Source: https://jmrplens.github.io/phonometry/buildings/insulation/flanking-lab/ # Laboratory Flanking Transmission (ISO 10848) EN 12354 predicts a building from its junctions, and ISO 10848 is how a junction gets its number. Two structurally decoupled elements meet in a laboratory junction rig; shakers and tapping machines drive one, and the velocity level differences across the junction condense into the **vibration reduction index** $K_{ij}$, together with the overall flanking descriptors $D_\mathrm{n,f}$ (airborne) and $L_\mathrm{n,f}$ (impact). This guide covers that measurement chain: the direction-averaged velocity level difference, the equivalent absorption lengths, the SEA validity checks of Part 4 and the three accredited fiches. The empirical junction values a prediction falls back on when no measurement exists live in [Predicting Sound Insulation (EN 12354)](https://jmrplens.github.io/phonometry/buildings/design/insulation-prediction/); the wave-theory $K_{ij}$ of ideal plate junctions is derived in [Bending-wave transmission at plate junctions](https://jmrplens.github.io/phonometry/vibration/structural/junction-transmission/). ## The vibration reduction index and the flanking descriptors ISO 10848:2006/2010 is the laboratory method that **measures** the junction **vibration reduction index** $K_{ij}$ that the [EN 12354 prediction](https://jmrplens.github.io/phonometry/buildings/design/insulation-prediction/) takes as an input, together with the overall flanking descriptors $D_\mathrm{n,f}$ (airborne) and $L_\mathrm{n,f}$ (impact). It is the measurement counterpart of the empirical `junction_vibration_reduction()` of that prediction. **Vibration reduction index (Formula (13)).** $K_{ij} = \overline{D}_{v,ij} + 10\log_{10}\!\big(l_{ij} / \sqrt{a_i a_j}\big)$ dB, from the direction-averaged velocity level difference $\overline{D}_{v,ij} = \tfrac{1}{2}(D_{v,ij} + D_{v,ji})$ (Formula (11), which makes $K_{ij}$ symmetric), the common-edge junction length $l_{ij}$ and the **equivalent absorption lengths** $a_j = 2.2\pi^2 S_j /(T_{\mathrm{s},j} c_0)\sqrt{f_\mathrm{ref}/f}$ (Formula (12), $f_\mathrm{ref} = 1000$ Hz). For lightweight well-damped elements $a_j = S_j / l_0$ ($l_0 = 1$ m) and Formula (13) reduces to the simplified Formula (14). The related **total loss factor** is $\eta = 2.2/(f T_\mathrm{s})$. **Overall descriptors.** $D_\mathrm{n,f} = L_1 - L_2 - 10\log_{10}(A/A_0)$ (Formula (4), airborne) and $L_\mathrm{n,f} = L_2 + 10\log_{10}(A/A_0)$ (Formula (5), tapping machine), $A_0 = 10\ \text{m}^2$; their $D_\mathrm{n,f,w}$ / $L_\mathrm{n,f,w}$ single numbers reuse the ISO 717 rating engines. The single-number $\overline{K}_{ij}$ is the arithmetic mean over 200–1250 Hz for one-third-octave bands, or over 125–1000 Hz for octave bands (Annex A).

