Detailed Per-Band Prediction (ISO 12354)

Standards: ISO 12354Key references: Hopkins 2007 Vigran 2008

The simplified model of Predicting Sound Insulation (EN 12354) returns one number, $R_{w}^{'}$ or $L_{n, w}^{'}$ , and hides everything that happens inside the spectrum. The detailed model (ISO 12354-1:2017 Clause 4.2 airborne, ISO 12354-2:2017 Clause 4.2 impact) carries every quantity through the one-third-octave bands instead: it converts the laboratory element data into their in-situ values, forms each transmission path band by band, sums them energetically and only then rates the spectrum through ISO 717. That is what a consultant runs when the element spectra are known and the question is not “does it pass” but “which path do I have to fix, and in which bands”.

This page walks the standard’s own worked building end to end, and closes with the lightweight (Type B) branch and the checks the standard offers on its own numbers.

The chain, band by band

Before any of it: the standard splits every element in two, and the whole chain below is one of the two branches. A Type A element (clause 3.3.5) is one whose structural reverberation time is primarily determined by the elements it is connected to, up to at least the 1 kHz one-third-octave band, and across which the vibration level falls by less than 6 dB in the direction perpendicular to the junction line. Cast in-situ concrete, solid wood including cross-laminated timber, glass, plastic, metal and blockwork with a finish that mechanically connects it are the standard’s own examples. A Type B element (3.3.6) is anything else, typically plasterboard or timber cladding on a timber or metal frame. The distinction is not academic: it is exactly why the Type A chain assembles the loss factor from the junction perimeter, because for a Type A element the junctions are the damping. For a Type B element the standard takes $T_{s, situ} = T_{s, lab}$ , so the in-situ correction is 0 dB and $R_{situ} = R$ .

The Annex L building, and steps 1 to 5 below, are the Type A branch. Two consequences are worth carrying. The classification is per frequency band — Notes 2 to both definitions say a masonry wall can be Type A low and mid and Type B at the top of the range — so the binary heading of the lightweight section further down is a simplification of a boundary that actually moves with frequency. And at a mixed junction (clause 4.2.2.3, “for example Type B wall on Type A floor”) Formula (10) may still be used as an approximation, with the Type B element’s equivalent absorption length taken as its area over the reference length, $a_{i, situ} = S_{i, situ} / l_{0}$ (Formula 13). Running in_situ_element on a framed partition instead assembles a total loss factor from junctions that do not control its damping, and nothing will warn you.

Both parts share the same machinery, so a building is described once and the airborne and impact chains read the same in-situ element data.

1. Element performance. For a homogeneous element the standard calculates the sound reduction index from the material properties (Annex B):

τ = (\frac{2 ρ _{o} c _{o}}{2 π f m ^{'}})^{2} \cdot \frac{π f _{c} σ ^{2}}{2 f η _{tot}} (f > f_{c})

with the radiation factor for free bending waves $σ$ (Formulae B.4-B.6), the radiation factor for forced waves $σ_{f}$ (Formula B.3) below $f_{c}$ , and a third branch for the band that straddles $f_{c}$ . Above about 1 kHz a thick element stops improving, and Formula (B.10) floors the transmission factor at a plateau set by $ρ c_{L}$ .

2. In-situ conversion. The element radiates and is damped differently in the building than in the test frame. The total loss factor in situ is (Formula C.1)

η_{tot} = η_{int} + \frac{2 ρ _{o} c _{o} σ}{2 π f m ^{'}} + \frac{c _{o}}{π ^{2} S f f _{c}} k \sum l_{k} α_{k}

the three terms being the internal losses of the material, the radiation into the air, and the losses at the perimeter. The perimeter coefficients follow from the junctions themselves, $α_{k} = \sum_{j} f_{c, j} / f_{ref} 1 0^{- K_{ij} /10}$ (Formula C.4). From $η_{tot}$ come the structural reverberation time $T_{s} = 2, 2/ (f η_{tot})$ and the equivalent absorption length $a_{situ} = 2, 2 π^{2} S f_{ref} / f / (c_{o} T_{s, situ})$ (Formula 11).

