Source: https://jmrplens.github.io/phonometry/guides/insulation-prediction/ # Predicting Sound Insulation (EN 12354) A laboratory rating describes an element in isolation; a building also transmits sound along every flanking path. This page covers the EN 12354 prediction of in-situ performance from laboratory element data: the airborne and impact flanking models of EN 12354-1/2 with their junction vibration reduction indices, and the façade insulation and outdoor radiation of EN 12354-3/4. The measured quantities the model is checked against live in [Field Insulation Measurement and Ratings](https://jmrplens.github.io/phonometry/guides/insulation-field/); the laboratory inputs come from [Laboratory Insulation Measurement](https://jmrplens.github.io/phonometry/guides/insulation-lab/). ## Predicting performance (EN 12354) A laboratory rating describes an element in isolation, yet the sound a building actually transmits also travels *around* the partition (along the floor, up the façade, through the flanking walls), re-radiating into the receiving room. This **flanking transmission** is the whole difference between the laboratory $R$ and the field $R'$. EN 12354 predicts the in-situ apparent rating from the laboratory ratings of the elements plus the vibration transmission of their junctions. Each junction between a flanking element and the separating element carries three paths, $Ff$ (flanking→flanking), $Df$ (direct→flanking) and $Fd$ (flanking→direct), alongside the single direct path $Dd$. [Watch the high-resolution video (WebM)](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/anim_flanking_paths.webm) The **simplified single-number model** combines them energetically (Formula 26): $$ R'_w = -10 \log_{10}\Big[ 10^{-R_{Dd,w}/10} + \sum 10^{-R_{Ff,w}/10} + \sum 10^{-R_{Df,w}/10} + \sum 10^{-R_{Fd,w}/10} \Big], $$ with the direct path $R_{Dd,w} = R_{s,w} + \Delta R_{Dd,w}$ (Formula 27) and each flanking path (Formula 28a) $$ R_{ij,w} = \tfrac{R_{i,w} + R_{j,w}}{2} + \Delta R_{ij,w} + K_{ij} + 10 \log_{10}\frac{S_s}{l_0\ l_f}, $$ where $l_0 = 1$ m is the reference coupling length, $l_f$ the junction coupling length and $K_{ij}$ the junction's **vibration reduction index** (Annex E, empirical in the mass ratio $M = \log_{10}(m'_{\perp,i}/m'_i)$). ```python import numpy as np from phonometry import building # EN 12354-1 Annex H.3: a separating wall Rs,w = 57 dB, area Ss = 11.5 m², with # four flanking elements. The simplified model reads each junction's Kij at # 500 Hz from the mass ratio m'perp / m' (Annex E) — here the floor's rigid # cross-junction (the mass ratio is itself rounded, hence 12.5 vs Annex 12.4): print(round(building.junction_vibration_reduction("rigid_cross", "through", 1.61), 1)) # 12.5 KFf print(round(building.junction_vibration_reduction("rigid_cross", "corner", 1.61), 1)) # 8.9 KFd = KDf # Build each element's three flanking paths (Ff, Df, Fd) from the Annex H # tabulated Kij, then combine the direct path Dd energetically (Formula 26). elements = [ # (name, Rw, KFf, KFd = KDf, coupling length lf) ("floor", 49, 12.4, 8.9, 4.50), ("ceiling", 46, 14.4, 9.2, 4.50), ("facade", 42, 12.6, 6.7, 2.55), ("int-wall", 33, 33.5, 15.7, 2.55), ] paths = [] for name, rw, k_ff, k_fd, lf in elements: paths += building.flanking_element(label=name, r_flanking=rw, r_separating=57, k_ff=k_ff, k_fd=k_fd, k_df=k_fd, separating_area=11.5, coupling_length=lf) res = building.predicted_airborne_insulation(r_direct=57.0, flanking_paths=paths) print(round(res.r_prime_w, 1)) # 52.2 -> R'w = 52 dB print(res.dominant.label, round(res.dominant.fraction, 2)) # Dd 0.33 (direct dominates) res.plot() # per-path share of the transmitted energy, largest first (needs matplotlib) ```

