Source: https://jmrplens.github.io/phonometry/buildings/rooms/open-plan-acoustics/ # Open-Plan Office Acoustics (ISO 3382-3) An open-plan office is not a reverberation problem; it is a privacy problem, and a room that flatters the closed-room parameters can still fail it. ISO 3382-3 therefore characterises the office with four single numbers measured along a line of workstations, walking away from a talker. This guide covers that measurement chain: the quantities, the to-scale measurement line and the accredited fiche. The impulse responses and levels behind it are acquired as in [Measuring the Room Impulse Response](https://jmrplens.github.io/phonometry/buildings/rooms/room-impulse-response/); the per-position STI comes from the [Speech Transmission Index guide](https://jmrplens.github.io/phonometry/perception/speech/speech-transmission/); the closed-room decay parameters live in [Room Acoustics](https://jmrplens.github.io/phonometry/buildings/rooms/room-acoustics/). ## Speech privacy along a line of workstations Open-plan acoustics are about **speech privacy**: how fast a talker's speech fades to unintelligibility as you walk away. Levels and STI are measured along a line of workstations (at least 4 positions, 6–10 preferred), and four single-number quantities summarise the room. The **spatial decay rate** of A-weighted speech is the slope of the level against $\log_{10}(r/r_0)$, scaled to a per-doubling figure using only the 2–16 m positions, $$ D_\mathrm{2,S} = -\log_{10}(2)\ b, \qquad L = a + b\ \log_{10}(r/r_0),\ r_0 = 1\ \text{m}, $$ with **$L_{p,\mathrm{A,S},4\,\mathrm{m}}$** read off the same line at 4 m. The **distraction distance** $r_\mathrm{D}$ (STI = 0.50) and **privacy distance** $r_\mathrm{P}$ (STI = 0.20) come from a linear regression of STI against distance. Good offices push $r_\mathrm{D}$ below ~5 m; poor ones leave speech distracting past 10 m. ```python import numpy as np from phonometry import room r = np.array([2.0, 4.0, 6.0, 8.0, 12.0, 16.0]) # distances from the talker (m) lp = 65.0 - 7.0 * np.log2(r) # A-weighted speech level (dB) sti = 0.70 - 0.03 * r # STI per position m = room.open_plan_metrics(r, lp, sti) print(round(m.d2s, 1), round(m.lp_as_4m, 1)) # 7.0 dB, 51.0 dB print(round(m.rd, 1), round(m.rp, 1)) # 6.7 m, 16.7 m m.plot() # the spatial-decay regression of the figure below ```

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import room r = np.array([2.0, 4.0, 6.0, 8.0, 12.0, 16.0]) # distances from the talker (m) lp = 65.0 - 7.0 * np.log2(r) # A-weighted speech level (dB) sti = 0.70 - 0.03 * r # STI per position m = room.open_plan_metrics(r, lp, sti) # One line: the D2,S regression rebuilt from the result fields, with the # rD / rP crossings marked (the figure above adds the measured points and # the STI axis on top of it): m.plot() plt.show() ``` ```python import matplotlib.pyplot as plt import numpy as np from phonometry import room r = np.array([2.0, 4.0, 6.0, 8.0, 12.0, 16.0]) # distances from the talker (m) lp = 65.0 - 7.0 * np.log2(r) # A-weighted speech level (dB) sti = 0.70 - 0.03 * r # STI per position m = room.open_plan_metrics(r, lp, sti) # Spatial decay: measured Lp,A,S vs distance on a log axis, the D2,S # regression rebuilt from the result fields, and STI with the rD / rP # crossings on a twin axis: b = -m.d2s / np.log10(2.0) # regression slope vs lg(r) a = m.lp_as_4m - b * np.log10(4.0) # intercept from the 4 m level rr = np.logspace(np.log10(2.0), np.log10(16.0), 100) fig, ax = plt.subplots() ax.semilogx(r, lp, "o", label="Measured Lp,A,S") ax.semilogx(rr, a + b * np.log10(rr), "--", label=f"D2,S = {m.d2s:.1f} dB") ax.plot(4.0, m.lp_as_4m, "D", label=f"Lp,A,S,4m = {m.lp_as_4m:.0f} dB") ax.set_xlabel("Distance from the talker r [m]") ax.set_ylabel("A-weighted speech level [dB]") ax.set_xlim(1.8, 20.0) twin = ax.twinx() twin.semilogx(r, sti, "s-", color="#2ca02c", label="STI") twin.axvline(m.rd, ls=":", color="#2ca02c") twin.axvline(m.rp, ls=":", color="#9467bd") twin.annotate(f"rD = {m.rd:.1f} m", (m.rd, 0.52)) twin.annotate(f"rP = {m.rp:.1f} m", (m.rp, 0.22)) twin.set_ylabel("STI") twin.set_ylim(0.0, 1.0) lines, labels = ax.get_legend_handles_labels() tl, tlab = twin.get_legend_handles_labels() ax.legend(lines + tl, labels + tlab, loc="best") plt.show() ```