3. Junctions. The situation-invariant $K_{ij}$ becomes the level drop the junction actually produces (Formula 10):

\overline{D}_{v, ij, situ} = K_{ij} - 10 lo g_{10} (\frac{l _{ij}}{a _{i, situ} a _{j, situ}}) \geq 0 dB

4. Paths. The direct path is $R_{D d} = R_{s, situ} + Δ R_{D, situ} + Δ R_{d, situ}$ (Formula 14) and every flanking path (Formula 15)

R_{ij} = \frac{R _{i, situ}}{2} + Δ R_{i, situ} + \frac{R _{j, situ}}{2} + Δ R_{j, situ} + \overline{D}_{v, ij, situ} + 10 lo g_{10} (\frac{S _{s}}{S _{i} S _{j}})

The impact side runs in parallel: the bare slab’s per-band level is $L_{n} = 155 - 30 lo g_{10} m^{'} + 10 lo g_{10} T_{s} + 10 lo g_{10} σ + 10 lo g_{10} (f / f_{ref})$ (Part 2 Formula B.2), the direct path subtracts the covering and any ceiling (Formula 11), and each flanking path is Formula (12).

5. Assembly. $R^{'} = - 10 lo g_{10} \sum 1 0^{- R /10}$ over the thirteen paths of a four-flanking-element room, and $L_{n}^{'} = 10 lo g_{10} \sum 1 0^{L_{n} /10}$ over the five impact paths, then ISO 717.

Starting from measured element data

Clause 4.1 is explicit about where the numbers should come from: acoustic data on the elements involved should be taken primarily from standardized laboratory measurements, and the sources of data used shall be stated. The Annex B calculation the page opens with is the fallback for when no measurement exists. A real project usually starts from a catalogue sheet or an ISO 10140 test report, and that route has its own three steps.

The transfer to the building is a loss-factor transfer. The laboratory measured the element in a test frame whose damping is not the building’s, so Formula (9) rescales the index by the ratio of the two structural reverberation times, $R_{situ} = R - 10 l g (T_{s, situ} / T_{s, lab})$ , and Part 2 Formula (5) does the same for the impact level with the sign reversed. Read the sign: an element more heavily damped in the building than in the test frame has a shorter $T_{s}$ in situ, which raises its index and lowers its impact level; an element more lightly damped loses index. The standard’s own note adds that $R_{situ} = R$ is a usable first approximation, and for a Type B element it is exact.

$T_{s, lab}$ comes from the test report, or from Annex C. If the laboratory printed it, use it. If not, Formula (C.3) estimates the laboratory total loss factor as $η_{tot,lab} \approx η_{int} + m^{'} / (485 f) \approx 0, 01 + m^{'} / (485 f)$ , valid for elements below $m^{'}$ = 800 kg/m², with $η_{int}$ normally taken as 0,01 (Annex B Table B.1 lists it per material). laboratory_total_loss_factor is that formula and structural_reverberation_time turns it into $T_{s} = 2, 2/ (f η_{tot})$ ; $T_{s, situ}$ comes from the same Formula (C.1) chain the page already runs.

Flanking paths need one more correction than the direct path. Below its critical frequency a laboratory $R$ contains forced transmission, which a flanking path does not carry: only free bending waves cross a junction. Annex B.1 therefore corrects a measured $R$ to resonant transmission only before it enters a flanking path — the 8 dB estimate for a single frame element without a cavity — while the direct path keeps the forced transmission the laboratory measured. That is resonant_sound_reduction_index, and in_situ_element(..., resonant_only=True) does the same on a calculated element.

The four names below (laboratory_total_loss_factor, structural_reverberation_time, in_situ_reduction_index and in_situ_impact_level) are top-level phonometry names; add them to the import block of the previous section to run this.

# A measured laboratory R and Ln for the 220 mm separating floor, transferred to
# the building. `el` is the in-situ element of the section above, whose
# `reverberation_time` is Ts,situ.
eta_lab = laboratory_total_loss_factor(bands, mass_per_area=484.0,
                                       internal_loss_factor=0.005)   # (C.3)
ts_lab = structural_reverberation_time(bands, eta_lab)               # (C.1)
print(np.round(ts_lab[[0, 10]], 3))                    # [0.301 0.089] s
print(np.round(el.reverberation_time[[0, 10]], 3))     # [0.53  0.152] s, in situ

r_situ = in_situ_reduction_index(r_measured, el.reverberation_time, ts_lab)
ln_situ = in_situ_impact_level(ln_measured, el.reverberation_time, ts_lab)
# This floor is *less* damped in the building than in the test frame (Ts,situ is
# the longer of the two), so Formula (9) takes 2.0 to 2.5 dB off its index across
# the range and Part 2 Formula (5) adds the same to its impact level.

