Source: https://jmrplens.github.io/phonometry/reference/api/rooms/enclosed-space-absorption/ # Sound absorption in enclosed spaces (EN 12354-6) **EN 12354-6:2003** predicts the **total equivalent sound absorption area** of a room and its **reverberation time** from the absorption of its surfaces and objects, the design counterpart of the measured reverberation time. It is the absorption member of the EN 12354 building-acoustics family (the airborne and impact insulation members live in [Predicting Sound Insulation (EN 12354)](https://jmrplens.github.io/phonometry/guides/insulation-prediction/)). phonometry implements the normative Clause 4 model. (The informative Annex D method for irregular spaces is out of scope.) ## 1. Equivalent absorption area (clause 4.3) The total equivalent absorption area sums, over the surfaces $i$, the objects $j$ and the object arrays $k$, each surface's area times its absorption coefficient, the equivalent absorption areas of the objects, the object arrays (groups of identical objects treated as an absorbing surface of area $S_k$), and the air absorption (Formula 1): $$ A = \sum_i \alpha_{s,i}\,S_i + \sum_j A_{\mathrm{obj},j} + \sum_k \alpha_{s,k}\,S_k + A_{\mathrm{air}}. $$ For hard, irregular objects whose absorption is not measured, an empirical estimate from the volume is used (Formula 4): `Aobj = Vobj**(2/3)`. ```python from phonometry import room # EN 12354-6 Annex E, bare room (29.75 m3), 1000 Hz octave band. surfaces = [(12.39, 0.05), (12.39, 0.02), (10.90, 0.04), (10.90, 0.04), (6.55, 0.04), (6.55, 0.04)] print(round(room.equivalent_absorption_area(surfaces), 2)) # 2.26 m2 print(round(float(room.hard_object_absorption(0.65)), 3)) # 0.75 m2 ``` Air absorption uses the power attenuation coefficient ``m`` (Formula 2): `Aair = 4*m*V*(1 - psi)`. Below 1 kHz and for rooms under 200 m³ it can be neglected. ## 2. Reverberation time (clause 4.4) The reverberation time follows from the absorption area, the volume and the object fraction `psi = sum(Vobj)/V` (Formula 5): $$ T = \frac{55.3}{c_0}\,\frac{V\,(1 - \psi)}{A}, $$ where the speed of sound `c0 = 345.6 m/s` makes the factor `55.3/c0` the familiar `0.16`. ```python from phonometry import room surfaces = [(12.39, 0.05), (12.39, 0.02), (10.90, 0.04), (10.90, 0.04), (6.55, 0.04), (6.55, 0.04)] a = room.equivalent_absorption_area(surfaces) print(round(room.reverberation_time(a, 29.75), 1)) # 2.1 s # Annex E case 2: add furniture (hard objects) to the same room. volumes = [0.15, 0.60, 0.05, 0.05, 0.65, 0.65] aobj = room.hard_object_absorption(volumes) psi = room.object_fraction(volumes, 29.75) # 0.072 a2 = room.equivalent_absorption_area(surfaces, objects=aobj) print(round(a2, 2), round(room.reverberation_time(a2, 29.75, object_fraction=psi), 1)) # 5.03 0.9 ``` Per octave band, one call takes the surfaces (with per-band absorption coefficients) and the air condition and returns the whole spectrum: ```python from phonometry import room # Per-band absorption coefficients (125 Hz to 8 kHz) for each surface. plaster = [0.02, 0.03, 0.03, 0.04, 0.05, 0.05, 0.05] tile = [0.15, 0.35, 0.65, 0.85, 0.90, 0.90, 0.85] result = room.enclosed_space_reverberation( [(54.0, plaster), (20.0, plaster), (20.0, tile)], volume=60.0, air_condition="20C_50-70", ) print(result.reverberation_time.round(2)) # [2.13 1.03 0.62 0.48 0.43 0.42 0.4 ] result.plot() # the figure below: A and T per octave band ```

Show the code for this figure

```python import matplotlib.pyplot as plt from phonometry import room plaster = [0.02, 0.03, 0.03, 0.04, 0.05, 0.05, 0.05] tile = [0.15, 0.35, 0.65, 0.85, 0.90, 0.90, 0.85] walls_floor = [(54.0, plaster), (20.0, plaster)] for ceiling in (plaster, tile): room.enclosed_space_reverberation( [*walls_floor, (20.0, ceiling)], 60.0, air_condition="20C_50-70", ).plot() plt.show() ```

The `ReverberationResult` carries the per-band absorption area and reverberation time, the volume and the object fraction, and its `.plot()` draws the reverberation-time spectrum. This is the prediction counterpart of the measured reverberation time in [Room Acoustics](https://jmrplens.github.io/phonometry/reference/api/rooms/room-acoustics/) (ISO 3382) and of the reverberation-room absorption of [Acoustic Materials](https://jmrplens.github.io/phonometry/guides/materials/) (ISO 354). ## 3. Where the input data comes from **Surface coefficients.** The standard expects the $\alpha_{s,i}$ to come from laboratory measurements to EN ISO 354, the reverberation-room method of [Acoustic Materials](https://jmrplens.github.io/phonometry/guides/materials/); theoretical, empirical or field values are admitted as long as the data source is stated. ISO 354 delivers one-third-octave data, and an octave-band calculation takes the arithmetic mean of the three thirds as its input. A reverberation-room coefficient can exceed 1.0 (edge diffraction scatters more energy into the sample than its flat area intercepts); it enters Formula 1 as measured, without clamping, because the same diffuse-field convention that produced it is the one the model assumes. **Furniture and occupants.** Objects contribute through three routes: a measured equivalent absorption area $A_{obj}$ when one exists (persons and seating have tabulated values in the informative Annex C), the Formula 4 estimate $V_{obj}^{2/3}$ for hard, irregular, unmeasured objects (furniture, machinery), and object *arrays* rated as an absorbing surface $\alpha_s S_k$ when many similar objects cover a zone (an audience, a storage rack). Objects also displace air: their summed volume enters the object fraction $\psi$ that shortens $T$ in Formula 5 beyond what their absorption alone would. **Air.