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```python import matplotlib.pyplot as plt from phonometry import building # Build each element's three flanking paths (Ff, Df, Fd) from the Annex H # tabulated Kij, then combine the direct path Dd energetically (Formula 26). elements = [ # (name, Rw, KFf, KFd = KDf, coupling length lf) ("floor", 49, 12.4, 8.9, 4.50), ("ceiling", 46, 14.4, 9.2, 4.50), ("facade", 42, 12.6, 6.7, 2.55), ("int-wall", 33, 33.5, 15.7, 2.55), ] paths = [] for name, rw, k_ff, k_fd, lf in elements: paths += building.flanking_element(label=name, r_flanking=rw, r_separating=57, k_ff=k_ff, k_fd=k_fd, k_df=k_fd, separating_area=11.5, coupling_length=lf) res = building.predicted_airborne_insulation(r_direct=57.0, flanking_paths=paths) # Per-path sound reduction index and each path's share of the transmitted # energy for the Annex H.3 result computed above. labels = [p.label for p in res.paths] r_w = [p.r_w for p in res.paths] frac = [100.0 * p.fraction for p in res.paths] fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(9, 6), sharex=True) ax1.bar(labels, r_w, color="tab:blue") ax1.axhline(res.r_prime_w, ls="--", color="k", label=f"R'w = {res.r_prime_w:.1f} dB") ax1.set_ylabel("Path Rij,w [dB]"); ax1.legend() ax2.bar(labels, frac, color="tab:orange") ax2.set_ylabel("Energy share [%]"); ax2.set_xlabel("Transmission path") for ax in (ax1, ax2): ax.tick_params(axis="x", rotation=45) fig.suptitle("EN 12354-1 Annex H.3 — flanking transmission") fig.tight_layout() plt.show() ```

Every added flanking path strictly lowers $R'_w$ below the direct $R_{Dd,w} = 57$; `res.paths` exposes each path's share of the transmitted energy so the dominant path is visible. `flanking_element` is a convenience that builds one junction's three paths at once; the single-path constructor behind it, `flanking_path`, builds one `Ff`, `Df` or `Fd` path at a time (Formula 28a). Clause 4.4.2 also enforces a floor $K_{ij} \ge K_{ij,\min}$ from the junction geometry (Formula 29). Pass the flanking-element area to `flanking_element(..., flanking_area=...)` and the clamp is applied automatically per path; or compute the floor yourself with `junction_min_vibration_reduction` and pass it to `flanking_path(..., kij_min=...)`, which raises a below-floor $K_{ij}$ to the minimum: ```python from phonometry import building # Kij,min = 10 lg[lf·l0·(1/Si + 1/Sj)]; large elements give a low (here negative) # floor, so a realistic tabulated Kij is rarely clamped; but small, light # elements can push it above the tabulated value (e.g. lf = 4 m, S = 1.5 m² # gives 7.3 dB, over the 5 dB lightweight floor). print(round(building.junction_min_vibration_reduction(coupling_length=4.5, s_i=11.5, s_j=11.5), 1)) # -1.1 ``` The impact counterpart (EN 12354-2, Formula 21) is a direct subtraction: $L'_{n,w} = L_{n,w,eq} - \Delta L_w + K$, with the bare-floor equivalent level $L_{n,w,eq} = 164 - 35 \log_{10}(m'/m'_0)$ (Annex B), the covering improvement $\Delta L_w$ (ISO 717-2) and the flanking correction $K$ from Table 1. ```python from phonometry import building # EN 12354-2 Annex E.3: a 0.14 m concrete floor (m' = 322 kg/m²) with a floating # floor (ΔLw = 33 dB), rooms one above the other, mean flanking mass 145 kg/m². ln_eq = building.equivalent_impact_level(322.0) # 164 - 35 lg(m') k = building.impact_flanking_correction(322.0, 145.0) # Table 1 (sep 322, flk 145) imp = building.predicted_impact_insulation(ln_w_eq=ln_eq, delta_l_w=33.0, k_correction=k) print(round(ln_eq, 1), k, round(imp.l_prime_n_w, 1)) # 76.2 2 45.2 -> L'n,w = 45 dB # Exact Formula (3): L'nT,w = L'n,w - 10 lg(0.032 V). Annex E.3's own rounding # of the factor to 10 lg(V/30) sits 0.18 dB below; both give L'nT,w = 43 dB. print(round(building.standardized_impact_level(imp.l_prime_n_w, 50.0), 1)) # 43.2 L'nT,w imp.plot() # the Formula (21) terms as bars: Ln,w,eq - dLw + K -> L'n,w (needs matplotlib) ``` *The whole EN 12354-2 simplified model is one subtraction: the massive bare floor starts at `Ln,w,eq = 76.2 dB`, the floating floor buys back 33 dB, and the flanking correction returns 2 dB, landing at `L'n,w = 45 dB`.*