# A flanking path takes the resonant-only form of the same measured index;
# the direct path does not.
r_flanking = resonant_sound_reduction_index(r_situ, bands, critical_frequency=76.8)

What you need before you start

Quantity	Where it comes from
$R$ , $L_{n}$ per band	ISO 10140-2 / ISO 10140-3 test report — with the laboratory structural reverberation time from the same report
$Δ R$ of a lining	ISO 10140-1 Annex G, or ISO 12354-1 Annex D
$Δ L$ of a covering	ISO 16251-1 or ISO 10140-3
$K_{ij}$ per junction	ISO 10848-1/-4, or the Annex E catalogue
$m^{'}$ , $f_{c}$ , $η_{int}$ , $c_{L}$	the material data sheet, or Annex B Table B.1
Areas and coupling lengths	the drawings, measured surface to surface

That last row changes an answer: a coupling length measured surface to surface rather than centre to centre differs by a leaf thickness on a lined or double-leaf element, and $l_{ij}$ enters Formula (10) directly. Clause 4.1 also requires the source of every input to be stated, which on a fiche is what the notes field of ReportMetadata is for.

The worked building of Annex L / Annex G

ISO 12354-1:2017 Annex L and ISO 12354-2:2017 Annex G describe the same building: two dwellings one above the other, 55 m³ rooms, a 5,00 m × 4,00 m separating floor of 220 mm concrete carrying a 35 mm floating screed on mineral wool, two 365 mm autoclaved aerated concrete external walls and two 200 mm calcium-silicate internal walls, meeting at rigid T and cross junctions. Together they print about twenty per-band tables, one per intermediate quantity, which makes the example a complete oracle for the model. Eight defects of those printed tables are recorded in Errata, and the fixture below takes the corrected readings.

The ISO 12354-1 Annex L worked building: a section through two stacked dwellings showing the 220 mm separating floor with its floating screed, the two external and two internal walls with their masses and critical frequencies and the Kij of each junction, and a plan of the separating floor with the four coupling lengths dimensioned and the thirteen transmission paths counted

The drawing is what ties the element list to the numbers the snippet multiplies. The separating floor’s perimeter sum is 9 m of external edge plus 9 m of internal edge because the 5,00 m × 4,00 m floor meets an external wall along each 4,00 m edge and an internal wall along each 5,00 m edge, and each of those junctions carries the floor above and below it. An external wall’s own perimeter takes 8,0 m of horizontal junction (its top and bottom edges, 4,00 m each) and 2,75 m of vertical. The floor-to-external-wall junctions are rigid T, the floor-to-internal-wall junctions rigid cross. And the thirteen paths are one direct path plus three per flanking element, $1 + 4 \times 3$ .

import numpy as np
from phonometry import (
    HomogeneousElement, airborne_flanking_path, detailed_airborne_prediction,
    direct_reduction_index, floating_floor_improvement, in_situ_element,
    junction_vibration_reduction, perimeter_absorption_coefficient,
)

bands = np.array([50, 63, 80, 100, 125, 160, 200, 250, 315, 400, 500, 630,
                  800, 1000, 1250, 1600, 2000, 2500, 3150], float)

# Annex E junctions (unrounded): floor-to-external-wall rigid T, external wall
# in-line across it, floor-to-internal-wall rigid cross, internal wall in-line.
k_floor_ext = junction_vibration_reduction("rigid_t", "corner", 484.0 / 219.0)
k_ext_ext = junction_vibration_reduction("rigid_t", "through", 484.0 / 219.0)
k_floor_int = junction_vibration_reduction("rigid_cross", "corner", 360.0 / 484.0)
k_int_int = junction_vibration_reduction("rigid_cross", "through", 484.0 / 360.0)
print(round(k_floor_ext, 1), round(k_ext_ext, 1))     # 6.4 11.2  (Table L.5)
print(round(k_floor_int, 1), round(k_int_int, 1))     # 8.8 11.0  (Table L.6)

