Laboratory Insulation Measurement

By José M. Requena Plens · Published Jul 15, 2026, updated Jul 26, 2026

Standards: ISO 10140 ISO 15186 ISO 16251 ISO 717 ISO 10848Key references: Hopkins 2007 Vigran 2008 Foret et al. 2011

To rate a building element on its own (a wall type, a floating floor, a window) you take it to a qualified laboratory, where suppressed flanking makes the direct transmission the whole story. This page covers the laboratory chain: the ISO 10140 sound reduction index and normalized impact level, the sound-intensity alternative of ISO 15186, the small-mock-up floor-covering improvement of ISO 16251-1 and the flanking-transmission measurement of ISO 10848. Field measurement and ratings live in Field Insulation Measurement and Ratings, and the prediction that consumes these laboratory ratings in Predicting Sound Insulation (EN 12354).

Laboratory measurement (ISO 10140)

An ISO 16283 field measurement yields the primed quantities ( $R^{'}$ , $L_{n}^{'}$ ): the number a real building achieves, flanking transmission and all. To rate an element on its own (a wall type, a floating floor, a window), you take it to a qualified laboratory (ISO 10140), where suppressed flanking makes the direct transmission the whole story. The formulas lose their primes: the sound reduction index $R$ (not $R^{'}$ ) and the normalized impact level $L_{n}$ (not $L_{n}^{'}$ ), with the receiving room’s absorption area $A = 0.16 V / T$ now a known property of the facility:

R = L_{1} - L_{2} + 10 lo g_{10} \frac{S}{A}, L_{n} = L_{i} + 10 lo g_{10} \frac{A}{A _{0}}, A_{0} = 10 m^{2} .

	Field (ISO 16283)	Laboratory (ISO 10140)
Airborne element index	$R^{'}$ apparent (with flanking)	$R$ direct (flanking suppressed)
Airborne room pair	$D_{n T}$ , $D_{n}$ (no prime: room quantities)	—
Impact	$L_{n}^{'}$ , $L_{n T}^{'}$ apparent	$L_{n}$ direct
Single number	$R_{w}^{'}$ , $D_{n T, w}$ , $L_{n, w}^{'}$ , $L_{n T, w}^{'}$	$R_{w}$ , $L_{n, w}$
Absorption area	measured in the room	property of the facility

The apostrophe is the flanking marker of building acoustics, and it travels with the quantity into its single number: $R_{w}$ rates a laboratory spectrum, $R_{w}^{'}$ a field one. The standardized and normalized level differences $D_{n T}$ and $D_{n}$ carry no prime because they describe the room pair rather than an element, so there is no flanking-free counterpart to mark. In a well-built construction $R_{w}^{'}$ lands a few dB below the laboratory $R_{w}$ of the same partition; a much larger gap says flanking dominates, and the EN 12354 model tells you which path carries it.

The single-number ratings reuse the very same ISO 717-1/2 engines (weighted_rating, weighted_impact_rating): an $R$ spectrum rates to $R_{w}$ exactly as an $R^{'}$ spectrum rated to $R_{w}^{'}$ . Before forming the index the receiving-room levels must be corrected for background noise (Clause 4.3): the energy subtraction $10 lo g_{10} (1 0^{L_{s b} /10} - 1 0^{L_{b} /10})$ applies for a 6–15 dB signal-to-background margin, a fixed 1.3 dB correction (the limit of measurement) at or below 6 dB, and no correction at or above 15 dB.

import numpy as np
from phonometry import building

# Source/receiving levels and receiving-room T over the 16 one-third-octave
# bands; S is the free test-opening area, V the receiving-room volume.
l1 = np.full(16, 80.0)
l2 = np.full(16, 40.0)
t2 = np.full(16, 0.5)
lab = building.lab_airborne_insulation(l1, l2, t2, area=10.0, volume=50.0)
print(round(float(lab.r[0]), 1))              # 38.0  R = L1 - L2 + 10 lg(S/A)
print(round(float(lab.absorption[0]), 1))     # 16.0  A = 0.16 V / T (m^2)
print(lab.rating.rating, lab.rating.c, lab.rating.ctr)   # 38 0 0  ->  Rw(C;Ctr)

# Impact: the tapping-machine level Li normalized to A0 = 10 m^2 gives Ln
li = np.array([62.1, 63.2, 63.5, 66.2, 68.5, 70.0, 71.7, 73.1,
               73.8, 73.5, 73.8, 73.3, 73.1, 73.0, 72.4, 71.2])
imp = building.lab_impact_insulation(li, t2, volume=50.0)
print(round(float(imp.l_n[0]), 1))            # 64.1  Ln = Li + 10 lg(A/A0)
print(imp.rating.rating, imp.rating.ci)       # 81 -11  ->  Ln,w(CI)

# Background correction: margins 6 / 1 / 20 dB -> capped / capped / unchanged
corrected = building.background_correction([30.0, 33.0, 50.0], [24.0, 32.0, 30.0])
print(np.round(corrected, 1))                 # [28.7 31.7 50.0]  (1.3 dB cap twice)

lab.rating.plot()   # measured R vs shifted ISO 717-1 reference (needs matplotlib)

A margin at or below 6 dB emits a LabInsulationWarning and flags the band as the limit of measurement; catch it with warnings.simplefilter("error", LabInsulationWarning). The automatic rating is formed only when exactly 16 one-third-octave or 5 octave values are supplied (rating is None otherwise).