The line itself is worth a to-scale plan. `plot_open_plan_geometry` draws the source, the microphone line across the workstations and the two distances on the axis, and a result that retained its positions redraws its own line with `m.plot_geometry()`. *Every ISO 3382-3 quantity comes off this one line: six microphones from 2 m to 16 m through the workstations, with $r_\mathrm{D}$ and $r_\mathrm{P}$ landing between them.*

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```python import matplotlib.pyplot as plt from phonometry import room # The 2-16 m line of the example, with the distraction and privacy # distances marked on the axis. room.plot_open_plan_geometry([2.0, 4.0, 6.0, 8.0, 12.0, 16.0], rd=6.5, rp=13.0) plt.show() # A result retains its positions, so m.plot_geometry() draws its own # line with the regressed rD and rP. ```

### `open_plan_metrics()` parameters | Parameter | Type | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `positions_m` | 1D array | m | ≥ 4 positions, all > 0 | Source-to-receiver distances | | `spl_a_speech` | 1D array | dB | same length | A-weighted speech level $L_{p,\mathrm{A,S},n}$ per position | | `sti_values` | 1D array | — | same length | STI per position (full IEC 60268-16 method) | Returns an `OpenPlanResult` with `d2s`, `lp_as_4m`, `rd` and `rp`; its `.plot()` redraws the Clause 6.2 spatial-decay regression from those four fields and marks `rd` / `rp`. `d2s`/`lp_as_4m` are `nan` if fewer than two positions fall in 2–16 m; `rd`/`rp` are `nan` when STI does not decrease with distance. The per-position STI can itself be measured with the STIPA tools in the [Speech Transmission Index guide](https://jmrplens.github.io/phonometry/perception/speech/speech-transmission/). Two things stay outside the function. The fourth required single number, the average A-weighted background noise $L_{p,\mathrm{A,B}}$, is not computed here — it is the energetic A-weighted average of the per-position octave-band background levels, and it belongs in the report alongside the quantities this page produces. And nothing checks the measurement conditions of clauses 5.1 and 5.2: the function consumes distances, levels and STI values wherever they came from, so the source directivity, the furnished-and-unoccupied state and the background capture are the operator's responsibility, not the library's. ## ISO 3382-3 report (`.report()`) `OpenPlanResult.report(path)` renders a one-page PDF fiche laid out like an open-plan-office speech-privacy measurement report: a standard-basis line, an optional metadata header block, a compact metrics table of the four single-number quantities of Clause 4 ($D_\mathrm{2,S}$, $L_{p,\mathrm{A,S},4\,\mathrm{m}}$, the distraction distance $r_\mathrm{D}$ and the privacy distance $r_\mathrm{P}$) stacked above the full-width spatial-decay plot (`.plot()`, the Clause 6.2 regression on the logarithmic distance axis with the 4 m read-off and the $r_\mathrm{D}$ / $r_\mathrm{P}$ crossings marked), the boxed $D_\mathrm{2,S}$ with the other quantities alongside, and a footer with the fixed disclaimer. ISO 3382-3 **characterises** a space rather than defining an intrinsic pass/fail, so a verdict row appears only when a target spatial decay rate is supplied through the metadata's `requirement` field (`ReportMetadata(requirement=...)`, read as the minimum acceptable $D_\mathrm{2,S}$ in dB, reflecting the informative quality ranges of Annex A where a larger spatial decay is better; the room passes at or above it). It uses the same `ReportMetadata` container as the [ISO 3382-1/-2 room-acoustics fiche](https://jmrplens.github.io/phonometry/buildings/rooms/room-acoustics/#iso-3382-report-report); the open-plan-specific fields `area` (floor area), `source_positions` and `receiver_positions` (the number of measurement positions) populate the header, alongside `client`, `test_room`, `specimen`, `instrumentation`, `temperature`, `relative_humidity`, `pressure`, `measurement_standard`, `test_date`, `laboratory`, `operator`, `report_id` and `notes`. Passing `metadata=None` produces a bare characterisation fiche. The fiche embeds the spatial-decay chart, so rendering needs both reportlab and matplotlib (`pip install "phonometry[report,plot]"`); only `engine="reportlab"` is supported. The fiche renders in English by default; pass `language="es"` for a Spanish fiche (translated fixed strings and a comma decimal separator). ```python import numpy as np from phonometry import room, ReportMetadata r = np.array([2.0, 3.0, 4.0, 6.0, 8.0, 11.0, 16.0]) # distances from the talker (m) lp = 62.0 - 7.0 * np.log2(r) # A-weighted speech level (dB) sti = 0.65 - 0.03 * r # STI per position result = room.open_plan_metrics(r, lp, sti) result.report( "open_plan_fiche.pdf", metadata=ReportMetadata( test_room="Open-plan office B", specimen="Furnished, unoccupied, background noise present", area=420.0, source_positions=2, receiver_positions=7, measurement_standard="ISO 3382-3", temperature=22.0, relative_humidity=45.0, laboratory="Phonometry Reference Laboratory", requirement=7.0, # adds a verdict against a target D2,S ), ) # D2,S + Lp,A,S,4m, rD, rP and the decay curve ``` The example fiche, regenerated with `make reports`, is kept rendered in the repository. Click the preview to open the PDF: [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iso3382_3_open_plan_example.pdf) *Open-plan office acoustics fiche (`OpenPlanResult.report`), $D_\mathrm{2,S}$, $L_{p,\mathrm{A,S},4\,\mathrm{m}}$, $r_\mathrm{D}$, $r_\mathrm{P}$ and the spatial-decay curve.* ## Crowd self-noise in an occupied room ISO 3382-3 above **measures** an office. The complementary question at design time is a **prediction**: in a room whose only noise source is its own occupants, how loud does the background get, and does conversation still work? Long (*Architectural Acoustics* 2e, Chapter 17, Equations (17.50) to (17.54)) sets the two competing levels at a listener: $$ L_p(\text{signal}) = L_W + 10\log_{10}\!\left[\frac{Q}{4\pi r^2}\right] \quad \text{(Eq. (17.50))} $$ $$ L_p(\text{noise}) = L_W + 10\log_{10} N + 10\log_{10}\!\left[\frac{4}{N A_\text{tab}}\right] \quad \text{(Eq. (17.51))} $$ with $L_W$ the sound power level of one talker (about 70 dB in normal conversation), $Q$ the talker's forward directivity (about 2), $r$ the talker-to-listener distance and $A_\text{tab}$ the equivalent absorption area **per occupied table**, so $N A_\text{tab}$ is the room's total absorption. ```python from phonometry import room # Long's hard restaurant: about 20 metric sabins, a talker at Lw = 70 dB, # a listener 1.2 m away across the table. print(round(room.speech_direct_level(1.2))) # 60 dB direct field print(round(room.crowd_noise_level(1, 20.0))) # 63 dB with one talker print(round(room.crowd_noise_level(20, 20.0))) # 76 dB with 20 tables # An alpha 0.9 ceiling over the 13.7 x 13.7 m room adds 170 metric sabins. print(round(room.crowd_noise_level(20, 20.0 + 170.0))) # 66 dB ``` Subtracting the two gives the **speech-to-noise ratio**, and this is the result worth remembering: $$ L_\mathrm{SN} = 10\log_{10}\!\left[\frac{Q}{4\pi r^2}\right] + 10\log_{10}\!\left[\frac{A_\text{tab}}{4}\right] \quad \text{(Eq. (17.52))} $$ Neither $L_W$ nor $N$ survives. A busier room is not intrinsically worse, because each new table brings both a talker and its own share of absorption. What decides whether a restaurant works is the absorption **per table**, not the absorption of the room. Requiring $L_\mathrm{SN} > -6$ dB for adequate cross-table communication at a separation $r_s$, and $L_\mathrm{SN} < -9$ dB so a neighbouring table $r_t$ away is not overheard, turns into a pair of design bounds: $$ A_\text{tab} > 6.31\,r_s^2 \quad \text{(Eq. (17.53))}, \qquad A_\text{tab} < 3.16\,r_t^2 \quad \text{(Eq. (17.54))}, \qquad \text{both for } Q = 2 $$ > **The first constant is printed as 6.33.