Source: https://jmrplens.github.io/phonometry/buildings/insulation/insulation-intensity/ # Sound Insulation by Intensity (ISO 15186) A reverberation room reads transmitted sound power *indirectly*: the receiving room integrates every watt that arrives, whichever path carried it, and the absorption area converts the room level back into a power. The **sound-intensity** method of ISO 15186 replaces that inference with a direct reading: a p-p intensity probe scans a measurement surface that encloses the specimen and measures the power radiated by the test element alone, so flanking transmission stays out of the number. This guide covers the intensity sound reduction index $R_\mathrm{I}$ and its $K_\mathrm{c}$-modified form, the element-normalized level difference of small building elements, the surface qualification indicator and the accredited test fiches. The pressure-based laboratory chain lives in [Laboratory Insulation Measurement](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-lab/); the probe physics and its field indicators are the subject of the [Sound Intensity guide](https://jmrplens.github.io/phonometry/devices/emission/intensity/). ## Measuring the transmitted power directly (ISO 15186-1) The [ISO 10140 laboratory method](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-lab/) 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 $L_{p1}$ and the average normal intensity level $L_{I\mathrm{n}}$ over the surface (area $S_\mathrm{m}$), for a specimen of area $S$, $$ R_\mathrm{I} = L_{p1} - 6 - \left[ L_{I\mathrm{n}} + 10 \log_{10}\frac{S_\mathrm{m}}{S} \right], $$ 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 $R'_\mathrm{I}$ in the field (ISO 15186-2). Because the intensity method slightly *underestimates* the power radiated into a real receiving room, a **modified index** $R_\mathrm{I,M} = R_\mathrm{I} + K_\mathrm{c}$ reproduces the ISO 10140-2 pressure result; the adaptation term $K_\mathrm{c}$ (Annex B) is $10 \log_{10}(1 + S_{\mathrm{b}2}\lambda/8V_2)$ for a well-defined room, or the room-independent $10 \log_{10}(1 + 61.4/f)$. For small elements the **element normalized level difference** replaces $10\log_{10}(S_\mathrm{m}/S)$ with $10\log_{10}(S_\mathrm{m}/A_0) + 10\log_{10} N$ ($A_0 = 10\ \text{m}^2$, $N$ element units). ```python 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) ``` *The modified index $R_\mathrm{I,M} = R_\mathrm{I} + K_\mathrm{c}$ lifts $R_\mathrm{I}$ (most at the low bands, where $K_\mathrm{c}$ 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 $S_\mathrm{m}$ keeps the unsigned area sum.*

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```python 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() ```

Both levels are already-measured inputs: the scanning probe, the two-microphone acquisition and the phase-mismatch calibration behind $L_{p1}$ and $L_{I\mathrm{n}}$ are not implemented, and nothing here enforces the Clause 6.4 acquisition either — the 0.1 m to 0.3 m measurement distance, the 0.1 m/s to 0.3 m/s scan speed, the 90°-rotated second scan with its 1.0 dB validity test, the 10 dB background margin — so a single scan will produce a number just as readily as a qualified pair. ### `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 $S_\mathrm{m}$ | | `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 $S_{\mathrm{b}2}$ / $V_2$ 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 $R_\mathrm{I}$, reusing the same accredited two-panel layout as the ISO 10140 and ISO 16283 fiches. Because $R_\mathrm{I}$ is an ordinary sound reduction index, its single-number rating $R_\mathrm{I,w}$ is the ISO 717-1 airborne rating evaluated on the intensity spectrum: the fiche names ISO 15186-1 in its basis line, tabulates $R_\mathrm{I}$ 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 $K_\mathrm{c}$-modified index $R_\mathrm{I,M}$ (Formula (9)) beside $R_\mathrm{I}$ 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. ```python 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: [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iso15186_intensity_example.pdf) *Intensity fiche (`IntensityReductionResult.report`), $R_\mathrm{I,w}(C; C_\mathrm{tr})$.* ## Small building elements: the element-normalized level difference For a **small building element** (a ventilator, a socket, a small window) the intensity method reports the element-normalized level difference $D_\mathrm{I,n,e}$ (Formula (8)) instead, normalized to the reference absorption area $A_0 = 10\ \text{m}^2$. `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). ```python 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 ) 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.plot() # DI,n,e vs shifted ISO 717-1 reference (needs matplotlib) res.report("DIne.pdf", metadata=metadata) # DI,n,e,w (C; Ctr) ``` *The small element is rated exactly like a wall: $D_\mathrm{I,n,e}$ feeds the ISO 717-1 engine and the unfavourable deviations (reference above the measurement) set $D_\mathrm{I,n,e,w}$. The $10\log_{10}(S_\mathrm{m}/A_0)$ normalization replaces the specimen-area term, so the number describes the element irrespective of the wall it sits in.*

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```python 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() ```

[](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iso15186_element_example.pdf) *Element intensity fiche (`IntensityElementNormalizedResult.report`), $D_\mathrm{I,n,e,w}(C; C_\mathrm{tr})$.* ## Laboratory or field (ISO 15186-2) Part 1 is a laboratory method: the specimen sits in a test opening between two rooms, and the suppressed flanking of the facility makes $R_\mathrm{I}$ a property of the element. ISO 15186-2 takes the same probe, the same surface scan and the same formula into the finished building, where the result is the apparent index $R'_\mathrm{I}$ of the installed element, flanking radiation and all. The selectivity that motivated the method in the laboratory doubles in the field: because the probe reads only what its measurement surface radiates, partial surfaces isolate which element (the wall itself, a window, a leaky junction) carries the transmitted power, which no pressure-based field method can resolve. Qualify each scan with the same pressure-intensity indicator, and expect the probe's own limits (the [spacer phase error](https://jmrplens.github.io/phonometry/devices/emission/intensity/)) to set the usable low-frequency range. Part 2's own field procedure (the loudspeaker positions, the façade cases) and the low-frequency Part 3 variant are not implemented: the formulas here apply unchanged to field data, but nothing checks how that data was acquired. ## 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 laboratory sound-insulation measurement, including the intensity route and its relation to the pressure methods. - 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). [iso.org catalogue](https://www.iso.org/standard/26097.html). The intensity sound reduction index, the $K_\mathrm{c}$ adaptation and the element normalized level difference this page implements. - 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). [iso.org catalogue](https://www.iso.org/standard/30105.html). The field counterpart, giving the apparent index $R'_\mathrm{I}$ of the installed element. ## Standards ISO 15186-1:2000, which defines the intensity sound reduction index $R_\mathrm{I}$, its $K_\mathrm{c}$-modified form $R_\mathrm{I,M}$ (Annex B), the element normalized level difference $D_\mathrm{I,n,e}$ and the surface pressure-intensity indicator; ISO 15186-2:2003, which carries the same quantities into the field as the apparent $R'_\mathrm{I}$. The single-number ratings reuse ISO 717-1. ## See also - [Laboratory Insulation Measurement](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-lab/): the ISO 10140 pressure method that the $K_\mathrm{c}$ adaptation reproduces. - [Field Insulation Measurement (ISO 16283)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-field/): the pressure-based field quantities and their single-number ratings. - [Insulation Ratings (ISO 717)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-ratings/): the reference-curve engine behind $R_\mathrm{I,w}$ and $D_\mathrm{I,n,e,w}$. - [Sound Intensity](https://jmrplens.github.io/phonometry/devices/emission/intensity/): the two-microphone probe, its field indicators and the residual-index qualification behind every scan. - API reference: [`building.measurement.intensity_insulation`](https://jmrplens.github.io/phonometry/reference/api/building/intensity-insulation/).