and surface-reflected paths, and the sampled-area radius on the ground. Defaults are the standard heights (1,25 m source, 0,25 m microphone) with the sampled radius of the standard 5 ms window.

Parameters

Name	Description
`ax`	Existing axes, or `None` to create a figure.
`source_height`	Source height above the surface, in metres.
`mic_height`	Microphone height, in metres (< `source_height`).
`sampled_radius`	Sampled-area radius drawn on the ground, in metres; `None` omits it.
`language`	Label language, `"en"` (default) or `"es"`.
`kwargs`	Forwarded to the surface rectangle.

Returns: The axes.

power_reflection_coefficient

power_reflection_coefficient(
    incident_ir: ArrayLike,
    reflected_ir: ArrayLike,
    *,
    source_height: float = 1.25,
    mic_height: float = 0.25,
    incidence_angle: float = 0.0,
    n: int | None = None,
) -> Real

Sound-power reflection factor QW(f) (ISO 13472-1, 4.1 / Annex C).

The direct energy route $Q_{W} (f) = (1/ K_{r}^{2}) ∣ H_{r} (f) / H_{i} (f) ∣^{2}$ (Kr,theta for oblique incidence). It equals $∣ r ∣^{2}$ from insitu_reflection_factor but is formed from magnitudes only, so it is independent of any reflected-path time offset.

Parameters

Name	Description
`incident_ir`	Windowed incident impulse response `hi(t)`, real.
`reflected_ir`	Windowed reflected impulse response `hr(t)`, real.
`source_height`	Source-to-plane distance `ds`, in metres.
`mic_height`	Microphone-to-plane distance `dm`, in metres.
`incidence_angle`	Incidence angle `theta`, in radians.
`n`	FFT length; defaults to the longer input.

Returns: Sound-power reflection factor QW(f) (real).

reflected_path_delay

reflected_path_delay(
    mic_height: float = 0.25,
    speed_of_sound: float = 340.0,
) -> float

Reflected-path arrival delay dtau (ISO 13472-1:2002, Annex C).

$Δ τ = 2 d_{m} / c$ is the time difference between the direct and the surface-reflected impulses for the normal-incidence geometry; it is the delay undone by the phase-restoration term of insitu_reflection_factor.

Parameters

Name	Description
`mic_height`	Microphone-to-reference-plane distance `dm`, in metres.
`speed_of_sound`	Speed of sound `c`, in metres per second.

Returns: Delay dtau, in seconds.

Raises

Exception	When
ValueError	If `dm` or `c` is not positive.

RoadAbsorptionWarning

Advisory for out-of-range in-situ road-absorption frequencies.

SPOT_FREQUENCY_RANGE

Constant (tuple).

SPOT_FREQUENCY_RANGE = (250.0, 1600.0)

spot_internal_loss_correction

spot_internal_loss_correction(
    measured_absorption: ArrayLike,
    system_absorption: ArrayLike,
    *,
    clip_negative: bool = True,
) -> Real

Internal-loss (system) correction (ISO 13472-2:2010, Annex A).

The tube reads all thermal/viscous losses between the microphones and the surface as absorption. For reflective surfaces this is removed by subtracting the reading on a totally reflecting reference plate:

α (f) \approx α_{measured} (f) - α_{system} (f)

Valid because both terms are small (measured < 0.15, internal < 0.03). This is the subtractive Part-2 correction and must not be confused with the Part-1 ratio correction (absorption_reference_corrected). Negative one-third-octave results are set to zero when clip_negative is true (Clause 6.6 step 5).

Parameters

Name	Description
`measured_absorption`	Measured road absorption `alpha_m(f)`.
`system_absorption`	Reference-plate (system) absorption `alpha_system(f)`, same bands.
`clip_negative`	Set negative corrected values to zero (default `True`).

Returns: Corrected absorption coefficient alpha(f).

Raises

Exception	When
ValueError	If the two inputs differ in shape.

spot_microphone_spacing_bounds

spot_microphone_spacing_bounds(
    speed_of_sound: float = 340.0,
    *,
    f_min: float = 220.0,
    f_max: float = 1800.0,
) -> tuple[float, float]

Microphone-spacing bounds (s_min, s_max) (ISO 13472-2:2010, 5.4.2).

$s_{max} < 0.45 c_{0} / f_{max}$ avoids spacing approaching half a wavelength at the top frequency, and $s_{min} > 0.05 c_{0} / f_{min}$ keeps the spacing above 5 % of a wavelength at the bottom frequency. For the narrow band 220-1800 Hz ( $c_{0} \approx 340$ m/s) these give $s_{max} \approx 85$ mm and $s_{min} \approx 77$ mm, bracketing the nominal $s = (81 \pm 4)$ mm.

Parameters

Name	Description
`speed_of_sound`	Speed of sound `c0`, in metres per second.
`f_min`	Lowest frequency of interest `f_min`, in hertz.
`f_max`	Highest frequency of interest `f_max`, in hertz.

Returns: Tuple (s_min, s_max) of the lower and upper spacing limits, m.

Raises

Exception	When
ValueError	On non-positive speed or frequency, or `f_min >= f_max`.

SPOT_NARROW_BAND_RANGE

Constant (tuple).

SPOT_NARROW_BAND_RANGE = (220.0, 1800.0)

spot_tube_upper_frequency

spot_tube_upper_frequency(
    diameter: float,
    speed_of_sound: float = 340.0,
) -> float

Upper usable frequency of the spot tube (ISO 13472-2:2010, 5.4.1).

$f_{u} = 0.58 c_{0} / d$ (circular tube), the highest frequency at which only plane waves propagate. A 100 mm tube at $c_{0} = 340$ m/s gives $f_{u} \approx 1972$ Hz, comfortably above the 1800 Hz narrow-band top.

Parameters

Name	Description
`diameter`	Tube diameter `d`, in metres.
`speed_of_sound`	Speed of sound `c0`, in metres per second.

Returns: Upper usable frequency f_u, in hertz.

Raises

Exception	When
ValueError	If `d` or `c0` is not positive.

Created and maintained by José Manuel Requena Plens ORCID All projects