** The closed form above, at the same > $Q = 2$ that yields Long's own second constant 3.16 exactly, gives 6.31, and his > prose ("6.3 or more square metres, 68 sq ft") converts to 6.317 m². The library > computes both bounds from the speech-to-noise ratio rather than hardcoding > either constant, so they stay mutually consistent; the misprint is recorded in > the [errata registry](https://jmrplens.github.io/phonometry/reference/errata/). ```python from phonometry import room print(round(room.absorption_per_table(1.0, -6.0), 2)) # 6.31 m2 per table at 1 m print(round(room.absorption_per_table(2.5, -9.0), 1)) # 19.8 m2 at 2.5 m spacing crowd = room.crowd_noise([20.0, 95.0, 190.0], distance=1.2) crowd.plot() # self-noise vs occupancy, against the -6 dB limit ``` *The same 20 talkers in three rooms. The hard room (20 m² of absorption) crosses the communication limit before the fourth table is occupied; adding the absorptive ceiling of Long's example (190 m² in total) keeps all 20 tables below it. The curves are parallel because occupancy always costs $10\log_{10} N$: only the vertical offset, which is the absorption, is a design variable.* ### `crowd_noise()` parameters | Parameter | Type | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `absorption_areas` | float or 1D array | m² | > 0 | Total room absorption areas to compare | | `talkers` | 1D array, optional | — | ≥ 1, default 1..20 | Occupancy axis $N$ | | `distance` | float | m | > 0, default 1.2 | Talker-to-listener distance $r$ | | `sound_power_level` | float | dB re 1 pW | default 70 | Talker $L_W$ | | `directivity` | float | — | > 0, default 2 | Talker $Q$ | Returns a `CrowdNoiseResult` (`talkers`, `absorption_areas`, `levels`, `signal_level`, `communication_level`, `speech_to_noise()`) with `.plot()`. The pieces `speech_direct_level`, `crowd_noise_level`, `speech_to_noise_ratio` and `absorption_per_table` are callable directly. This is a *design* model and deliberately does not model the Lombard reflex: it cancels out of `L_SN` as long as everyone raises their voice equally, so the model explains why the level spirals upward in a hard room rather than predicting where it stops. It also assumes a diffuse reverberant field and a single absorption figure per table, so it says nothing about screens, local absorption or where in the room a given table sits. ## References - International Organization for Standardization. (2012). *Acoustics — Measurement of room acoustic parameters — Part 3: Open plan offices* (ISO 3382-3:2012; since revised as [ISO 3382-3:2022](https://www.iso.org/standard/77437.html)). [iso.org catalogue](https://www.iso.org/standard/46520.html). The open-plan speech-privacy quantities this page implements. - Long, M. (2014). *Architectural acoustics* (2nd ed.). Academic Press. [doi:10.1016/C2012-0-03257-5](https://doi.org/10.1016/C2012-0-03257-5). Chapter 17 (the crowd self-noise model, Equations (17.50) to (17.54)). ## Standards ISO 3382-3:2012 (open-plan office speech metrics: the spatial decay rate $D_\mathrm{2,S}$, the A-weighted speech level at 4 m, and the distraction and privacy distances from STI). Validated against the standard's own quantity definitions in the [conformance report](https://jmrplens.github.io/phonometry/reference/conformance/). The implemented edition is frozen at ISO 3382-3:2012; the superseding ISO 3382-3:2022 revision removes the privacy distance $r_\mathrm{P}$, adds the comfort distance $r_\mathrm{C}$ and moves the per-position STI to the indirect IEC 60268-16 method, and is not the one checked here. ## See also - [Room Acoustics](https://jmrplens.github.io/phonometry/buildings/rooms/room-acoustics/): the ISO 3382-1/2 decay parameters of the same room. - [Measuring the Room Impulse Response](https://jmrplens.github.io/phonometry/buildings/rooms/room-impulse-response/): the acquisition behind the per-position levels. - [Speech Transmission Index](https://jmrplens.github.io/phonometry/perception/speech/speech-transmission/): the STI/STIPA measurement that feeds the per-position `sti_values`. - [Speech Intelligibility Index](https://jmrplens.github.io/phonometry/perception/speech/speech-intelligibility/): the ANSI S3.5 view of the same intelligibility question. - [Levels](https://jmrplens.github.io/phonometry/signals/levels/levels/): the A-weighted levels behind the spatial decay. - API reference: [`room.open_plan`](https://jmrplens.github.io/phonometry/reference/api/rooms/open-plan/).