# The floor's perimeter: it butts into an external wall above and below at each
# of its two external edges, and crosses the internal walls at the other two.
a_at_ext = perimeter_absorption_coefficient([92.6, 92.6], [k_floor_ext] * 2)
a_at_int = perimeter_absorption_coefficient(
    [76.8, 128.4, 128.4], [junction_vibration_reduction(
        "rigid_cross", "through", 360.0 / 484.0), k_floor_int, k_floor_int])
floor_perimeter = 9.0 * (a_at_ext + a_at_int)         # 2.659 m (Formula C.4)

floor = HomogeneousElement("floor", 20.0, 5.0, 4.0, 484.0, 76.8, 0.005,
                           floor_perimeter, 2200.0, 3800.0)
el = in_situ_element(floor, bands)
print(np.round(el.total_loss_factor[[0, 10]], 4))     # [0.0831 0.029 ]  Table L.3
print(np.round(el.sound_reduction_index[[0, 10]], 1)) # [31.8 54.9]      Table L.3
print(np.round(el.impact_level[[0, 10]], 1))          # [57.3 63.6]      Table G.3
print(np.round(el.absorption_length[[0, 10]], 1))     # [10.8 11.9]      Table L.4

Every printed column of Tables L.2, L.3, L.4, G.3 and G.4 comes back within 0,06 dB, and the same fixture drives both totals.

# The floating floor: 35 mm screed, m' = 73,5 kg/m2 on s' = 8 MN/m3.
f0 = 160.0 * np.sqrt(8.0 / 73.5)                      # 52.8 Hz (Formula C.2)
delta = floating_floor_improvement(bands, resonance_frequency=f0)  # 30 lg(f/f0)

wall = in_situ_element(HomogeneousElement(
    "ext1", 11.0, 4.0, 2.75, 219.0, 92.6, 0.0125, 2.375, 600.0, 1900.0), bands)

# Path D1 (Df: separating floor -> external wall 1), Table L.4.
d1 = airborne_flanking_path(
    label="D1", kind="Df", element_i=el, element_j=wall,
    vibration_reduction_index=k_floor_ext, coupling_length=4.0,
    separating_area=20.0, delta_r_i=delta)
print(np.round(d1.values[[0, 10]], 1))                # [ 41.2  93.6]  Table L.1

Assembling the direct path and all twelve flanking paths gives the apparent index per band, its energy split and the ISO 717-1 rating in one call:

# `paths` holds the twelve flanking paths of the four elements, built the
# way `d1` was above; the code block under the figure builds all of them.
res = detailed_airborne_prediction(
    bands, direct_index=direct_reduction_index(el.sound_reduction_index,
                                               delta_r_source=delta),
    flanking_paths=paths)
print(np.round(res.r_prime[[0, 10]], 1))   # [28.8 55.9]   Table L.1 total
print(res.rating.rating, res.dominant[0])  # 57 'Dd'
res.plot()                                 # per-band path-contribution bars

Stacked per-band shares of the transmitted energy for the thirteen transmission paths of the ISO 12354-1 Annex L building, with the apparent sound reduction index R' overlaid: the direct path Dd carries half the energy at 50 Hz, falls away through the 80 Hz to 160 Hz transition and is negligible from 200 Hz upwards, after which flanking paths across the external and internal walls take over

This is the plot the whole detailed model exists for. Below 80 Hz the separating floor itself is the problem, so a heavier slab or a better floating floor would help; it fades through the 80 Hz to 160 Hz transition and from 200 Hz upwards it has left the budget entirely, the flanking paths across the walls setting $R^{'}$ on their own, so no amount of work on the floor would move the result there. The single number $R_{w}^{'} = 57$ dB says none of that.