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import building # EN 12354-2 Annex E.3: 0.14 m concrete floor (m' = 322 kg/m2), floating # floor delta-Lw = 33 dB, mean flanking mass 145 kg/m2. ln_eq = building.equivalent_impact_level(322.0) k = building.impact_flanking_correction(322.0, 145.0) imp = building.predicted_impact_insulation(ln_w_eq=ln_eq, delta_l_w=33.0, k_correction=k) # One line — the Formula (21) terms as bars: imp.plot() plt.show() # By hand, from the result's fields: labels = ["Ln,w,eq", "-dLw", "+K", "L'n,w"] values = [imp.ln_w_eq, -imp.delta_l_w, imp.k_correction, imp.l_prime_n_w] fig, ax = plt.subplots() ax.bar(np.arange(4), values) ax.axhline(0.0, color="k", lw=0.8) ax.set_xticks(np.arange(4), labels) ax.set_ylabel("Level / correction [dB]") ax.set_title(f"L'n,w = {imp.l_prime_n_w:.1f} dB (EN 12354-2 Annex E.3)") plt.show() ```

The airborne counterpart of that closure is Formula (5b), $D_{nT} = R' + 10\lg(0.32\,V/S_s)$, exposed as `standardized_level_difference`; it closes the Annex H.3 example (`standardized_level_difference(52.2, 50.0, 11.5)` gives 53.6 dB, the printed $V/(3S)$ chain 53.8 dB, both rounding to $D_{nT,w} = 54$ dB). The three insulation guides close a loop: the [laboratory](https://jmrplens.github.io/phonometry/guides/insulation-lab/) measures $R$ and $K_{ij}$ element by element and junction by junction, this model assembles them into a predicted $R'_w$, and the [field measurement](https://jmrplens.github.io/phonometry/guides/insulation-field/) checks the built result. When the measured value lands well below the prediction, look for a construction defect on the dominant path the model reports: a rigid bridge across a resilient junction, a missing lining, a leak around the separating element. ### `junction_vibration_reduction()` / `flanking_element()` parameters | Parameter | Type | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `junction_type` | str | — | `'rigid_cross'` / `'rigid_t'` / `'flexible_t'` / `'lightweight_facade'` / `'lightweight_double_homogeneous'` / `'lightweight_double_coupled'` / `'corner'` / `'thickness_change'` | Junction geometry (Annex E.3-E.9) | | `path` | str | — | `'through'` (K13) / `'corner'` (K12 = K23) / `'double_leaf'` (K24) | Path branch | | `mass_ratio` | float | — | > 0 | `m'⊥,i / m'i` (Formula E.2) | | `frequency` | float | Hz | default `500` | `flexible_t` and the E.7/E.8 double-leaf junctions are frequency-dependent | | `r_flanking` / `r_separating` | float | dB | — | Weighted indices of the flanking / separating element | | `k_ff` / `k_fd` / `k_df` | float | dB | — | Junction `Kij` for the three paths | | `separating_area` | float | m² | > 0 | Separating-element area `Ss` | | `coupling_length` | float | m | > 0 | Junction coupling length `lf` | | `delta_r_ff` / `delta_r_fd` / `delta_r_df` | float | dB | default `0` | Lining improvements per path | | `flanking_area` | float | m² | default `None` | Flanking-element area `SF`; enables the automatic `Kij,min` clamp (Clause 4.4.2 / Formula 29) | ### `flanking_path()` parameters | Parameter | Type | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `label` | str | — | — | Display name of the path | | `kind` | str | — | `'Ff'` / `'Df'` / `'Fd'` | Which flanking branch the path is | | `r_source` / `r_receive` | float | dB | — | Weighted indices of the source-side / receive-side elements | | `k_ij` | float | dB | — | Junction vibration-reduction index for this path | | `separating_area` | float | m² | > 0 | Separating-element area `Ss` | | `coupling_length` | float | m | > 0 | Junction coupling length `lf` | | `delta_r` | float | dB | default `0` | Lining improvement on this path | | `kij_min` | float | dB | default `None` | When given, `k_ij` is floored at this Formula (29) minimum | `predicted_airborne_insulation()` returns an `AirbornePredictionResult` (`r_prime_w`, `r_direct_w`, `paths` of `PathContribution`, `dominant`); `predicted_impact_insulation()` an `ImpactPredictionResult` (`l_prime_n_w`, `ln_w_eq`, `delta_l_w`, `k_correction`). The simplified model carries a reported standard deviation of about 2 dB (Clause 5). ### EN 12354 prediction report (`.report()`) Both prediction results write a one-page **prediction** report through a `report(path)` method. Unlike the measurement fiches, the reported result is an *estimate* of the in-situ performance from the elements' laboratory data plus the flanking transmission across the junctions; the sheet states this explicitly and is labelled a prediction, never a measurement. `AirbornePredictionResult.report()` renders the predicted apparent sound reduction index fiche (the transmission-path table beside the per-path share-of-energy plot, the boxed `R'w`); `ImpactPredictionResult.report()` renders the predicted apparent impact-level fiche (the Formula (21) term table beside the term plot, the boxed `L'n,w`). Each names EN/ISO 12354-1/-2 and the ISO 717 rating part in its basis line, prints the model's ~2 dB standard deviation and, when a `requirement` is supplied, adds a PASS/FAIL verdict (airborne passes at or above it, impact at or below it). `verbose=True` annexes each transmission path's share of the transmitted energy to the airborne table; metadata, `language="es"` and the `phonometry[report]` extra behave as in the measurement fiches. ```python from phonometry import building, ReportMetadata # Airborne prediction (EN 12354-1 Annex H.3): a separating wall Rs,w = 57 dB # flanked by four elements -> R'w = 52 dB. paths = [] for label, rw, kff, kfd, lf in [ ("floor", 49.0, 12.4, 8.9, 4.5), ("ceiling", 46.0, 14.4, 9.2, 4.5), ("facade", 42.0, 12.6, 6.7, 2.55), ("intwall", 33.0, 33.5, 15.7, 2.55), ]: ff, df, fd = building.flanking_element( label=label, r_flanking=rw, r_separating=57.0, k_ff=kff, k_fd=kfd, k_df=kfd, separating_area=11.5, coupling_length=lf) paths += [ff, df, fd] air = building.predicted_airborne_insulation(r_direct=57.0, flanking_paths=paths) air.report("Rpw_prediction.pdf", metadata=ReportMetadata( specimen="Separating wall, Rs,w = 57 dB", area=11.5, source_volume=53.0, receiving_volume=50.0, requirement=50.0, notes="Flanking: floor/ceiling/facade/internal wall.")) # R'w = 52 dB # Impact prediction (EN 12354-2 Annex E.3): a concrete floor (m' = 322 kg/m2) # with a floating floor (DLw = 33 dB) -> L'n,w = 45 dB. ln_eq = building.equivalent_impact_level(322.0) k = building.impact_flanking_correction(322.0, 145.0) imp = building.predicted_impact_insulation(ln_w_eq=ln_eq, delta_l_w=33.0, k_correction=k) imp.report("Lnw_prediction.pdf", metadata=ReportMetadata(mass_per_area=322.0, requirement=53.0)) # L'n,w = 45 dB ``` [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iso12354_airborne_prediction_example.pdf) [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iso12354_impact_prediction_example.pdf) ### Façade insulation & radiated power (EN 12354-3 / -4) Parts 3 and 4 predict the two directions across the building envelope, both from the same energy summation of the element **transmission factors** $\tau = 10^{-R/10}$, area-weighted by $S_i/S$ (a small element or air path enters through its element-normalized level difference $D_{n,e}$ with the reference area $A_0 = 10\ \text{m}^2$): $$ R' = -10 \log_{10}\!\Big( \sum_i \tfrac{S_i}{S}\,10^{-R_i/10} + \sum_k \tfrac{A_0}{S}\,10^{-D_{n,e,k}/10} \Big). $$ **Part 3: outdoor → indoor.