The two laboratory quantities of ISO 10140 with their ISO 717 ratings: the airborne $R$ is rated where the reference sits above the measurement, the impact $L_{n}$ where the measurement sits above the reference (a higher impact level is worse). lab.plot() and imp.plot() draw either panel on its own.

Show the code for this figure

import matplotlib.pyplot as plt
import numpy as np
from phonometry import building

# The ISO 717-1 Annex C wall in an ISO 10140 suite (S = 10 m2, V = 50 m3,
# T = 0.8 s) and the ISO 717-2 Annex C floor under the tapping machine.
r = np.array([20.4, 16.3, 17.7, 22.6, 22.4, 22.7, 24.8, 26.6,
              28.0, 30.5, 31.8, 32.5, 33.4, 33.0, 31.0, 25.5])
l1 = np.full(16, 90.0)
t2 = np.full(16, 0.8)
lab = building.lab_airborne_insulation(l1, l1 - r, t2, area=10.0, volume=50.0)
li = np.array([62.1, 63.2, 63.5, 66.2, 68.5, 70.0, 71.7, 73.1,
               73.8, 73.5, 73.8, 73.3, 73.1, 73.0, 72.4, 71.2])
imp = building.lab_impact_insulation(li, t2, volume=50.0)

# One line each — R (or Ln) vs its shifted ISO 717 reference:
lab.plot()
imp.plot()
plt.show()

# By hand, both panels from the results' fields:
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(11, 4.5))
ax1.semilogx(lab.rating.band_centers, lab.r, "o-", label="measured R")
ax1.semilogx(lab.rating.band_centers, lab.rating.shifted_reference, "s--",
             label="shifted reference")
ax1.set_title(f"Rw = {lab.rating.rating} dB")
ax2.semilogx(imp.rating.band_centers, imp.l_n, "o-", label="normalized Ln")
ax2.semilogx(imp.rating.band_centers, imp.rating.shifted_reference, "s--",
             label="shifted reference")
ax2.set_title(f"Ln,w = {imp.rating.rating} dB")
for ax in (ax1, ax2):
    ax.set_xlabel("Frequency [Hz]")
    ax.legend()
ax1.set_ylabel("Sound reduction index R [dB]")
ax2.set_ylabel("Impact sound pressure level Ln [dB]")
plt.show()

`lab_airborne_insulation()` / `lab_impact_insulation()` parameters

Parameter	Type	Units	Range / default	Notes
`l1` / `l2`	1D or 2D array	dB	one/band, or `(positions, bands)`	Source / receiving levels (airborne)
`li`	1D or 2D array	dB	one/band, or `(positions, bands)`	Impact SPL from the tapping machine (impact)
`t2`	1D array	s	> 0, one per band	Receiving-room reverberation time
`area`	float	m²	> 0	Free test-opening area `S` (airborne only)
`volume`	float	m³	> 0	Receiving-room volume `V`

lab_airborne_insulation() returns a LabAirborneInsulationResult (r, absorption, rating); lab_impact_insulation() a LabImpactInsulationResult (l_n, absorption, rating); background_correction(signal_and_background, background) returns the corrected levels directly.

ISO 10140 laboratory test report (`.report()`)

Both laboratory results write the one-page ISO 10140 test report directly, laid out like the accredited laboratory reports rated per ISO 717. LabAirborneInsulationResult.report() renders the sound reduction index $R$ fiche (ISO 10140-2:2010) and LabImpactInsulationResult.report() the normalized impact sound pressure level $L_{n}$ fiche (ISO 10140-3:2010). Each fiche names the laboratory standard in its basis line, evaluates the ISO 717-1 / ISO 717-2 single-number rating (16 one-third-octave bands from 100 Hz to 3150 Hz, or the 5 octave bands), states the quantity to one decimal place both in tabular form and as a curve against the shifted reference curve, boxes the laboratory rating (Rw (C; Ctr) or Ln,w (CI)) and prints the statement that the evaluation is based on laboratory measurement results obtained by a precision method. Because a qualified suite suppresses flanking transmission, the reported quantity is the direct $R$ / $L_{n}$ , not the field $R^{'}$ / $L_{n}^{'}$ .

verbose=True annexes the per-band equivalent sound absorption area $A = 0, 16 V / T$ (ISO 10140-4:2010) beside the reported quantity, the normalization datum the laboratory report carries. Metadata (client, specimen, mounting, room volumes, climatic conditions), the requirement verdict (airborne passes at or above it, impact at or below it), language="es" and the phonometry[report] extra behave exactly as in the ISO 717 and ISO 16283 fiches.

