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phonometry

room.reverberation_prediction

Reverberation-time prediction from room geometry and absorption.

Predicts the reverberation time T of an enclosed space from its volume, boundary areas and the sound-absorption coefficients of its surfaces, through the classical statistical-acoustics formulae. Given a diffuse field and an exponential energy decay, T is the time for the level to fall by 60 dB.

Five models are provided, in order of increasing account of a non-uniform absorption distribution:

  • Sabine — the original diffuse-field estimate, T = k V / (A + 4 m V) with the total equivalent absorption area A = sum_i S_i alpha_i and the air term 4 m V. Exact only for low, uniform absorption.
  • Eyring (Norris-Eyring) — replaces A by -S ln(1 - alpha_bar) with the mean absorption alpha_bar = A / S over the total surface S; correct in the strong-absorption limit where Sabine overestimates T.
  • Millington-Sette — -sum_i S_i ln(1 - alpha_i) sums the Eyring term per surface, so a single perfectly absorbing surface drives T to zero.
  • Fitzroy — an area-weighted arithmetic mean of three axial Eyring reverberation times, one per pair of opposing walls; captures rooms with the absorption concentrated on one axis (e.g. a carpeted, otherwise hard room).
  • Arau-Puchades — an area-weighted geometric mean of the same three axial Eyring times (Arau-Puchades, Acustica 65 (1988) 163): T = prod_i T_i ** (S_i / S). Recommended by its author over Fitzroy for anisotropic rooms.

The Sabine constant is k = 24 ln 10 / c0 (= 55.26 / c0); with the default c0 = 343 m/s it takes the familiar textbook value 0.161. (The enclosed_space_absorption EN 12354-6 model instead rounds k to 55.3 and uses c0 = 345.6 to pin the factor at exactly 0.16.)

Air absorption enters every model through the air_attenuation power coefficient m (in neper per metre) as the additive term 4 m V; obtain a physical m from temperature and humidity with phonometry.air_absorption.air_attenuation_m.

Each model enforces its own mathematical domain on the absorption coefficients. Sabine’s linear sum is finite for any non-negative coefficient, so it accepts measured ISO 354 values at or above 1 (up to a unit-error guard at 2). The logarithmic models are stricter exactly where the maths requires it: Millington-Sette needs every coefficient below 1, while Eyring, Fitzroy and Arau-Puchades need each mean entering ln(1 - alpha) below 1.

The Fitzroy and Arau-Puchades models require a rectangular (shoebox) room and take the room dimensions together with the mean absorption of each of the three wall pairs. All five reduce to Eyring for a uniform absorption distribution, and Eyring reduces to Sabine as the absorption tends to zero — the identities the conformance suite anchors on, absent a machine-readable worked example in the source texts.

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

arau_puchades_reverberation_time

Section titled “arau_puchades_reverberation_time”
arau_puchades_reverberation_time(
    dimensions: Sequence[float],
    absorptions: Sequence[ArrayLike],
    *,
    air_attenuation: ArrayLike = 0.0,
    speed_of_sound: float = 343.0,
) -> np.ndarray | float

Arau-Puchades reverberation time — area-weighted geometric mean of axial times.

T = prod_i T_i ** (S_i / S) with T_i the Eyring time of the wall pair perpendicular to axis i (Arau-Puchades, Acustica 65 (1988) 163, Formula 18). Preferred by its author over Fitzroy for rooms with an anisotropic absorption distribution. Reduces to Eyring for a uniform distribution. Each input is itself a mean entering ln(1 - alpha_i), so each must be below 1.

Parameters

NameDescription
dimensionsRoom lengths (Lx, Ly, Lz), m.
absorptionsMean absorption (alpha_x, alpha_y, alpha_z) of the three wall pairs (perpendicular to x, y, z); each a scalar or per-band array.
air_attenuationAir power-attenuation coefficient m (1/m).
speed_of_soundSpeed of sound c0, m/s.

Returns: The reverberation time T, s.

eyring_reverberation_time

Section titled “eyring_reverberation_time”
eyring_reverberation_time(
    volume: float,
    surfaces: Sequence[Surface],
    *,
    air_attenuation: ArrayLike = 0.0,
    speed_of_sound: float = 343.0,
) -> np.ndarray | float

Eyring (Norris-Eyring) reverberation time.