** From $R'$ (Formula 10) follow the loudspeaker- and traffic-referenced indices $R_{45} = R'+1$ and $R_{tr,s} = R'$, and the primary output, the standardized level difference at 2 m (Formula 13) $$ D_{2m,nT} = R' + \Delta L_{fs} + 10 \log_{10}\frac{V}{6\,T_0\,S}, \qquad T_0 = 0.5\ \text{s}, $$ with the façade-shape term $\Delta L_{fs}$ (Annex C; 0 dB for a flat reflecting façade; `facade_shape_level_difference` looks it up from the Figure C.2 table for galleries, balconies and terraces, interpolating over the underside absorption $\alpha_w$). Single-number ratings reuse EN ISO 717-1 (`weighted_rating`). ```python from phonometry import building # EN 12354-3 Annex F: an 11.3 m² façade (V = 50 m³, flat so ΔLfs = 0) of a double # wall, a window, a small skylight and an acoustically-treated air inlet (a Dn,e # element). elements = [ building.FacadeElement("wall", area=6.0, r=[41, 46, 52, 58, 64]), # octave 125-2000 building.FacadeElement("window", area=4.5, r=[23, 22, 30, 36, 37]), building.FacadeElement("skylight", area=0.5, r=[24, 27, 30, 33, 30]), building.FacadeElement("air inlet", dn_e=[28, 23, 25, 38, 44]), # small element ] fac = building.facade_sound_reduction(elements, area=11.3, volume=50.0, frequencies=[125, 250, 500, 1000, 2000], bands="octave") print(fac.r_tr_s_w, fac.c_tr, fac.d_2m_nt_w) # 31 -3 33 (R'tr,s,w / Ctr / D2m,nT,w) fac.plot() # per-element partial indices with R' and D2m,nT overlaid (needs matplotlib) ```

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```python import numpy as np import matplotlib.pyplot as plt from phonometry import building # EN 12354-3 Annex F: an 11.3 m² façade (V = 50 m³, flat so ΔLfs = 0) of a double # wall, a window, a small skylight and an acoustically-treated air inlet (a Dn,e # element). elements = [ building.FacadeElement("wall", area=6.0, r=[41, 46, 52, 58, 64]), # octave 125-2000 building.FacadeElement("window", area=4.5, r=[23, 22, 30, 36, 37]), building.FacadeElement("skylight", area=0.5, r=[24, 27, 30, 33, 30]), building.FacadeElement("air inlet", dn_e=[28, 23, 25, 38, 44]), # small element ] fac = building.facade_sound_reduction(elements, area=11.3, volume=50.0, frequencies=[125, 250, 500, 1000, 2000], bands="octave") x = np.arange(5) fig, ax = plt.subplots(figsize=(9, 5.5)) for name, rp in fac.element_r.items(): ax.plot(x, rp, "--", alpha=0.6, marker=".", label=f"Rp — {name}") ax.plot(x, fac.r_prime, "k-", lw=2.5, marker="o", label="R′ (façade)") ax.plot(x, fac.d_2m_nt, lw=2, marker="s", label="D2m,nT") ax.set_xticks(x); ax.set_xticklabels([125, 250, 500, 1000, 2000]) ax.set_xlabel("Frequency [Hz]"); ax.set_ylabel("Index / level difference [dB]") ax.set_title("EN 12354-3 façade sound insulation (Annex F)") ax.legend(ncol=2); ax.grid(alpha=0.4) fig.tight_layout(); plt.show() ```

The façade prediction also writes a one-page **prediction** report through a `report(path)` method, the same layout as the airborne and impact prediction fiches. `FacadePredictionResult.report()` renders the façade-element table (each element's weighted partial index `Rp,w`) beside the per-element / `R'` / `D2m,nT` plot, the boxed predicted `D2m,nT,w` (with `R'tr,s,w` and `Ctr`), the prediction statement and, when a `requirement` is supplied, a PASS/FAIL verdict (the level difference passes at or above it). `verbose=True` annexes each element's share of the transmitted sound energy, which singles out the limiting element (the air inlet here, not the wall). The report needs the ISO 717-1 single-number ratings, so build the result on the 5 octave or 16 one-third-octave bands. The applicable `ReportMetadata` fields describe the predicted situation: `specimen` (the façade element set), `area` (the exposed façade area), the receiving-room `receiving_volume`, the outdoor/traffic situation in `test_room`, plus the calculator / laboratory identity fields (`client`, `manufacturer`, `measurement_standard`, `laboratory`, `operator`, `report_id`, `test_date`), a free-text façade-shape and model summary in `notes` and the target `D2m,nT,w` in `requirement`. Metadata, `language="es"` and the `phonometry[report]` extra behave as in the measurement fiches. ```python from phonometry import building, ReportMetadata # EN 12354-3 Annex F facade -> D2m,nT,w = 33 dB (R'tr,s,w = 31, Ctr = -3). elements = [ building.FacadeElement("Masonry wall", area=6.0, r=[41, 46, 52, 58, 64]), building.FacadeElement("Glazing", area=4.5, r=[23, 22, 30, 36, 37]), building.FacadeElement("Roof light", area=0.5, r=[24, 27, 30, 33, 30]), building.FacadeElement("Air inlet", dn_e=[28, 23, 25, 38, 44]), ] fac = building.facade_sound_reduction(elements, area=11.3, volume=50.0, frequencies=[125, 250, 500, 1000, 2000], bands="octave") fac.report("D2mnT_prediction.pdf", metadata=ReportMetadata( specimen="Masonry wall + window + roof light + air inlet", area=11.3, receiving_volume=50.0, requirement=30.0, notes="Flat facade, ΔLfs = 0 dB (Annex C).")) # D2m,nT,w = 33 dB ``` [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iso12354_facade_prediction_example.pdf) **Part 4: indoor → outdoor.** The sound power level radiated by a segment (Formula 2) is $L_W = L_{p,in} + C_d - R' + 10 \log_{10}(S/S_0)$ with $S_0 = 1$ m² and the inside-field diffusivity term $C_d$ (Annex B; −6 dB ideal diffuse, −5 dB average industrial). Openings are elements whose "R" is the silencer insertion loss (a bare opening is 0 dB). The exterior level follows from the simplified Annex E attenuation $A_{tot}$ of a finite radiating side, $L_p = L_W - A_{tot}$. ```python from phonometry import building # EN 12354-4 Annex G, side 1: a 10×20 m concrete wall segment with a 6×4 m # industrial door, inside level Lp,in, Cd = -5 dB. The 40 dB cap on R' is an # Annex G example footnote (field leaks), not part of Formula (2)/(3): pass it # explicitly to reproduce Annex G; by default no cap is applied. bands = [63, 125, 250, 500, 1000, 2000, 4000, 8000] seg = building.radiated_sound_power( [building.FacadeElement("wall", area=176.0, r=[32, 36, 36, 33, 39, 49, 57, 63]), building.FacadeElement("door", area=24.0, r=[21, 23, 28, 30, 30, 30, 30, 30])], lp_in=[70, 74, 76, 72, 70, 67, 62, 57], area=200.0, c_d=-5.0, r_prime_cap=40.0, octave_bands=bands) print(round(seg.l_w[0], 1), round(seg.l_w[1], 1)) # 59.8 61.2 (LW at 63/125 Hz) # Exterior level 5 m in front of the centre of the 60×10 m side (LWA = 62.9 dB(A)). a_tot = building.outdoor_attenuation(width=60.0, height=10.0, distance=5.0) print(round(a_tot, 1), round(building.outdoor_level(62.9, a_tot), 1)) # 26.3 36.6 seg.plot() # radiated LW per octave with the A-weighted LWA line (needs matplotlib) ``` *The Annex G side-1 segment: the wall dominates the area but the door's weaker `R` carries the radiated power, so the octave spectrum stays flat where the wall alone would fall. The dashed line is the A-weighted single number `LWA` formed from the octave bands.*

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import building # EN 12354-4 Annex G, side 1: a 10×20 m concrete wall segment with a 6×4 m # industrial door, inside level Lp,in, Cd = -5 dB. bands = [63, 125, 250, 500, 1000, 2000, 4000, 8000] seg = building.radiated_sound_power( [building.FacadeElement("wall", area=176.0, r=[32, 36, 36, 33, 39, 49, 57, 63]), building.FacadeElement("door", area=24.0, r=[21, 23, 28, 30, 30, 30, 30, 30])], lp_in=[70, 74, 76, 72, 70, 67, 62, 57], area=200.0, c_d=-5.0, r_prime_cap=40.0, octave_bands=bands) # One line — LW per octave with the A-weighted LWA line: seg.plot() plt.show() # By hand, from the result's fields: x = np.arange(len(bands)) fig, ax = plt.subplots() ax.bar(x, seg.l_w, label="radiated LW per octave") ax.axhline(seg.l_w_dba, ls="--", color="tab:red", label=f"LWA = {seg.l_w_dba:.1f} dB(A)") ax.set_xticks(x, [str(b) for b in bands]) ax.set_xlabel("Frequency [Hz]") ax.set_ylabel("Radiated sound power level [dB re 1 pW]") ax.set_title("EN 12354-4 radiated sound power (Annex G)") ax.legend() plt.show() ```