Show the code for this figure

import matplotlib.pyplot as plt
import numpy as np
from phonometry import (
    HomogeneousElement, airborne_flanking_path, detailed_airborne_prediction,
    direct_reduction_index, floating_floor_improvement, in_situ_element,
    junction_vibration_reduction, perimeter_absorption_coefficient,
)

bands = np.array([50, 63, 80, 100, 125, 160, 200, 250, 315, 400, 500, 630,
                  800, 1000, 1250, 1600, 2000, 2500, 3150], float)
k = {
    "floor-ext": junction_vibration_reduction("rigid_t", "corner", 484.0 / 219.0),
    "ext-ext": junction_vibration_reduction("rigid_t", "through", 484.0 / 219.0),
    "floor-floor": junction_vibration_reduction("rigid_cross", "through", 360.0 / 484.0),
    "floor-int": junction_vibration_reduction("rigid_cross", "corner", 360.0 / 484.0),
    "int-int": junction_vibration_reduction("rigid_cross", "through", 484.0 / 360.0),
    "int-ext": junction_vibration_reduction("rigid_t", "corner", 360.0 / 219.0),
    "extT-ext": junction_vibration_reduction("rigid_t", "through", 360.0 / 219.0),
    "corner": junction_vibration_reduction("corner", "corner", 1.0),
    "int-int-x": junction_vibration_reduction("rigid_cross", "through", 1.0),
}
a = perimeter_absorption_coefficient
floor_sum = 9.0 * (a([92.6, 92.6], [k["floor-ext"]] * 2)
                   + a([76.8, 128.4, 128.4],
                       [k["floor-floor"], k["floor-int"], k["floor-int"]]))
ext_top = a([76.8, 92.6], [k["floor-ext"], k["ext-ext"]])
ext_side = a([92.6], [k["corner"]]) + a([128.4, 92.6], [k["int-ext"], k["extT-ext"]])
int_top = a([76.8, 76.8, 128.4], [k["floor-int"], k["floor-int"], k["int-int"]])
int_side = a([92.6, 92.6], [k["int-ext"]] * 2) + a([128.4] * 3, [k["int-int-x"]] * 3)

specs = {
    "floor": (20.0, 5.0, 4.0, 484.0, 76.8, 0.005, floor_sum, 2200.0, 3800.0),
    "ext1": (11.0, 4.0, 2.75, 219.0, 92.6, 0.0125,
             8.0 * ext_top + 2.75 * ext_side, 600.0, 1900.0),
    "ext2": (13.75, 5.0, 2.75, 219.0, 92.6, 0.0125,
             10.0 * ext_top + 2.75 * ext_side, 600.0, 1900.0),
    "int1": (11.0, 4.0, 2.75, 360.0, 128.4, 0.01,
             8.0 * int_top + 2.75 * int_side, 1800.0, 2500.0),
    "int2": (13.75, 5.0, 2.75, 360.0, 128.4, 0.01,
             10.0 * int_top + 2.75 * int_side, 1800.0, 2500.0),
}
situ = {name: in_situ_element(HomogeneousElement(name, *spec), bands)
        for name, spec in specs.items()}
delta = floating_floor_improvement(bands,
                                   resonance_frequency=160.0 * np.sqrt(8.0 / 73.5))

paths = []
for tag, name, lij in (("1", "ext1", 4.0), ("2", "ext2", 5.0),
                       ("3", "int1", 4.0), ("4", "int2", 5.0)):
    wall = situ[name]
    cross = k["floor-ext"] if name.startswith("ext") else k["floor-int"]
    through = k["ext-ext"] if name.startswith("ext") else k["int-int"]
    paths += [
        airborne_flanking_path(label=f"D{tag}", kind="Df", element_i=situ["floor"],
                               element_j=wall, vibration_reduction_index=cross,
                               coupling_length=lij, separating_area=20.0,
                               delta_r_i=delta),
        airborne_flanking_path(label=f"{tag}d", kind="Fd", element_i=wall,
                               element_j=situ["floor"], vibration_reduction_index=cross,
                               coupling_length=lij, separating_area=20.0),
        airborne_flanking_path(label=f"{tag}{tag}", kind="Ff", element_i=wall,
                               element_j=wall, vibration_reduction_index=through,
                               coupling_length=lij, separating_area=20.0),
    ]
res = detailed_airborne_prediction(
    bands,
    direct_index=direct_reduction_index(situ["floor"].sound_reduction_index,
                                        delta_r_source=delta),
    flanking_paths=paths)