T = k V / (-S ln(1 - alpha_bar) + 4 m V) with the total surface S and its area-weighted mean absorption alpha_bar.

The formula constrains only the mean: ln(1 - alpha_bar) requires alpha_bar < 1, while individual coefficients at or above 1 (a measured ISO 354 outcome) are accepted as long as the mean stays below 1 and each coefficient stays within the shared unit-error ceiling of 2.

Parameters

NameDescription
volumeRoom volume V, m3.
surfacesSequence of (area, absorption_coefficient) pairs.
air_attenuationAir power-attenuation coefficient m (1/m).
speed_of_soundSpeed of sound c0, m/s.

Returns: The reverberation time T, s.

fitzroy_reverberation_time

Section titled “fitzroy_reverberation_time”
fitzroy_reverberation_time(
    dimensions: Sequence[float],
    absorptions: Sequence[ArrayLike],
    *,
    air_attenuation: ArrayLike = 0.0,
    speed_of_sound: float = 343.0,
) -> np.ndarray | float

Fitzroy reverberation time — area-weighted arithmetic mean of axial times.

T = sum_i (S_i / S) T_i with T_i the Eyring time of the wall pair perpendicular to axis i (Fitzroy, J. Acoust. Soc. Am. 31 (1959) 893). Equivalent to T = k V / S**2 * sum_i S_i / (-ln(1 - alpha_i)) without air. Reduces to Eyring for a uniform absorption distribution. Each input is itself a mean entering ln(1 - alpha_i), so each must be below 1.

Parameters

NameDescription
dimensionsRoom lengths (Lx, Ly, Lz), m.
absorptionsMean absorption (alpha_x, alpha_y, alpha_z) of the three wall pairs (perpendicular to x, y, z); each a scalar or per-band array.
air_attenuationAir power-attenuation coefficient m (1/m).
speed_of_soundSpeed of sound c0, m/s.

Returns: The reverberation time T, s.

mean_absorption

Section titled “mean_absorption”
mean_absorption(surfaces: Sequence[Surface]) -> np.ndarray | float

Area-weighted mean absorption coefficient alpha_bar = A / S.

Parameters

NameDescription
surfacesSequence of (area, absorption_coefficient) pairs; each coefficient a scalar or a per-band array.

Returns: The mean absorption sum_i S_i alpha_i / sum_i S_i; a float for scalar coefficients, otherwise a per-band array.

millington_sette_reverberation_time

Section titled “millington_sette_reverberation_time”
millington_sette_reverberation_time(
    volume: float,
    surfaces: Sequence[Surface],
    *,
    air_attenuation: ArrayLike = 0.0,
    speed_of_sound: float = 343.0,
) -> np.ndarray | float

Millington-Sette reverberation time.

T = k V / (-sum_i S_i ln(1 - alpha_i) + 4 m V): the Eyring absorption term summed surface by surface rather than through a single mean. A surface approaching total absorption (alpha_i -> 1) drives T to zero. Because the logarithm applies per surface, every coefficient must be strictly below 1; measured ISO 354 coefficients at or above 1 are outside this model’s domain (use Sabine, or Eyring while the mean stays below 1).

Parameters

NameDescription
volumeRoom volume V, m3.
surfacesSequence of (area, absorption_coefficient) pairs.
air_attenuationAir power-attenuation coefficient m (1/m).
speed_of_soundSpeed of sound c0, m/s.

Returns: The reverberation time T, s.

reverberation_time_models

Section titled “reverberation_time_models”
reverberation_time_models(
    dimensions: Sequence[float],
    absorptions: Sequence[ArrayLike],
    *,
    air_attenuation: ArrayLike = 0.0,
    frequencies: ArrayLike | None = None,
    speed_of_sound: float = 343.0,
) -> ReverberationModelResult

Predict the reverberation time of a rectangular room by all five models.

A convenience front-end that builds the six boundary surfaces of the room from dimensions and the three wall-pair mean absorptions, then evaluates sabine_reverberation_time, eyring_reverberation_time, millington_sette_reverberation_time, fitzroy_reverberation_time and arau_puchades_reverberation_time on a common footing. Because the bundle evaluates the logarithmic models too, the inputs must satisfy the strictest of the five domains: every absorption below 1.