** The air term $A_{air} = 4mV(1-\psi)$ uses the power attenuation coefficient $m$ from the standard's Table 1, resolved by the `air_condition` strings (temperature and relative-humidity class, derived from ISO 9613-1); it only matters above 1 kHz and grows with the volume. The six built-in profiles, `"10C_30-50"` through `"20C_70-90"` (clause 4.3 recommends `"20C_50-70"` when no conditions are specified), cover the standard 125 Hz to 8 kHz octave bands only and cannot be combined with a custom frequency axis; `air_condition=None` (the default) omits the air term, and for other frequencies or conditions compute $m$ per ISO 9613-1 and chain `air_absorption_area` into `equivalent_absorption_area`. **Validity limits (clause 4.6).** The model assumes an ordinary, reasonably diffuse room: no dimension more than 5 times another, opposite surface pairs whose coefficients differ by less than a factor of 3 (unless scattering objects are present) and an object fraction below 0.2. Outside those limits the field is not diffuse and the model errs on the optimistic side: the standard's own accuracy clause records measured reverberation times up to twice the prediction in low-diffusivity rooms. The classical alternatives for those cases live in [Reverberation-time prediction](https://jmrplens.github.io/phonometry/reference/api/rooms/reverberation-prediction/). ## 4. Enclosed-space report (`.report()`) `ReverberationResult.report(path)` renders a one-page PDF fiche characterising the enclosed space: a basis line naming EN 12354-6:2003, an optional metadata header block (client, room, description, room volume, object fraction, climate), a per-band table of the equivalent sound absorption area $A$ and the reverberation time $T$ beside the reverberation-time plot (`.plot()`), and the boxed mid-frequency reverberation time with the mid-frequency absorption area alongside. EN 12354-6 gives a diffuse-field **estimate**, not a measurement, so no PASS/FAIL verdict is emitted; a target reverberation time supplied through the metadata's `requirement` field is printed as a reference line only, since a room reverberation time is a target range rather than a strictly higher/lower-is-better quantity. It uses the same `ReportMetadata` container (documented under [Field insulation](https://jmrplens.github.io/phonometry/guides/insulation-field/#report-metadata-reportmetadata)) and rendering engine as the other fiches; passing `metadata=None` produces a bare characterisation fiche. Rendering needs reportlab (`pip install phonometry[report]`); 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 from phonometry import ( enclosed_space_reverberation, hard_object_absorption, object_fraction, ReportMetadata, ) surfaces = [ # per octave band, 125 Hz - 8 kHz (20.0, [0.05, 0.10, 0.20, 0.30, 0.40, 0.50, 0.55]), # carpeted floor (20.0, [0.20, 0.40, 0.65, 0.75, 0.80, 0.80, 0.75]), # acoustic ceiling (45.0, [0.02, 0.02, 0.03, 0.04, 0.05, 0.05, 0.05]), # painted-plaster walls ] volumes = [0.5, 0.8, 0.3] # furniture, m^3 result = enclosed_space_reverberation( surfaces, 50.0, objects=hard_object_absorption(volumes), object_fraction=object_fraction(volumes, 50.0), air_condition="20C_50-70", ) result.report( "enclosed_space_fiche.pdf", metadata=ReportMetadata( specimen="Meeting room, furnished", test_room="Meeting room M2", measurement_standard="EN 12354-6", temperature=20.0, relative_humidity=55.0, laboratory="Phonometry Reference Laboratory", requirement=0.6, # printed as a target reference line, no verdict ), ) # the per-band A/T table + the boxed T_mid ``` 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/enclosed_space_absorption_example.pdf) *Enclosed-space fiche (`ReverberationResult.report`), the per-band A/T table and the boxed $T_\text{mid}$.* ## References - European Committee for Standardization. (2003). *Building acoustics — Estimation of acoustic performance of buildings from the performance of elements — Part 6: Sound absorption in enclosed spaces* (EN 12354-6:2003). [BSI Knowledge record (BS EN 12354-6:2003)](https://knowledge.bsigroup.com/products/building-acoustics-estimation-of-acoustic-performance-of-buildings-from-the-performance-of-elements-sound-absorption-in-enclosed-spaces). The Clause 4 model, its input-data rules and its validity limits. - International Organization for Standardization. (2003). *Acoustics — Measurement of sound absorption in a reverberation room* (ISO 354:2003). [iso.org catalogue](https://www.iso.org/standard/34545.html). The laboratory measurement the surface and array coefficients come from. - Kuttruff, H. (2016). *Room acoustics* (6th ed.). CRC Press. [doi:10.1201/9781315372150](https://doi.org/10.1201/9781315372150). The statistical reverberation theory the standard's formulae specialise. ## Standards EN 12354-6:2003, *Building acoustics — Estimation of acoustic performance of buildings from the performance of elements — Part 6: Sound absorption in enclosed spaces*: the total equivalent absorption area (clause 4.3, Formulae 1-4, Table 1) and the reverberation time (clause 4.4, Formula 5), validated against the three worked cases of Annex E.