# One line — the per-band path contributions with R' overlaid:
res.plot()
plt.show()

The impact side of the same building runs on the same situ dictionary:

from phonometry import (detailed_impact_prediction, direct_impact_level,
                        impact_flanking_path)

direct = direct_impact_level(situ["floor"].impact_level, delta_l=delta)
flanking = [
    impact_flanking_path(label=f"Df{tag}", floor=situ["floor"], element_j=situ[name],
                         vibration_reduction_index=(
                             k["floor-ext"] if name.startswith("ext") else k["floor-int"]),
                         coupling_length=lij, delta_l=delta)
    for tag, name, lij in (("1", "ext1", 4.0), ("2", "ext2", 5.0),
                           ("3", "int1", 4.0), ("4", "int2", 5.0))
]
imp = detailed_impact_prediction(bands, direct_level=direct, flanking_paths=flanking)
print(np.round(imp.l_prime_n[[3, 10]], 1))     # [54.  35.9]   Table G.1 total
print(imp.rating.rating, imp.rating.ci)        # 41 2           printed 41,0 (2)

Stacked per-band shares of the transmitted energy for the five impact paths of the ISO 12354-2 Annex G building with the apparent normalized impact sound pressure level overlaid, the direct path through the excited floor dominating in every band and the floating floor resonance marked on the frequency axis

The impact half of the same building, and it is a different picture from the airborne one. There are five paths, not thirteen, because only the floor is excited: the tapping machine stands on it, so there is one direct path and one Df path into each of the four walls, and no Ff or Fd. The direct path through the excited floor governs in every band. That is the practical lesson — an impact problem is fixed at the source floor, not at the junctions.

Show the code for this figure

# One line — the per-band path contributions with L'n overlaid:
imp.plot()
plt.show()

Read the rating the same way. $L_{n, w}^{'} = 41$ dB with $C_{I} = + 2$ dB means the unweighted, walking-relevant level sits above the weighted rating, which is the signature of a floor whose improvement is concentrated high up — exactly what a floating floor with $f_{0} = 52, 8$ Hz and a 30 lg law does. Three levers move it, in the order the model responds to them: a softer resilient layer lowers $f_{0}$ and lifts the whole improvement curve; a heavier base slab lowers the bare level directly through Part 2’s Formula (B.2); and a better junction does almost nothing until the direct path has been dealt with. Note too that the floating floor’s $Δ L$ is subtracted from the direct path and from every flanking path alike, because all five start at the same excited floor.

Simplified against detailed

The standard applies its simplified model to the same building (Tables L.10 / G.10): $R_{w}^{'} = 57, 0$ dB and $L_{n, w}^{'} = 39, 7$ dB against the detailed model’s $R_{w}^{'} = 57$ dB and $L_{n, w}^{'} = 41$ dB. The two agree well inside the models’ own stated spread, and the library’s test suite pins that agreement. The detailed model’s advantage is not accuracy on the single number but the spectrum behind it: the airborne prediction of the detailed model carries no bias error and a standard deviation of 1,5 dB to 2,5 dB (Clause 5) against about 2 dB for the simplified one.

Lightweight constructions (Type B)

For elements whose structural reverberation time is not set by the connected elements the standard takes $T_{s, situ} = T_{s, lab}$ and describes the junction with the normalized velocity level difference $\overline{D}_{v, ij, n}$ instead of $K_{ij}$ (Formula 17), or with a laboratory measurement of the flanking level difference $D_{n, f}$ (Formula 16). Below $f_{c}$ the element indices must first be corrected to resonant transmission only (Annex B.1/B.2, an 8 dB estimate for single frame elements without a cavity). The impact side offers the same two routes: Part 2 Formula (14) from $\overline{D}_{v, ij, n}$ and Part 2 Formula (13) from a measured normalized flanking impact level $L_{n, f}$ .

Unlike the Type A chain, this branch consumes measured junction data, so its four inputs are per-band arrays over bands that come from somewhere specific. r_wall_leaf is the leaf’s laboratory sound reduction index per band (ISO 10140-2), corrected below its critical frequency to resonant transmission only because a flanking path carries free bending waves alone. dv_n is the normalized direction-averaged velocity level difference of the junction in dB, measured per ISO 10848-2 and referred to a reference length of 1 m. dnf_13 is the normalized flanking level difference $D_{n, f}$ of a junction measured in a laboratory, in dB, which the call re-scales by the ratio of the site and laboratory coupling lengths. And lnf_13 is its impact counterpart, the normalized flanking impact level $L_{n, f}$ in dB, which re-scales by both area and coupling length. The block below is an excerpt: it starts from those four arrays.