import numpy as np
from phonometry import building, ReportMetadata

# Laboratory airborne: source/receiving levels and T per one-third-octave band
l1 = np.full(16, 90.0)
r = np.array([20.4, 16.3, 17.7, 22.6, 22.4, 22.7, 24.8, 26.6,
              28.0, 30.5, 31.8, 32.5, 33.4, 33.0, 31.0, 25.5])
lab = building.lab_airborne_insulation(
    l1, l1 - r, np.full(16, 0.8), area=10.0, volume=50.0
)
lab.plot()   # measured R vs shifted ISO 717-1 reference (needs matplotlib)
metadata = ReportMetadata(
    specimen="100 mm autoclaved aerated concrete block wall",
    client="Example client",
    area=10.0, mass_per_area=75.0,
    source_volume=53.0, receiving_volume=50.0,
    test_room="Transmission suite (example)",
    mounting="Type A mounting, mortar-bedded perimeter (ISO 10140-1)",
    measurement_standard="ISO 10140-2",
    laboratory="Phonometry Reference Laboratory",
    report_id="PHN-2026-0143",
    requirement=30.0,               # Rw >= 30 dB -> PASS/FAIL row
)
lab.report("Rw_lab.pdf", metadata=metadata)            # Rw (C; Ctr)
lab.report("Rw_lab_chain.pdf", metadata=metadata,
           verbose=True)                               # f | A | R

# Laboratory impact: tapping-machine levels in the receiving room
li = np.array([62.1, 63.2, 63.5, 66.2, 68.5, 70.0, 71.7, 73.1,
               73.8, 73.5, 73.8, 73.3, 73.1, 73.0, 72.4, 71.2])
imp = building.lab_impact_insulation(li, np.full(16, 0.8), volume=50.0)
imp.report("Lnw_lab.pdf",
           metadata=ReportMetadata(requirement=80.0))  # Ln,w (CI)

Both example fiches are regenerated with make reports and kept in the repository. Click either preview to open the PDF:

Laboratory airborne ISO 10140-2 example report (PDF) — Laboratory airborne fiche (LabAirborneInsulationResult.report), Rw (C; Ctr).

Laboratory impact ISO 10140-3 example report (PDF) — Laboratory impact fiche (LabImpactInsulationResult.report), Ln,w (CI).

Sound insulation by intensity (ISO 15186)

The ISO 10140 laboratory method above reads the transmitted power indirectly, from the receiving-room level and its absorption area; this breaks down when flanking paths leak power the room integrates in anyway. The sound-intensity method (ISO 15186) sidesteps that: an intensity probe scans a measurement surface that encloses the specimen and measures the radiated power directly, so only the element under test contributes. It is the tool of choice when flanking is high (ISO 15186-1:2000, Clause 1). From the source-room level $L_{p 1}$ and the average normal intensity level $L_{I n}$ over the surface (area $S_{m}$ ), for a specimen of area $S$ ,

R_{I} = L_{p 1} - 6 - [L_{I n} + 10 lo g_{10} \frac{S _{m}}{S}],

where the $6$ dB is the diffuse-field offset between the sound pressure level and the incident intensity level. The same formula gives the apparent index $R_{I}^{'}$ in the field (ISO 15186-2). Because the intensity method slightly underestimates the power radiated into a real receiving room, a modified index $R_{I, M} = R_{I} + K_{c}$ reproduces the ISO 10140-2 pressure result; the adaptation term $K_{c}$ (Annex B) is $10 lo g_{10} (1 + S_{b 2} λ /8 V_{2})$ for a well-defined room, or the room-independent $10 lo g_{10} (1 + 61.4/ f)$ . For small elements the element normalized level difference replaces $10 l g (S_{m} / S)$ with $10 l g (S_{m} / A_{0}) + 10 l g N$ ( $A_{0} = 10 m^{2}$ , $N$ element units).

import numpy as np
from phonometry import building

# Source-room level Lp1 and the average normal intensity level LIn over the
# measurement surface (Sm), for a specimen of area S; 16 one-third-octave bands.
lp1 = np.full(16, 85.0)
l_in = np.full(16, 40.0)
freqs = [100, 125, 160, 200, 250, 315, 400, 500, 630, 800,
         1000, 1250, 1600, 2000, 2500, 3150]   # nominal 1/3-octave centres
kc = building.adaptation_term_kc(freqs)                  # Annex B (B.2)
res = building.intensity_sound_reduction(lp1, l_in, measurement_area=12.0, area=10.0, kc=kc)
print(round(float(res.r_i[0]), 2))          # 38.21  RI = Lp1 - 6 - [LIn + 10 lg(Sm/S)]
print(round(float(res.r_i_modified[0]), 2)) # 40.29  RI,M = RI + Kc
print(res.rating.rating)                     # 38  ->  RI,w (ISO 717-1 engine)

# Qualify the measurement surface: FpI = Lp - LIn must stay < 10 dB (< 6 dB when
# the receiving side is absorbing); the probe's residual index must exceed FpI+10.
fpi = building.surface_pressure_intensity_indicator(np.full(16, 46.0), l_in)
print(round(float(fpi[0]), 1))               # 6.0

res.plot()   # measured RI vs shifted ISO 717-1 reference (needs matplotlib)

Intensity sound reduction index RI and the Kc-modified index RI,M across the one-third-octave bands, with the Annex B adaptation lift shaded between the two curves

The modified index $R_{I, M} = R_{I} + K_{c}$ lifts $R_{I}$ (most at the low bands, where $K_{c}$ is largest), so an intensity measurement reproduces the ISO 10140-2 pressure result. The automatic rating is formed only for exactly 16 one-third-octave or 5 octave values (rating/rating_modified are None otherwise). Subareas scanned separately are combined first with combine_subareas (Formulas (11)-(12)); a subarea whose net energy flows back towards the specimen enters with a negative area, applying the minus-sign rule of Clause 6.4.6 while $S_{m}$ keeps the unsigned area sum.