> **Worked-example note.** The 2000 worked examples carry small internal rounding > inconsistencies at the higher octave bands (Part 3's printed $R'$ disagrees with > its own per-element partial indices at 1 k/2 k; Part 4's $R'$ rows above 500 Hz > disagree with its Table G.2 inputs). The implementation is faithful to the > formulas: it reproduces the low bands, every single-number rating and the whole > Annex E propagation exactly. ### `FacadeElement` / `facade_sound_reduction()` / `radiated_sound_power()` parameters | Parameter | Type | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `FacadeElement.area` | float | m² | > 0 for `r` / `insertion_loss` | Element area $S_i$ (ignored for `dn_e`) | | `FacadeElement.r` / `dn_e` / `insertion_loss` | float or seq | dB | give exactly one | Area element $R_i$ / small-element $D_{n,e}$ / opening insertion loss | | `facade_sound_reduction(area)` | float | m² | > 0 | Total façade area $S$ | | `facade_sound_reduction(volume)` | float | m³ | > 0 | Receiving-room volume $V$ (Formula 13) | | `facade_sound_reduction(delta_l_fs)` | float | dB | default `0` | Façade-shape term $\Delta L_{fs}$ (Annex C; look it up with `facade_shape_level_difference`) | | `radiated_sound_power(lp_in)` | float or seq | dB | — | Inside level $L_{p,in}$ per band | | `radiated_sound_power(c_d)` | float | dB | default `-6` | Diffusivity term $C_d$ (Annex B) | | `radiated_sound_power(r_prime_cap)` | float | dB | default `None` (off) | Optional field cap on $R'$, an Annex G example footnote (it uses 40 dB), not part of Formula (2)/(3) | | `radiated_sound_power(octave_bands)` | seq of int | Hz | default `None` | Octave centres matching the bands; enables the A-weighted $L_{WA}$ | | `facade_sound_reduction(frequencies)` | seq | Hz | default `None`; length = band count | Band centres carried on the result for plotting | | `outdoor_attenuation(width, height, distance)` | float | m | > 0 | Finite radiating side and reception distance (Annex E) | | `outdoor_level(l_w, attenuation)` | float or seq | dB | broadcast-compatible | Exterior $L_p$ from one or more sides (Formula E.1) | `facade_sound_reduction()` returns a `FacadePredictionResult` (`r_prime`, `r_45`, `r_tr_s`, `d_2m_nt`, `element_r`, and the `r_tr_s_w` / `d_2m_nt_w` / `c_tr` single numbers); `radiated_sound_power()` a `RadiatedPowerResult` (`l_w`, `r_prime`, `l_w_dba`). Both expose `.plot()`. ## References - Hopkins, C. (2007). *Sound insulation*. Butterworth-Heinemann. ISBN 978-0-7506-6526-1. [doi:10.4324/9780080550473](https://doi.org/10.4324/9780080550473). The full treatment of flanking transmission and the EN 12354 prediction framework, from the vibration reduction index to its statistical basis. ## Standards EN 12354-1:2000 and EN 12354-2:2000, which give the simplified flanking-transmission predictions (Annex E junctions, worked examples H.3 and E.3); EN 12354-3:2000 and EN 12354-4:2000, which cover the façade sound insulation and outdoor-radiation predictions (Annex F and Annex G worked examples). ## See also - [Field Insulation Measurement and Ratings](https://jmrplens.github.io/phonometry/guides/insulation-field/): the measured in-situ quantities the prediction is checked against. - [Laboratory Insulation Measurement](https://jmrplens.github.io/phonometry/guides/insulation-lab/): the ISO 10140 ratings and ISO 10848 junction data the model consumes. - [Sound absorption in enclosed spaces (EN 12354-6)](https://jmrplens.github.io/phonometry/reference/api/rooms/enclosed-space-absorption/): the absorption member of the same EN 12354 family. - [Dynamic stiffness of resilient materials (EN 29052-1)](https://jmrplens.github.io/phonometry/reference/api/materials/dynamic-stiffness/): the s' input to the EN 12354-2 floating-floor term. - API reference: [`building.building_prediction`](https://jmrplens.github.io/phonometry/reference/api/building/building-prediction/) and [`building.facade_prediction`](https://jmrplens.github.io/phonometry/reference/api/building/facade-prediction/).