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import building freqs = [100, 125, 160, 200, 250, 315, 400, 500, 630, 800, 1000, 1250, 1600, 2000, 2500, 3150, 4000, 5000] # Direction-averaged velocity level difference of a rigid T-junction (dB): dv = np.array([4.5, 4.8, 5.2, 5.6, 6.0, 6.5, 7.0, 7.6, 8.1, 8.7, 9.2, 9.8, 10.3, 10.9, 11.4, 11.9, 12.3, 12.7]) res = building.vibration_reduction_index( dv, junction_length=4.0, area_i=12.0, area_j=10.0, frequency=freqs, structural_reverberation_time_i=0.35, structural_reverberation_time_j=0.40, ) print(res.single_number) # mean Kij over 200-1250 Hz (Annex A) res.plot() plt.show() ```

**Validity.** $K_{ij}$ rests on a statistical-energy-analysis simplification: `strong_coupling_satisfied()` checks the Formula (15) inequality and, for the heavy junctions of Part 4, `modal_density()`, `band_mode_count()` and `modal_overlap_factor()` (Formulae (5)/(4)/(6)) quantify where the mode count is too low for $K_{ij}$ to be reliable. Pass the per-band modal overlap factor to `vibration_reduction_index(..., modal_overlap=M)`: bands with $M < 0.25$ are flagged in `result.bracketed` and excluded from the single-number $\overline{K}_{ij}$, as Part 4 Clause 9 requires. Because ISO 10848 contains no worked numeric example, conformance is anchored on closed-form identities (simplified $K_{ij}$, $a_j$ at $f_\mathrm{ref}$, $\eta$). Those checks are the only enforcement there is. The acquisition itself — shielding the other elements, a shield meeting $\Delta R_\text{min}$, the position counts and separations, the accelerometer mass-loading inequality, $T_\mathrm{s}$ measured on the elements in their installed state rather than assumed — is the operator's responsibility, and nothing here checks any of it. ```python import numpy as np from phonometry import building freqs = [200, 250, 315, 400, 500, 630, 800, 1000, 1250] lij, s_i, s_j = 4.0, 12.0, 10.0 # junction length (m), element areas (m^2) ts = np.linspace(0.30, 0.10, 9) # structural reverberation time Ts (s) dv_ij = [5.6, 6.0, 6.5, 7.0, 7.6, 8.1, 8.7, 9.2, 9.8] # element i excited (dB) dv_ji = [6.4, 6.8, 7.3, 7.8, 8.4, 8.9, 9.5, 10.0, 10.6] # element j excited (dB) # Kij from both excitation directions (symmetric via the direction average): dbar = building.direction_averaged_level_difference(dv_ij, dv_ji) res = building.vibration_reduction_index(dbar, lij, s_i, s_j, frequency=freqs, structural_reverberation_time_i=ts, structural_reverberation_time_j=ts) res.k_ij # Kij per band (Formula (13)) res.single_number # mean Kij over 200-1250 Hz, or None without the band set res.octave_bands() # Kij in octave bands (its single number averages 125-1000 Hz) # Overall airborne flanking descriptor and a Part-4 modal-overlap validity check: dnf = building.normalized_flanking_level_difference(np.full(9, 75.0), np.full(9, 42.0), absorption_area=np.full(9, 12.0)) m = building.modal_overlap_factor(s_i, critical_frequency=85.0, structural_reverberation_time=ts) res_m = building.vibration_reduction_index(dbar, lij, s_i, s_j, frequency=freqs, modal_overlap=m) # M < 0.25 bands bracketed res_m.bracketed # per-band flags; bracketed bands leave the single number # With 16 one-third-octave (or 5 octave) bands, dnf.plot() draws Dn,f vs the # shifted ISO 717-1 reference with Dn,f,w annotated (needs matplotlib): ``` *The overall flanking descriptor $D_\mathrm{n,f}$ is an airborne quantity, so its single number $D_\mathrm{n,f,w}$ comes from the unchanged ISO 717-1 engine; it drops straight into the EN 12354-1 model as the flanking-path datum of the tested junction (the impact counterpart $L_\mathrm{n,f}$ rates per ISO 717-2 the same way).