Show the code for this figure

import matplotlib.pyplot as plt
import numpy as np
from phonometry import building

# A light wall: source-room SPL Lp1 = 85 dB and the measured normal intensity
# level LIn over the Sm = 12 m2 surface, 16 one-third-octave bands.
freqs = [100, 125, 160, 200, 250, 315, 400, 500, 630, 800,
         1000, 1250, 1600, 2000, 2500, 3150]
l_in = np.array([57.8, 61.9, 60.5, 55.6, 55.8, 55.5, 53.4, 51.6,
                 50.2, 47.7, 46.4, 45.7, 44.8, 45.2, 47.2, 52.7])
kc = building.adaptation_term_kc(freqs)           # Annex B adaptation term
res = building.intensity_sound_reduction(np.full(16, 85.0), l_in,
                                         measurement_area=12.0, area=10.0,
                                         kc=kc)

x = np.arange(len(freqs))
fig, ax = plt.subplots()
ax.fill_between(x, res.r_i, res.r_i_modified, alpha=0.2, label="Kc adaptation")
ax.plot(x, res.r_i, "-o", label="RI (intensity)")
ax.plot(x, res.r_i_modified, "--s", label="RI,M = RI + Kc")
ax.set_xticks(x, [str(f) for f in freqs], rotation=45)
ax.set(xlabel="Frequency [Hz]", ylabel="Sound reduction index [dB]",
       title=f"RI,w = {res.rating.rating} dB, RI,M,w = {res.rating_modified.rating} dB")
ax.legend()
plt.show()

`intensity_sound_reduction()` / `adaptation_term_kc()` parameters

Parameter	Type	Units	Range / default	Notes
`lp1`	1D or 2D array	dB	one/band, or `(positions, bands)`	Source-room sound pressure level
`l_in`	1D or 2D array	dB	one/band, or `(positions, bands)`	Normal intensity level over the surface
`measurement_area`	float	m²	> 0	Measurement-surface area `Sm`
`area`	float	m²	> 0	Specimen area `S`
`kc`	1D array	dB	one per band / `None`	Adaptation term for the modified index
`freq`	1D array	Hz	> 0	Midband frequencies (`adaptation_term_kc`)
`boundary_area` / `volume`	float	m² / m³	> 0, both or neither	Room `Sb2` / `V2` for Formula (B.1)

intensity_sound_reduction() returns an IntensityReductionResult (r_i, r_i_modified, rating, rating_modified); intensity_element_normalized_difference() an IntensityElementNormalizedResult (d_i_n_e, rating); surface_pressure_intensity_indicator() and combine_subareas() return arrays.

ISO 15186-1 intensity test report (`.report()`)

IntensityReductionResult.report() writes the one-page ISO 15186-1:2000 test report of the intensity sound reduction index $R_{I}$ , reusing the same accredited two-panel layout as the ISO 10140 and ISO 16283 fiches. Because $R_{I}$ is an ordinary sound reduction index, its single-number rating $R_{I, w}$ is the ISO 717-1 airborne rating evaluated on the intensity spectrum: the fiche names ISO 15186-1 in its basis line, tabulates $R_{I}$ to one decimal place beside the measured-versus-shifted-reference curve, boxes RI,w (C; Ctr) and prints the statement that the transmitted sound power was measured directly over the measurement surface. verbose=True annexes the $K_{c}$ -modified index $R_{I, M}$ (Formula (9)) beside $R_{I}$ when an adaptation term was supplied.

The applicable ReportMetadata fields describe the intensity measurement: specimen (the tested element), area (specimen area $S$ ), client, manufacturer, test_room, laboratory, operator, report_id and test_date, plus the room/climate fields shared with the other insulation fiches. There is no dedicated field for the measurement-surface geometry or the scanning-versus-discrete-point acquisition method; record those in notes and name the standard in measurement_standard ("ISO 15186-1"). The requirement verdict, language="es" and the phonometry[report] extra behave exactly as in the sibling fiches.