from phonometry import (flanking_impact_level_from_flanking_level,
                        flanking_reduction_index_from_flanking_level,
                        flanking_reduction_index_from_normalized_difference,
                        resonant_sound_reduction_index)

# ISO 12354-1 L.2.1: a wood frame building, floor 20 m2, junction 4 m.
r_wall_leaf = ...   # measured R of the inner leaf per band, dB (ISO 10140-2)
dv_n = ...          # normalized junction velocity level difference, dB (ISO 10848-2)
dnf_13 = ...        # laboratory normalized flanking level difference Dn,f, dB
lnf_13 = ...        # laboratory normalized flanking impact level Ln,f, dB

r_star = resonant_sound_reduction_index(r_wall_leaf, bands,
                                        critical_frequency=2200.0)   # +8 dB below fc
r_ff = flanking_reduction_index_from_normalized_difference(
    index_i=r_star, index_j=r_star, normalized_velocity_level_difference=dv_n,
    separating_area=20.0, coupling_length=4.0)                        # Table L.11

# ISO 12354-1 L.2.2: a measured junction between two timber frame walls.
r13 = flanking_reduction_index_from_flanking_level(
    dnf_13, separating_area=10.44, coupling_length=2.41,
    laboratory_coupling_length=2.5)                                   # Table L.15

# ISO 12354-2 Formula (13): the impact twin, from a measured Ln,f.
ln_13 = flanking_impact_level_from_flanking_level(
    lnf_13, area=20.0, laboratory_area=10.0,
    coupling_length=4.0, laboratory_coupling_length=4.5)

Checks the standard gives you

Two identities let a spectrum check itself. For a homogeneous floor the airborne index and the impact level add up to a function of frequency alone (Part 2 Formulae B.3/B.4), $R + L_{n} = 38 + 30 lo g_{10} f$ in one-third-octave bands and $43 + 30 lo g_{10} f$ in octave bands, valid where forced transmission is negligible; reciprocity_impact_level implements it. And Table B.2 of Part 2 tabulates the octave-band $L_{n}$ of four monolithic floors calculated the way this module does, a useful sanity target for a new floor build-up.

`in_situ_element()` parameters

Parameter	Type	Units	Range / default	Notes
`element`	`HomogeneousElement`	—	—	Area, side lengths, $m^{'}$ , $f_{c}$ , $η_{int}$ , $\sum l_{k} α_{k}$ , and optionally $ρ$ / $c_{L}$
`frequencies`	array	Hz	> 0	Band centres
`bands`	str	—	`'third'` (default) / `'octave'`	Sets the band that carries the $f \approx f_{c}$ branch
`resonant_only`	bool	—	default `False`	Drops the forced-transmission term below $f_{c}$ (Annex B.1, flanking paths)
`speed_of_sound`	float	m/s	default `340`	The value ISO 12354-1 Annex A fixes
`air_density`	float	kg/m³	default `1.29`	$ρ_{o}$ of the Annex B model

`airborne_flanking_path()` / `impact_flanking_path()` parameters

Parameter	Type	Units	Range / default	Notes
`label`	str	—	—	Display name of the path
`kind`	str	—	`'Ff'` / `'Df'` / `'Fd'`	Airborne only; the impact builder is always `Df`
`element_i` / `element_j`	`InSituElementResult`	—	—	Source-room and receiving-room elements (`floor` / `element_j` for impact)
`vibration_reduction_index`	float or array	dB	—	$K_{ij}$ of this path
`coupling_length`	float	m	> 0	Junction coupling length $l_{ij}$
`separating_area`	float	m²	> 0	$S_{s}$ (airborne only)
`delta_r_i` / `delta_r_j`	float or array	dB	default `0`	Lining improvements
`delta_l`	float or array	dB	default `0`	Floor-covering improvement (impact only)

Detailed prediction report (`.report()`)

DetailedAirborneResult.report() and DetailedImpactResult.report() write the per-band counterpart of the simplified prediction fiches: the same one-page layout, a basis line naming ISO 12354-1/-2:2017 Clause 4.2, the per-path share-of-energy table beside the per-band path-contribution figure, the boxed $R_{w}^{'}$ / $L_{n, w}^{'}$ , the detailed model’s 1,5 dB to 2,5 dB standard deviation and a PASS/FAIL verdict against a requirement. verbose=True annexes the band in which each path peaks. Both need the ISO 717 rating, so the spectrum must cover 100 Hz to 3150 Hz (or 125 Hz to 2000 Hz in octaves).

airborne.report("airborne-prediction.pdf")   # R'w, thirteen paths
impact.report("impact-prediction.pdf")       # L'n,w, five paths

The example fiches are regenerated with make reports and kept rendered in the repository; click a preview to open the PDF. Both show the Annex L building of this page: the same elements, junctions and floating floor the tables above are built from.

