room.crowd_noise

Crowd self-noise in a restaurant: the cocktail-party equilibrium.

In a room where the only source of noise is the occupants themselves, the background against which each conversation has to be understood is generated by the other conversations. Long (Architectural Acoustics 2nd ed., Chapter 17, Equations (17.50) to (17.54)) writes the two competing levels at a listener:

• the signal, the direct field of the person across the table (Equation (17.50)), $L_p^{\text{signal}}=L_W+10{\log }_{10}[Q/(4\pi r^2)]$;

• the noise, the reverberant field built up by N simultaneous talkers spread over the room (Equation (17.51)), $L_p^{\text{noise}}=L_W+10{\log }_{10}N+10{\log }_{10}[4/(N{A}_{\text{tab}})]$;

where Lw is the sound power level of one talker (about 70 dB for normal conversation), Q the talker’s directivity factor (about 2 in the forward direction), r the talker-to-listener distance and A_tab the equivalent absorption area per occupied table, so that $N{A}_{\text{tab}}$ is the room’s total absorption. Their difference is the speech-to-noise ratio (Equation (17.52)):

$$L_{SN}=10{\log }_{10}\left[\frac{Q}{4\pi r^2}\right]+10{\log }_{10}\left[\frac{A_{\text{tab}}}{4}\right]$$

which is independent of the talker’s power and of the number of talkers: adding a table adds both a talker and its share of absorption. What decides whether a restaurant works is therefore the absorption per table, not its total absorption. Requiring $L_{SN}>-6$ dB for adequate cross-table communication at a separation rs, and $L_{SN}<-9$ dB for privacy between tables a distance rt apart, turns into a pair of design bounds (Equations (17.53) and (17.54)):

$$A_{\text{tab}}>16\pi 10^{-0.6}{r}_s^2/Q\approx 6.31r_s^2(Q=2)$$ $$A_{\text{tab}}<16\pi 10^{-0.9}{r}_t^2/Q\approx 3.16r_t^2(Q=2)$$

Note

Long prints the first constant as 6.33; the closed form with the same $Q=2$ and -6 dB that yield his second constant 3.16 gives 6.31, which is also what his own conversion of the result (“6.3 or more square metres (68 sq ft)”) implies (see docs/ERRATA.md). This module computes both constants from speech_to_noise_ratio, so they stay mutually consistent.

His prose also puts the direct field at an adjacent table 3 m away at “about 54 dB”, where speech_direct_level with the same $Q=2$ and $L_w=70$ dB gives 52.5 dB. That one is left as printed rather than reconciled, because the intended reading cannot be established from the book; it is recorded under the non-errata notes of docs/ERRATA.md.

The Lombard reflex (talkers raising their voices as the background grows) is deliberately not modelled: it cancels out of L_SN as long as everyone raises their voice equally, and Long uses the model in exactly that way, as the explanation of why the level spirals upward in a hard room rather than as a predictor of the final level.

This is a design model for the self-generated noise of an occupied room. The measurement standard for the spatial decay of speech in an open-plan office is ISO 3382-3, implemented separately in phonometry.room.open_plan: that one derives D2,S, the distraction distance and the privacy distance from measured levels along a line of workstations, and predicts nothing.

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

absorption_per_table

absorption_per_table(
    distance: ArrayLike,
    speech_to_noise: float,
    *,
    directivity: float = 2.0,
) -> np.ndarray | float

Absorption per table giving a chosen L_SN (inverse of (17.52)).

$A_{\text{tab}}=16\pi r^{2}10^{L_{SN}/10}/Q$. With $L_{SN}=-6$ dB this is Long’s communication bound (Equation (17.53)), with -9 dB his privacy bound (Equation (17.54)).

Parameters

Name	Description
distance	Separation r, m: the cross-table distance rs for the communication bound, the table-to-table distance rt for the privacy bound.
speech_to_noise	Target speech-to-noise ratio L_SN, dB.
directivity	Talker directivity factor Q.

Returns: The equivalent absorption area per table A_tab, m2.

COMMUNICATION_SNR

Constant (float).

COMMUNICATION_SNR = -6.0

crowd_noise

crowd_noise(
    absorption_areas: ArrayLike,
    *,
    talkers: ArrayLike | None = None,
    distance: float = 1.2,
    sound_power_level: float = 70.0,
    directivity: float = 2.0,
) -> CrowdNoiseResult

Self-noise of an occupied room versus occupancy (Long 17.50-17.52).

Evaluates Equation (17.51) over an occupancy axis for each of the supplied total absorption areas, together with the direct-field signal of Equation (17.50) at the listener across the table.