*

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import building # A lightweight junction in the laboratory: source-room level, receiving-room # level over the flanking path, and the receiving-room absorption area. l1 = np.full(16, 80.0) dnf_target = np.array([48, 49, 50, 51, 52, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65], dtype=float) dnf = building.normalized_flanking_level_difference( l1, l1 - dnf_target, absorption_area=np.full(16, 10.0) ) # One line — Dn,f vs the shifted ISO 717-1 reference: dnf.plot() plt.show() # By hand, from the rating the result carries: w = dnf.rating fig, ax = plt.subplots() ax.semilogx(w.band_centers, dnf.d_n_f, "o-", label="Dn,f (flanking)") ax.semilogx(w.band_centers, w.shifted_reference, "s--", label="shifted reference") ax.fill_between(w.band_centers, w.measured, w.shifted_reference, where=w.measured < w.shifted_reference, interpolate=True, alpha=0.3, label="unfavourable deviations") ax.set_xlabel("Frequency [Hz]") ax.set_ylabel("Normalized flanking level difference [dB]") ax.set_title(f"Dn,f,w = {w.rating} dB (C={w.c:+d}; Ctr={w.ctr:+d})") ax.legend() plt.show() ```

## Suspended ceilings: the plenum flanking path (ISO 140-9, Vigran 9.2.3) Two offices separated by a partition that stops at the suspended ceiling share one continuous plenum above it. Sound leaves the source room through the ceiling tiles, travels sideways over the partition and comes back down through the tiles of the receiving room. That path is often the weakest link in an open-plan fit-out, and it is not what a partition's $R_\mathrm{w}$ describes. *Left: the plenum charges a fixed penalty against the sum of the two ceilings, and a deeper plenum pays some of it back. Right: the same measured quantity rated as a ceiling attenuation class.* **The one-dimensional model.** Mechel's one-dimensional variant, as presented by Vigran in Section 9.2.3, treats the plenum as a duct lined on one side. The ceiling on each side has a transmission factor $\tau_\mathrm{S} = \tau_\mathrm{S,pl}\tau_\mathrm{S,a}$ (plates times any plenum absorber, Eq. (9.14)); the injected power splits, a fraction $s_\mathrm{S}$ heading for the partition, and decays as $\exp(-mx)$ with the power attenuation coefficient $m = 2\,\mathrm{Re}\{\Gamma\} = -2\,\mathrm{Im}\{k'\}$ (Eqs. (9.15) and (9.16)). Integrating over the ceiling length on both sides gives Eq. (9.18), whose receiving side carries the leakage back into the room, $m'_\mathrm{R} = m_\mathrm{R} + s_\mathrm{R}\tau_\mathrm{R}/h$ (Eq. (9.17)). Vigran prints the *unprimed* $m_\mathrm{R}$ in that expression's denominator; that is a misprint, recorded in [the errata register](https://jmrplens.github.io/phonometry/reference/errata/), and the derived $m'_\mathrm{R}$ is used here. Read literally, the printed form is non-monotonic in the plenum damping (adding absorber would predict a worse path than none) and unbounded as $m_\mathrm{R} \to 0$. For a plenum with little attenuation and $s_\mathrm{S} = s_\mathrm{R} = 0{,}5$ that collapses to the compact form that makes the geometry visible (Eqs. (9.19) and (9.20)): $$ R_\mathrm{cl} = R_\mathrm{S} + R_\mathrm{R} - 10\log_{10}\!\left[\frac{\varepsilon^2 L_\mathrm{R}}{4h}\right], $$ with $\varepsilon = 1$ for totally absorbing plenum sidewalls and $\varepsilon = 2$ for totally reflecting ones. A deep plenum helps, a long room hurts, and doubling the tile insulation helps twice over because $R_\mathrm{S}$ and $R_\mathrm{R}$ both appear. Referred to the partition area instead of the ceiling, $R_\mathrm{cl,p} = R_\mathrm{cl} + 10\log_{10}(H_\mathrm{S}/L_\mathrm{S})$ (Eq. (9.13)), which is what lets the ceiling path be added to the direct path as transmission factors. ```python from phonometry import ( partition_referenced_reduction_index, plenum_flanking_reduction_index, ) freqs = [63.0, 125.0, 250.0, 500.0, 1000.0, 2000.0, 4000.0] ceiling = [17.0, 21.0, 25.0, 29.0, 32.0, 30.0, 38.0] # 9.5 mm plasterboard # Vigran's example geometry: LS = LR = 4.75 m, plenum 0.43 m, reflecting walls. res = plenum_flanking_reduction_index( ceiling, ceiling, ceiling_length=4.75, plenum_height=0.43, frequency=freqs ) print(round(res.geometry_term, 1)) # 10.4 dB charged against RS + RR res.plot() # Rcl against the two ceilings # A lined plenum attenuates the sideways path (Eq. (9.18) instead of (9.20)): damped = plenum_flanking_reduction_index( ceiling, ceiling, ceiling_length=4.75, plenum_height=0.43, attenuation_source=[0.5] * 7, attenuation_receiving=[0.5] * 7, ) # Referred to the partition instead of the ceiling (Eq. (9.13)): print(partition_referenced_reduction_index(res.reduction_index, 2.7, 4.75)) ``` **The measured quantity.** A ceiling is not rated by $R_\mathrm{cl}$ but by the **normalized ceiling attenuation** $D_\mathrm{n,c} = D - 10\log_{10}(A/A_0)$ (ISO 140-9:1985 clause 3.3), with $A$ the receiving-room equivalent absorption area and the reference $A_0 = 10\ \text{m}^2$. The facility has two rooms of at least 50 m³ whose volumes differ by at least 10 %, a dividing wall tapered to at most 100 mm at the top, and a plenum 650 mm to 760 mm deep with one sidewall and both end walls lined; the standard prints the required lining absorption $\alpha_\mathrm{s} \ge 0{,}65$ at 125 Hz and $\ge 0{,}80$ from 250 Hz to 4000 Hz, and requires $\alpha < 0{,}10$ on the other sidewall and on the plenum ceiling. The North American counterpart, ASTM E1414, uses $A_0 = 12\ \text{m}^2$, so an ASTM value runs about $10\log_{10}(12/10) = 0{,}79$ dB higher for the same rooms. ISO rates $D_\mathrm{n,c}$ with the ISO 717-1 curve, giving $D_\mathrm{n,c,w}$; ASTM E1414 rates it through ASTM E413 as the **ceiling attenuation class**. E413 rounds the data to the nearest integer (clause 5.2), raises its reference contour in 1 dB steps while the sum of the deficiencies stays at or below 32 dB and no single deficiency exceeds 8 dB (clauses 5.3 and 5.4), and reads the rating off the shifted contour at 500 Hz (clause 5.5). ```python from phonometry import ( ceiling_attenuation_class, normalized_ceiling_attenuation, weighted_rating, ) # ASTM E1414 normalizes to A0 = 12 m2, ISO 140-9 to A0 = 10 m2. dnc = normalized_ceiling_attenuation(l1, l2, absorption, reference_area=12.0) # A 28 mm perforated plaster acoustic tile, measured to ASTM E1414 (CAC 34). dnc = [14.4, 18.6, 21.7, 24.1, 23.4, 30.3, 33.7, 35.2, 41.6, 44.2, 42.1, 36.8, 35.7, 36.0, 36.9, 37.9] res = ceiling_attenuation_class(dnc) print(res.rating, res.deficiency_sum, res.max_deficiency) # 34, 27.0, 7.0 res.plot() # Dn,c vs the contour # The ISO single number of the same spectrum, shifted to A0 = 10 m2: iso = [v - 0.79 for v in dnc] print(weighted_rating(iso).rating) # Dn,c,w ``` ## ISO 10848 flanking-transmission reports (`.report()`) Each of the three results renders a one-page PDF fiche. `VibrationReductionResult.report()` writes a **junction characterization** report of $K_{ij}$ (ISO 10848-1:2006): the standard-basis line, an optional metadata header, the per-band $K_{ij}$ table beside the $K_{ij}(f)$ curve and a boxed single-number mean $K_{ij}$ over the Annex A band range, with the count of averaged and bracketed bands. Bands bracketed for poor modal overlap ($M < 0.25$, ISO 10848-4:2010 Clause 9) print their value in brackets and are excluded from the mean; `verbose=True` adds a column stating whether each band enters the mean. `FlankingLevelDifferenceResult.report()` and `FlankingImpactLevelResult.report()` write **measurement** reports of the overall