ISO 12354-1 detailed airborne prediction example report (PDF) — Detailed airborne prediction fiche (DetailedAirborneResult.report), the thirteen paths of the Annex L building and their energy shares.

ISO 12354-2 detailed impact prediction example report (PDF) — Detailed impact prediction fiche (DetailedImpactResult.report), the same building excited by the tapping machine.

What this guide covers

Covered
The Clause 4.2 per-band chain for Type A elements: the Annex B homogeneous-element sound reduction index and impact level and the Annex C in-situ conversion through HomogeneousElement, in_situ_element and perimeter_absorption_coefficient; the transfer of measured laboratory data through laboratory_total_loss_factor, structural_reverberation_time, in_situ_reduction_index and in_situ_impact_level (Formula 9 and Part 2 Formula 5); the Formula (10) in-situ junction drop; the Formula (14)/(15) direct and flanking airborne paths through direct_reduction_index and airborne_flanking_path and their impact twins direct_impact_level and impact_flanking_path; the Formula (16)/(17) Type B routes and the Annex B.1/B.2 resonant correction through resonant_sound_reduction_index; the assembly and ISO 717 rating through detailed_airborne_prediction and detailed_impact_prediction; the Part 2 B.3/B.4 reciprocity identity through reciprocity_impact_level; and the two fiches through .report(). The airborne model is stated by Clause 5 to carry no bias error and a standard deviation of 1,5 dB to 2,5 dB for buildings of homogeneous elements, assuming good workmanship — the lower figure when every aspect is taken into account, the higher for complex situations or when the structural reverberation time is neglected.
Not covered
Only homogeneous Annex B elements are calculated here; the spectrum of a lightweight, double or composite element is an input, from Predicting Panel Sound Insulation or from a test report. The Annex E junction catalogue itself lives on Predicting Sound Insulation, and the Part 1 Annex D lining improvement on Predicting Resilient-Layer Performance; the Annex D and F default tables of EN 12354-5 are implemented nowhere. The Type B branch is shown from its standard inputs rather than worked end to end. Airborne transmission through cavities and suspended ceilings is not carried at all, and clause 3.3.4 Note 1 warns it “can contribute to or even dominate” there. And the ISO 717 rating needs the whole spectrum: 100 Hz to 3150 Hz in one-third octaves, or 125 Hz to 2000 Hz in octaves.

References

Hopkins, C. (2007). Sound insulation. Butterworth-Heinemann. https://doi.org/10.4324/9780080550473The physical background of every term of the detailed model: radiation efficiency, structural reverberation time, the equivalent absorption length and the statistical-energy-analysis footing of the path summation. ISBN 978-0-7506-6526-1.
International Organization for Standardization. (2017). Building acoustics — Estimation of acoustic performance of buildings from the performance of elements — Part 1: Airborne sound insulation between rooms (ISO 12354-1:2017). Clause 4.2 defines the detailed per-band airborne model; Annex B the calculated element performance and radiation factors, Annex C the structural reverberation time, Annex E the junction indices and Annex L the worked examples.
International Organization for Standardization. (2017). Building acoustics — Estimation of acoustic performance of buildings from the performance of elements — Part 2: Impact sound insulation between rooms (ISO 12354-2:2017). Clause 4.2 defines the detailed per-band impact model; Annex B the calculated impact level of a bare floor, Annex C the floating-floor improvement and Annex G the worked examples sharing ISO 12354-1 Annex L's building.
Vigran, T. E. (2008). Building acoustics. Taylor & Francis. The homogeneous-element transmission model and the impact-level closed form behind Annex B of both parts. ISBN 978-0-415-42853-8.

Created and maintained by José Manuel Requena Plens ORCID All projects