Parameters

NameDescription
dimensionsRoom lengths (Lx, Ly, Lz), m.
absorptionsMean absorption (alpha_x, alpha_y, alpha_z) of the three wall pairs (perpendicular to x, y, z); each a scalar or a per-band array aligned with frequencies.
air_attenuationAir power-attenuation coefficient m (1/m), scalar or per-band.
frequenciesBand centre frequencies, in hertz, used only to label the result and its plot; defaults to an integer index over the bands.
speed_of_soundSpeed of sound c0, m/s.

Returns: The ReverberationModelResult.

ReverberationModelResult

Section titled “ReverberationModelResult”
ReverberationModelResult(
    frequencies: np.ndarray,
    sabine: np.ndarray,
    eyring: np.ndarray,
    millington_sette: np.ndarray,
    fitzroy: np.ndarray,
    arau_puchades: np.ndarray,
    volume: float,
    surface_area: float,
)

Predicted reverberation time of a rectangular room by five models.

Attributes

NameDescription
frequenciesBand centre frequencies, in hertz.
sabineSabine reverberation time per band, s.
eyringEyring (Norris-Eyring) reverberation time per band, s.
millington_setteMillington-Sette reverberation time per band, s.
fitzroyFitzroy reverberation time per band, s.
arau_puchadesArau-Puchades reverberation time per band, s.
volumeRoom volume V, m3.
surface_areaTotal boundary area S, m2.

ReverberationModelResult.models

Section titled “ReverberationModelResult.models”

property

The five reverberation-time curves keyed by model name.

ReverberationModelResult.plot()

Section titled “ReverberationModelResult.plot()”
ReverberationModelResult.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the reverberation-time curves of the five models.

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

ReverberationModelResult.report()

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

Render a reverberation-time prediction fiche to a PDF.

Writes a one-page report of the reverberation time predicted by the five statistical-acoustics models (Sabine, Eyring, Millington-Sette, Fitzroy and Arau-Puchades): a standard-basis line marking it a design-stage prediction, an optional metadata header block (client, room, description, room volume, total surface area, climate …), a per-band table with one reverberation-time column per model beside the result’s own model-comparison plot (plot), the boxed mid-frequency reverberation time from Arau-Puchades (the recommended model for a non-uniform absorption distribution) with the per-model spread alongside, and a footer with the fixed disclaimer. This is a prediction, not a measurement: the five models bracket the reverberation time likely to occur. A supplied metadata.requirement is printed as a target reverberation-time reference line without a PASS/FAIL verdict, since a room reverberation time is a target range rather than a strictly higher/lower-is-better quantity.

Parameters

NameDescription
pathDestination path of the PDF file.
metadataOptional ReportMetadata; None produces a bare prediction fiche (body, result and disclaimer only).
engineRendering back end; only "reportlab" is supported.
verboseAccepted for parity with the other fiches; the model table already shows every computed value, so it has no effect.
languageFiche language: "en" (default, English) or "es" (Spanish, with a comma decimal separator).

Returns: The written path as a str.

Raises

ExceptionWhen
ValueErrorIf engine is not "reportlab".
ImportErrorIf reportlab is not installed (pip install phonometry[report]).

sabine_reverberation_time

Section titled “sabine_reverberation_time”
sabine_reverberation_time(
    volume: float,
    surfaces: Sequence[Surface],
    *,
    air_attenuation: ArrayLike = 0.0,
    speed_of_sound: float = 343.0,
) -> np.ndarray | float

Sabine reverberation time T = k V / (A + 4 m V).

A = sum_i S_i alpha_i is finite for any non-negative coefficient, so unlike the logarithmic models Sabine accepts coefficients at or above 1: measured ISO 354 reverberation-room values of 1.05 to 1.20 (the edge effect) and the exact 1.0 that the ISO 11654 practical rating caps at are legitimate inputs. Coefficients above 2 are rejected as a probable unit error (a percentage passed instead of a fraction).

Parameters

NameDescription
volumeRoom volume V, m3.
surfacesSequence of (area, absorption_coefficient) pairs; each coefficient a scalar or a per-band array in [0, 2].
air_attenuationAir power-attenuation coefficient m, in neper per metre (scalar or per-band); see phonometry.air_absorption.air_attenuation_m. Default 0 (air absorption neglected).
speed_of_soundSpeed of sound c0, m/s (default DEFAULT_SPEED_OF_SOUND, giving the factor 0.161).

Returns: The reverberation time T, s; a float for scalar inputs, otherwise a per-band array.

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