descriptors $D_\mathrm{n,f}$ (airborne) and $L_\mathrm{n,f}$ (impact, tapping machine), reusing the same two-panel insulation layout: the per-band quantity beside the measured-versus-shifted-ISO 717-reference curve and the boxed single number $D_\mathrm{n,f,w}$ (C; Ctr) (ISO 717-1) or $L_\mathrm{n,f,w}$ (CI) (ISO 717-2). `verbose=True` annexes the ISO 717 evaluation per band (the value, the shifted reference and the unfavourable deviation). A `requirement` supplied on the `ReportMetadata` adds a verdict ($D_\mathrm{n,f,w}$ passes at or above it, $L_\mathrm{n,f,w}$ at or below it), and `language="es"` renders every fiche in Spanish. reportlab is required, and matplotlib too for the figure the fiche embeds (`pip install "phonometry[report,plot]"`). ```python import numpy as np from phonometry import building, ReportMetadata freqs = [100, 125, 160, 200, 250, 315, 400, 500, 630, 800, 1000, 1250, 1600, 2000, 2500, 3150, 4000, 5000] dv = np.array([4.5, 4.8, 5.2, 5.6, 6.0, 6.5, 7.0, 7.6, 8.1, 8.7, 9.2, 9.8, 10.3, 10.9, 11.4, 11.9, 12.3, 12.7]) m = np.full(18, 1.0); m[:3] = 0.1 # bracket the low bands kij = building.vibration_reduction_index( dv, junction_length=4.0, area_i=12.0, area_j=10.0, frequency=freqs, structural_reverberation_time_i=0.35, structural_reverberation_time_j=0.40, modal_overlap=m, ) kij.report("Kij.pdf", metadata=ReportMetadata(specimen="Rigid T-junction")) l1 = np.full(16, 80.0) dnf = np.array([48, 49, 50, 51, 52, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65], dtype=float) dres = building.normalized_flanking_level_difference( l1, l1 - dnf, absorption_area=np.full(16, 10.0) ) dres.report("Dnf.pdf", metadata=ReportMetadata(requirement=55.0)) # Dn,f,w (C; Ctr) recv = np.array([58, 57, 56, 55, 54, 52, 50, 48, 46, 44, 42, 40, 38, 36, 34, 32], dtype=float) lres = building.normalized_flanking_impact_level(recv, absorption_area=np.full(16, 10.0)) lres.report("Lnf.pdf", metadata=ReportMetadata(requirement=55.0)) # Ln,f,w (CI) ``` The example fiches are regenerated with `make reports` and kept in the repository. Click a preview to open the PDF: [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iso10848_kij_example.pdf) *Vibration reduction index fiche (`VibrationReductionResult.report`), mean $K_{ij}$.* [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iso10848_dnf_example.pdf) *Flanking level difference fiche (`FlankingLevelDifferenceResult.report`), $D_\mathrm{n,f,w}$ (C; Ctr).* [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iso10848_lnf_example.pdf) *Flanking impact level fiche (`FlankingImpactLevelResult.report`), $L_\mathrm{n,f,w}$ (CI).* ## 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 reference monograph for flanking transmission and the vibration reduction index, including the statistical-energy-analysis footing of the validity checks. - International Organization for Standardization. (2006). *Acoustics — Laboratory measurement of the flanking transmission of airborne and impact sound between adjoining rooms — Part 1: Frame document* (ISO 10848-1:2006). [iso.org catalogue](https://www.iso.org/standard/38284.html). The frame document: definitions, the vibration reduction index, the equivalent absorption length and the normalized flanking descriptors. - International Organization for Standardization. (2010). *Acoustics — Laboratory measurement of the flanking transmission of airborne and impact sound between adjoining rooms — Part 4: Application to junctions with at least one heavy element* (ISO 10848-4:2010). [iso.org catalogue](https://www.iso.org/standard/45360.html). The heavy-junction application with the modal-density and modal-overlap validity checks behind the bracketed bands. - International