import numpy as np
from phonometry import building, ReportMetadata

freqs = np.array([100, 125, 160, 200, 250, 315, 400, 500, 630, 800,
                  1000, 1250, 1600, 2000, 2500, 3150], dtype=float)
lp1, sm, s = 85.0, 12.0, 10.0
l_in = np.array([57.8, 61.9, 60.5, 55.6, 55.8, 55.5, 53.4, 51.6,
                 50.2, 47.7, 46.4, 45.7, 44.8, 45.2, 47.2, 52.7])
kc = building.adaptation_term_kc(freqs)                 # Annex B, Formula (B.2)
res = building.intensity_sound_reduction(
    np.full(16, lp1), l_in, measurement_area=sm, area=s, kc=kc
)
metadata = ReportMetadata(
    specimen="100 mm autoclaved aerated concrete block wall",
    area=10.0, measurement_standard="ISO 15186-1",
    test_room="Transmission suite (example)",
    laboratory="Phonometry Reference Laboratory",
    report_id="PHN-2026-0150",
    requirement=30.0,                                   # RI,w >= 30 dB -> PASS
)
res.report("RIw.pdf", metadata=metadata)                # RI,w (C; Ctr)
res.report("RIw_kc.pdf", metadata=metadata, verbose=True)  # f | RI | RI,M

The example fiche is regenerated with make reports and kept in the repository. Click the preview to open the PDF:

Intensity ISO 15186-1 example report (PDF) — Intensity fiche (IntensityReductionResult.report), RI,w (C; Ctr).

For a small building element (a ventilator, a socket, a small window) the intensity method reports the element-normalized level difference $D_{I, n, e}$ (Formula (8)) instead, normalized to the reference absorption area $A_{0} = 10 m^{2}$ . IntensityElementNormalizedResult.report() writes the same one-page fiche through the shared renderer, boxing DI,n,e,w (C; Ctr) rated per ISO 717-1; verbose=True shows the ISO 717 evaluation per band and a requirement adds a PASS/FAIL verdict (the element insulation passes at or above the target).

import numpy as np
from phonometry import building, ReportMetadata

lp1, sm, n = 85.0, 12.0, 1                              # source SPL, surface, units
l_in = np.array([57.9, 62.0, 60.6, 55.7, 55.9, 55.6, 53.5, 51.7,
                 50.3, 47.8, 46.5, 45.8, 44.9, 45.3, 47.3, 52.8])
res = building.intensity_element_normalized_difference(
    np.full(16, lp1), l_in, measurement_area=sm, n=n
)
res.plot()   # DI,n,e vs shifted ISO 717-1 reference (needs matplotlib)
metadata = ReportMetadata(
    specimen="Trickle ventilator in a 100 mm masonry wall",
    measurement_standard="ISO 15186-1",
    laboratory="Phonometry Reference Laboratory",
    report_id="PHN-2026-0151",
    requirement=30.0,                                   # DI,n,e,w >= 30 dB -> PASS
)
res.report("DIne.pdf", metadata=metadata)               # DI,n,e,w (C; Ctr)

The small element is rated exactly like a wall: $D_{I, n, e}$ feeds the ISO 717-1 engine and the unfavourable deviations (reference above the measurement) set $D_{I, n, e, w}$ . The $10 l g (S_{m} / A_{0})$ normalization replaces the specimen-area term, so the number describes the element irrespective of the wall it sits in.

Show the code for this figure

import matplotlib.pyplot as plt
import numpy as np
from phonometry import building

# A trickle ventilator in a masonry wall: source-room SPL 85 dB and the
# normal intensity level over the Sm = 12 m2 measurement surface.
l_in = np.array([57.9, 62.0, 60.6, 55.7, 55.9, 55.6, 53.5, 51.7,
                 50.3, 47.8, 46.5, 45.8, 44.9, 45.3, 47.3, 52.8])
res = building.intensity_element_normalized_difference(
    np.full(16, 85.0), l_in, measurement_area=12.0, n=1
)

# One line — DI,n,e vs the shifted ISO 717-1 reference:
res.plot()
plt.show()

# By hand, from the rating the result carries:
w = res.rating
fig, ax = plt.subplots()
ax.semilogx(w.band_centers, res.d_i_n_e, "o-", label="DI,n,e (element)")
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("Element normalized level difference [dB]")
ax.set_title(f"DI,n,e,w = {w.rating} dB  (C={w.c:+d}; Ctr={w.ctr:+d})")
ax.legend()
plt.show()

Intensity ISO 15186-1 element example report (PDF) — Element intensity fiche (IntensityElementNormalizedResult.report), DI,n,e,w (C; Ctr).

Floor-covering impact improvement (ISO 16251-1)

ISO 16251-1:2014 is a laboratory method for the improvement of impact sound insulation $Δ L$ of a soft, locally-reacting floor covering (carpet, PVC, linoleum). The two ISO 10140 rooms are replaced by a small softly-supported concrete plate; a standard tapping machine excites it and the structure-borne acceleration level on the underside is measured with and without the covering. For locally-reacting coverings that acceleration-level difference equals the ISO 10140 impact sound reduction.