Parameters

Name	Description
absorption_areas	Total equivalent absorption areas A of the room to compare, m2 (scalar or 1-D).
talkers	Occupancy axis N, the number of simultaneous talkers; default the integers 1..20.
distance	Talker-to-listener distance r, m (default 1.2 m, Long’s cross-table distance).
sound_power_level	Sound power level Lw of one talker, dB re 1 pW (default NORMAL_VOICE_POWER_LEVEL).
directivity	Talker directivity factor Q (default TALKER_DIRECTIVITY).

Returns: A CrowdNoiseResult.

crowd_noise_level

crowd_noise_level(
    talkers: ArrayLike,
    absorption_area: ArrayLike,
    *,
    sound_power_level: float = 70.0,
) -> np.ndarray | float

Reverberant level of N simultaneous talkers (Long Equation (17.51)).

$L_p=L_W+10{\log }_{10}N+10{\log }_{10}(4/A)$ with the room’s total equivalent absorption area A ($=N{A}_{\text{tab}}$ when the absorption is counted per occupied table).

Parameters

Name	Description
talkers	Number N of simultaneous talkers (scalar or array, at least 1).
absorption_area	Total equivalent absorption area A of the room, metric sabins (m2) (scalar or array).
sound_power_level	Sound power level Lw of one talker, dB re 1 pW (default NORMAL_VOICE_POWER_LEVEL).

Returns: The self-generated reverberant level, dB.

CrowdNoiseResult

CrowdNoiseResult(
    talkers: np.ndarray,
    absorption_areas: np.ndarray,
    levels: np.ndarray,
    signal_level: float,
    distance: float,
    sound_power_level: float,
    directivity: float,
    communication_level: float,
)

Self-generated noise of an occupied room versus occupancy and absorption.

Attributes

Name	Description
talkers	Number of simultaneous talkers on the occupancy axis.
absorption_areas	Total room absorption areas compared, m2, one per row of levels.
levels	Reverberant self-noise level, dB, shaped (len(absorption_areas), len(talkers)).
signal_level	Direct-field level of the talker across the table, dB.
distance	Talker-to-listener distance r, m.
sound_power_level	Sound power level of one talker, dB re 1 pW.
directivity	Talker directivity factor Q.
communication_level	Noise level at which the speech-to-noise ratio falls to COMMUNICATION_SNR, dB: above it, cross-table conversation stops working.

CrowdNoiseResult.plot()

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

Plot the self-noise level against occupancy, one curve per absorption.

The direct-field level of the talker across the table and the speech-to-noise limit of Equation (17.53) are drawn as references, so the crossing point reads directly as the occupancy at which the room stops working. Requires matplotlib (pip install phonometry[plot]).

CrowdNoiseResult.speech_to_noise()

CrowdNoiseResult.speech_to_noise() -> np.ndarray

Speech-to-noise ratio for every point of levels, dB.

NORMAL_VOICE_POWER_LEVEL

Constant (float).

NORMAL_VOICE_POWER_LEVEL = 70.0

PRIVACY_SNR

Constant (float).

PRIVACY_SNR = -9.0

speech_direct_level

speech_direct_level(
    distance: ArrayLike,
    *,
    sound_power_level: float = 70.0,
    directivity: float = 2.0,
) -> np.ndarray | float

Direct-field level of one talker (Long Equation (17.50)).

$L_p=L_W+10{\log }_{10}[Q/(4\pi r^2)]$, the signal a listener across the table receives.

Parameters

Name	Description
distance	Talker-to-listener distance r, m (scalar or array).
sound_power_level	Talker sound power level Lw, dB re 1 pW (default NORMAL_VOICE_POWER_LEVEL).
directivity	Talker directivity factor Q (default TALKER_DIRECTIVITY).

Returns: The direct-field sound pressure level, dB.

speech_to_noise_ratio

speech_to_noise_ratio(
    distance: ArrayLike,
    absorption_per_table: ArrayLike,
    *,
    directivity: float = 2.0,
) -> np.ndarray | float

Speech-to-noise ratio across a table (Long Equation (17.52)).

$L_{SN}=10{\log }_{10}[Q/(4\pi r^2)]+10{\log }_{10}[A_{\text{tab}}/4]$, the difference between Equations (17.50) and (17.51). Neither the talker’s power nor the number of talkers appears: a busier room brings its own absorption with it.

Parameters

Name	Description
distance	Talker-to-listener distance r, m.
absorption_per_table	Equivalent absorption area per occupied table A_tab, m2.
directivity	Talker directivity factor Q.

Returns: The speech-to-noise ratio, dB.

TALKER_DIRECTIVITY

Constant (float).

TALKER_DIRECTIVITY = 2.0