Organization for Standardization. (1985). *Acoustics — Measurement of sound insulation in buildings and of building elements — Part 9: Laboratory measurement of room-to-room airborne sound insulation of a suspended ceiling with a plenum above it* (ISO 140-9:1985). [iso.org catalogue](https://www.iso.org/standard/3944.html). The normalized ceiling attenuation $D_\mathrm{n,c}$ (clause 3.3) and the plenum test facility. - ASTM International. (2022). *Classification for Rating Sound Insulation* (ASTM E413-22). [astm.org catalogue](https://www.astm.org/e0413-22.html). The reference contour and fitting rules that ASTM E1414 invokes for the ceiling attenuation class. - Vigran, T. E. (2008). *Building acoustics*. CRC Press. ISBN 978-0-415-42853-8. [doi:10.1201/9781482266016](https://doi.org/10.1201/9781482266016). Section 9.2.3 presents Mechel's one-dimensional plenum model. ## Standards ISO 10848-1:2006, ISO 10848-2:2006, ISO 10848-3:2006 and ISO 10848-4:2010, which cover the laboratory measurement of flanking transmission: the vibration reduction index $K_{ij}$, the equivalent absorption length, the normalized flanking descriptors $D_\mathrm{n,f}$ / $L_\mathrm{n,f}$ and the modal-overlap validity checks that feed the EN 12354 prediction. Parts 2, 3 and 4 differ in which junction and specimen types they apply to; phonometry implements only the Part 1 formulae generically, plus the Part 4 modal-overlap validity check, not the facility-specific test setups the other parts describe. Because ISO 10848 contains no worked numeric example, conformance is anchored on closed-form identities (simplified $K_{ij}$, $a_j$ at $f_\mathrm{ref}$, $\eta$). The suspended-ceiling branch adds ISO 140-9:1985, which defines the normalized ceiling attenuation $D_\mathrm{n,c}$ and its laboratory, and ASTM E413-22, the rating classification that ASTM E1414 invokes for the ceiling attenuation class. The one-dimensional plenum model itself is not standardized: it comes from Mechel through Vigran Section 9.2.3, and every published output of it is a figure, so it is anchored on its closed forms and on structural properties a wrong reading breaks: monotonicity in the plenum damping, the bound $\tau_\mathrm{cl} \le 1$, and the convergence of Eq. (9.18) to Eq. (9.20). The $D_\mathrm{n,c}$ measurement chain and the class are anchored on accredited ASTM E1414 laboratory reports. The plenum propagation constant $k'$ of a lined duct is an input here, not a prediction. ## See also - [Predicting Sound Insulation (EN 12354)](https://jmrplens.github.io/phonometry/buildings/design/insulation-prediction/): the flanking model that consumes the measured $K_{ij}$, and its empirical Annex E junction values. - [Bending-wave transmission at plate junctions](https://jmrplens.github.io/phonometry/vibration/structural/junction-transmission/): the wave-theory transmission coefficients behind an ideal junction's $K_{ij}$. - [Laboratory Insulation Measurement](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-lab/): the ISO 10140 suite whose direct transmission these flanking paths bypass. - [Insulation Ratings (ISO 717)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-ratings/): the reference-curve engines behind $D_\mathrm{n,f,w}$ and $L_\mathrm{n,f,w}$. - [Room-to-room and open-plan acoustics](https://jmrplens.github.io/phonometry/buildings/rooms/open-plan-acoustics/): the open-plan context the ceiling flanking path usually appears in. - API reference: [`building.measurement.flanking_transmission`](https://jmrplens.github.io/phonometry/reference/api/building/flanking-transmission/) and [`building.prediction.ceiling_plenum`](https://jmrplens.github.io/phonometry/reference/api/building/ceiling-plenum/).