Acceleration level (Formula (1)). $L_{a} = 10 l g (⟨ a^{2} ⟩ / a_{0}^{2})$ dB, reference $a_{0} = 1 0^{- 6} m/s^{2}$ . Background correction (Formula (2)) follows the ISO 10140 three-branch rule (unchanged ≥ 15 dB; energy subtraction for 6 ≤ margin < 15 dB; the 1.3 dB limit below 6 dB, flagged as $> Δ L$ ). The improvement is the position-averaged difference $Δ L = L_{0} - L_{1}$ (Formulae (3)/(4)); octaves follow $Δ L_{oct} = - 10 l g [\frac{1}{3} \sum 1 0^{- Δ L_{n} /10}]$ (Formula (5)).

Weighted improvement. $Δ L_{w}$ is the ISO 717-2 weighted reduction: the improvement is applied to the heavyweight reference floor $L_{n, r, 0}$ (ISO 717-2 Table 4), $L_{n, r} = L_{n, r, 0} - Δ L$ , and $Δ L_{w} = 78 - L_{n, r, w}$ , computed by weighted_impact_improvement(), which reuses the verified ISO 717-2 rating engine. A clause 6.3 measurement spans 18 bands (100–5000 Hz, optionally extended to 50 Hz); the rating is formed on the 100–3150 Hz sub-range of whatever spectrum contains it. The statement of results (clause 8 e)) also carries the spectrum adaptation term $C_{I, Δ} = C_{I, r, 0} - C_{I, r}$ (ISO 717-2:2020 Formula (A.4)), exposed as ci_delta on the result and standalone as impact_improvement_adaptation_term().

ISO 16251-1 floor-covering impact sound improvement: the improvement delta-L of a soft carpet rising with frequency across one-third-octave bands from 100 Hz to 3150 Hz, with the shaded improvement area and the weighted single-number delta-Lw annotated

Show the code for this figure

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]
bare = np.full(16, 78.0)                       # bare-plate acceleration level
# A real textile carpet measured on the CSTB mock-up (Foret et al. 2011, Fig. 4).
covering = bare - np.array([5, 8, 10, 14, 18, 23, 30, 31,
                            39, 49, 53, 57, 60, 67, 68, 71])
res = building.impact_improvement(bare, covering, freqs)
print(res.delta_lw)   # weighted improvement delta-Lw = 29 dB (ISO 717-2)
res.plot()
plt.show()

from phonometry import building

# delta-Lw straight from an improvement spectrum (16 one-third-octave bands):
delta_l = [5, 8, 10, 14, 18, 23, 30, 31, 39, 49, 53, 57, 60, 67, 68, 71]
print(building.weighted_impact_improvement(delta_l))    # 29 dB (carpet)

# From the measured bare/covered acceleration levels, with a background trace:
freqs = [100, 125, 160, 200, 250, 315, 400, 500, 630, 800,
         1000, 1250, 1600, 2000, 2500, 3150]
bare_levels = [72, 73, 74, 74, 75, 75, 76, 76, 77, 77, 78, 78, 79, 79, 80, 80]
covered_levels = [b - d for b, d in zip(bare_levels, delta_l)]
bg = [40.0] * 16
res = building.impact_improvement(bare_levels, covered_levels, freqs, background=bg)
res.improvement       # delta-L per band
res.delta_lw          # weighted single number (rated on the 100-3150 Hz sub-range)
res.ci_delta          # spectrum adaptation term CI,delta (Formula (A.4))
res.limited           # bands at the 1.3 dB limit of measurement (> delta-L)
res.octave_bands()    # (octave freqs, delta-L_oct) via Formula (5)
res.plot()            # the delta-L(f) improvement spectrum above (needs matplotlib)

ISO 16251-1 impact-improvement report (`.report()`)

FloorCoveringImprovementResult.report(path) writes a one-page accredited impact-improvement fiche: the standard-basis line, a metadata header, the per-band table (frequency and $Δ L$ , bands at the 1.3 dB limit prefixed >) beside the $Δ L (f)$ improvement curve, the boxed single-number $Δ L_{w} (C_{I, Δ})$ (the ISO 16251-1 Clause 8 e) statement of results), and a footer. Pass a ReportMetadata for the header; the applicable fields are specimen (the floor covering under test), client, manufacturer, mounting, mass_per_area, test_room, test_date, temperature, pressure, measurement_standard, laboratory, operator, report_id, notes and requirement (a higher weighted improvement is better, so the verdict passes at or above it). The bare reference floor is the standardised heavyweight floor of ISO 717-2:2020 Table 4, fixed by the standard. verbose=True adds the reference-floor-with-covering column $L_{n, r} = L_{n, r, 0} - Δ L$ , the derivation basis of $Δ L_{w}$ .

from phonometry import building, ReportMetadata

freqs = [100, 125, 160, 200, 250, 315, 400, 500,
         630, 800, 1000, 1250, 1600, 2000, 2500, 3150]
delta_l = [5, 8, 10, 14, 18, 23, 30, 31, 39, 49, 53, 57, 60, 67, 68, 71]
bare = [78.0] * 16
res = building.impact_improvement(bare, [b - d for b, d in zip(bare, delta_l)], freqs)
res.report("dLw.pdf",
           metadata=ReportMetadata(
               specimen="Textile floor covering (carpet), laid loose",
               measurement_standard="ISO 16251-1",
               requirement=20.0))  # delta-Lw (CI,delta) = 29 (-13) dB

The example fiche is regenerated with make reports and kept in the repository. Click the preview to open the PDF:

Floor-covering impact improvement ISO 16251-1 example report (PDF) — Floor-covering impact-improvement fiche (FloorCoveringImprovementResult.report), delta-Lw (CI,delta).

Laboratory flanking transmission (ISO 10848)

ISO 10848:2006/2010 is the laboratory method that measures the junction vibration reduction index $K_{ij}$ that the EN 12354 prediction takes as an input, together with the overall flanking descriptors $D_{n, f}$ (airborne) and $L_{n, f}$ (impact). It is the measurement counterpart of the empirical junction_vibration_reduction() of that prediction.

Vibration reduction index (Formula (13)). $K_{ij} = \overline{D}_{v, ij} + 10 l g (l_{ij} / a_{i} a_{j})$ dB, from the direction-averaged velocity level difference $\overline{D}_{v, ij} = \frac{1}{2} (D_{v, ij} + D_{v, j i})$ (Formula (11), which makes $K_{ij}$ symmetric), the common-edge junction length $l_{ij}$ and the equivalent absorption lengths $a_{j} = 2.2 π^{2} S_{j} / (T_{s, j} c_{0}) f_{ref} / f$ (Formula (12), $f_{ref} = 1000$ 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 $η = 2.2/ (f T_{s})$ .

Overall descriptors. $D_{n, f} = L_{1} - L_{2} - 10 l g (A / A_{0})$ (Formula (4), airborne) and $L_{n, f} = L_{2} + 10 l g (A / A_{0})$ (Formula (5), tapping machine), $A_{0} = 10 m^{2}$ ; their $D_{n, f, w}$ / $L_{n, f, w}$ 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).

ISO 10848 junction vibration reduction index Kij rising across one-third-octave bands from 100 Hz to 5000 Hz for a rigid T-junction of two heavy walls, with the single-number mean Kij over 200-1250 Hz drawn as a dashed line

Show the code for this figure

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 $f_{ref}$ , $η$ ).

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 $D_{n, f}$ is an airborne quantity, so its single number $D_{n, f, w}$ 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 $L_{n, f}$ rates per ISO 717-2 the same way).

Show the code for this figure

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()

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 $D_{n, f}$ (airborne) and $L_{n, f}$ (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 Dn,f,w (C; Ctr) (ISO 717-1) or Ln,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 ( $D_{n, f, w}$ passes at or above it, $L_{n, f, w}$ at or below it), and language="es" renders every fiche in Spanish. reportlab is required (pip install phonometry[report]).

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:

ISO 10848-1 junction vibration reduction index report (PDF) — Vibration reduction index fiche (VibrationReductionResult.report), mean Kij.

ISO 10848-2 airborne flanking level difference report (PDF) — Flanking level difference fiche (FlankingLevelDifferenceResult.report), Dn,f,w (C; Ctr).

ISO 10848-2 flanking impact level report (PDF) — Flanking impact level fiche (FlankingImpactLevelResult.report), Ln,f,w (CI).

What this guide covers

Covered. ISO 10140-2:2010 (the laboratory sound reduction index $R$ with the Clause 4.3 background-noise correction) and ISO 10140-3:2010 (the laboratory normalized impact level $L_{n}$ ), via building.lab_airborne_insulation, building.lab_impact_insulation and building.background_correction; ISO 15186-1:2000’s intensity sound reduction index $R_{I}$ (Clause 3.8), its $K_{c}$ -modified $R_{I, M}$ (Annex B) and the element-normalized $D_{I, n, e}$ (Clause 3.9), via building.intensity_sound_reduction, building.adaptation_term_kc and building.intensity_element_normalized_difference; ISO 16251-1:2014’s floor-covering impact improvement $Δ L$ and its weighted $Δ L_{w}$ against the ISO 717-2 Table 4 reference floor, via building.impact_improvement and building.weighted_impact_improvement; and ISO 10848-1:2006 (the frame document’s vibration reduction index $K_{ij}$ , Formula (13), the equivalent absorption length and the Part 4 modal-density/modal-overlap validity checks of Clause 9), with the overall $D_{n, f}$ / $L_{n, f}$ descriptors, via building.vibration_reduction_index, building.normalized_flanking_level_difference and building.normalized_flanking_impact_level.

Not covered. ISO 10140-1’s general test-facility and mounting-type requirements are not implemented; the guide only cites them as a label string in report metadata ("Type A mounting, mortar-bedded perimeter (ISO 10140-1)"). The sound-intensity measurement itself (the scanning probe, the two-microphone acquisition and phase-mismatch calibration behind $L_{p 1}$ and $L_{I n}$ ) is not implemented: both levels are taken as already-measured inputs, and the ISO 15186-1 report fiche states explicitly that it has no field for the measurement-surface geometry or the scanning-versus-discrete-point acquisition method. ISO 10848 Parts 2, 3 and 4 differ in which junction and specimen types they apply to; phonometry implements only the Part 1 $K_{ij}$ / $D_{n, f}$ / $L_{n, f}$ formulae generically, plus the Part 4 modal-overlap validity check, not the facility-specific test setups the other parts describe.

References

Foret, R., Chéné, J.-B., & Guigou-Carter, C. (2011). A comparison of the reduction of transmitted impact noise by floor coverings measured using ISO 140-8 and ISO/CD 16251-1. Forum Acusticum 2011, Aalborg (CSTB). The measured textile-carpet improvement spectrum used as the ISO 16251-1 worked example on this page (ΔL_w = 29 dB); the per-band ΔL was digitized from its Figure 4.
Hopkins, C. (2007). Sound insulation. Butterworth-Heinemann. https://doi.org/10.4324/9780080550473The reference monograph for laboratory sound-insulation measurement, flanking transmission and the vibration reduction index. ISBN 978-0-7506-6526-1.
International Organization for Standardization. (2000). Acoustics — Measurement of sound insulation in buildings and of building elements using sound intensity — Part 1: Laboratory measurements (ISO 15186-1:2000). The sound-intensity sound reduction index R_I, its Kc-modified form and the element normalized level difference (laboratory); the tool of choice when flanking is high (Clause 1).
International Organization for Standardization. (2003). Acoustics — Measurement of sound insulation in buildings and of building elements using sound intensity — Part 2: Field measurements (ISO 15186-2:2003). The field counterpart of the intensity method, giving the apparent index R'_I.
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). The frame document of the flanking-transmission measurement: definitions, the vibration reduction index Kij, the equivalent absorption length and the normalized flanking descriptors D_n,f / L_n,f that feed the EN 12354 prediction. Because ISO 10848 contains no worked numeric example, conformance is anchored on closed-form identities.
International Organization for Standardization. (2006). Acoustics — Laboratory measurement of the flanking transmission of airborne and impact sound between adjoining rooms — Part 2: Application to light elements when the junction has a small influence (ISO 10848-2:2006). Application to light elements whose junction has a small influence.
International Organization for Standardization. (2006). Acoustics — Laboratory measurement of the flanking transmission of airborne and impact sound between adjoining rooms — Part 3: Application to light elements when the junction has a substantial influence (ISO 10848-3:2006). Application to light elements whose junction has a substantial influence.
International Organization for Standardization. (2010). Acoustics — Laboratory measurement of sound insulation of building elements — Part 2: Measurement of airborne sound insulation (ISO 10140-2:2010). The laboratory sound reduction index R with the background-noise correction (Clause 4.3).
International Organization for Standardization. (2010). Acoustics — Laboratory measurement of sound insulation of building elements — Part 3: Measurement of impact sound insulation (ISO 10140-3:2010). The laboratory normalized impact level Ln.
International Organization for Standardization. (2010). Acoustics — Laboratory measurement of sound insulation of building elements — Part 4: Measurement procedures and requirements (ISO 10140-4:2010). The measurement procedures and the background-noise correction shared by the airborne R and impact Ln.
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). Application to junctions with at least one heavy element, with the modal-density, band-mode-count and modal-overlap validity checks (M < 0.25 bands bracketed, Clause 9).
International Organization for Standardization. (2014). Acoustics — Laboratory measurement of the reduction of transmitted impact noise by floor coverings on a small floor mock-up — Part 1: Heavyweight compact floor (ISO 16251-1:2014). The small-mock-up laboratory method for the impact-sound improvement ΔL of soft, locally-reacting floor coverings, with ΔL_w via the ISO 717-2 reference floor and the CI,delta adaptation term.
International Organization for Standardization. (2020). Acoustics — Rating of sound insulation in buildings and of building elements — Part 2: Impact sound insulation (ISO 717-2:2020). The impact single-number rating engine reused here and the reference floor L_n,r,0 (Table 4) behind ΔL_w, with the Formula (A.4) spectrum adaptation term CI,delta.
Vigran, T. E. (2008). Building acoustics. CRC Press. https://doi.org/10.1201/9781482266016The transmission theory of single and double constructions that laboratory indices quantify. ISBN 978-0-415-42853-8.

Created and maintained byJosé Manuel Requena Plens· GitHub· PyPI· All projects

Laboratory Insulation Measurement

Laboratory measurement (ISO 10140)

lab_airborne_insulation() / lab_impact_insulation() parameters

ISO 10140 laboratory test report (.report())

Sound insulation by intensity (ISO 15186)

intensity_sound_reduction() / adaptation_term_kc() parameters

ISO 15186-1 intensity test report (.report())

Floor-covering impact improvement (ISO 16251-1)

ISO 16251-1 impact-improvement report (.report())

Laboratory flanking transmission (ISO 10848)

ISO 10848 flanking-transmission reports (.report())

What this guide covers

See also

References

`lab_airborne_insulation()` / `lab_impact_insulation()` parameters

ISO 10140 laboratory test report (`.report()`)

`intensity_sound_reduction()` / `adaptation_term_kc()` parameters

ISO 15186-1 intensity test report (`.report()`)

ISO 16251-1 impact-improvement report (`.report()`)

ISO 10848 flanking-transmission reports (`.report()`)