Source: https://jmrplens.github.io/phonometry/reference/api/building/installed-structure-borne/ # Installed structure-borne sound from equipment (EN 12354-5) **EN 12354-5:2009** predicts the sound pressure level in a receiving room caused by building service equipment (pumps, fans, lifts, water installations) that injects **structure-borne sound** into the building. It closes the structural-vibroacoustics chain: the source is described by its characteristic structure-borne sound power level `L_Ws,c`, derived from the EN 15657 reception-plate measurement through the Formula (15)/(17) conversion and a mobility correction (**not** the raw plate-injected level; see [EN 15657](https://jmrplens.github.io/phonometry/reference/api/building/structure-borne-power/)); the source and receiver point mobilities set how much power is actually coupled into the structure, and the building transmission carries it to the receiving room. The Annex I mobility correction `installed_power_from_reception_plate` refers the characteristic reception-plate level `L_Ws,n` to the actual receiver, `L_Ws,inst = L_Ws,n + 10 lg(Y_∞,i / Y_∞,rec)` with `Y_∞,rec = 5·10⁻⁶ m/(N·s)`; with the source mobility instead it yields `L_Ws,c` (Annex I.3, Table I.8).

Show the code for this figure

```python import matplotlib.pyplot as plt import numpy as np from phonometry import building # EN 15657 characteristic source power and illustrative point mobilities. bands = np.array([63.0, 125.0, 250.0, 500.0, 1000.0, 2000.0, 4000.0]) lws_c = np.array([78.0, 82.0, 84.0, 81.0, 77.0, 72.0, 66.0]) ys = (2e-4 + 1e-4j) * (bands / 250.0) # source mobility yi = (3e-5 + 1e-5j) * np.ones_like(bands) # receiver mobility dc = np.array([float(building.coupling_term(a, b)) for a, b in zip(ys, yi)]) # Two transmission paths: the excited floor and a flanking wall. paths = [ {"adjustment_term": 6.0, "element_area": 12.0, "flanking_reduction_index": np.linspace(44.0, 62.0, 7)}, {"adjustment_term": 7.0, "element_area": 9.0, "flanking_reduction_index": np.linspace(46.0, 64.0, 7)}, ] res = building.installed_source_prediction(lws_c, dc, paths, frequencies=bands) res.plot() # characteristic and installed power, per-path levels and the total plt.show() ```

## 1. Coupling and installed power Only part of the characteristic power is injected into the supporting element; the loss is the **coupling term** `D_C` (always positive), set for a point excitation by the source mobility `Y_s` and the receiver mobility `Y_i` (Formula 19b): $$ D_{C,i} = 10\lg\frac{|Y_s + Y_i|^2}{|Y_s|\,\mathrm{Re}\{Y_i\}}, $$ which reduces to `10 lg(|Y_s|/Re{Y_i})` for a **force source** (high source mobility, Formula 19c) and to `−10 lg(|Y_s|·Re{Z_i})` for a **velocity source** (low source mobility, Formula 19d); an elastic support adds its transfer mobility `Y_k` inside the modulus (Formula 19e). The **installed** power level is then (Formula 18b) `L_Ws,inst = L_Ws,c − D_C`. The physics behind `D_C` is the classical power input of a point-excited plate: only the real part of the receiver's driving-point mobility absorbs power, and the mismatch between `Y_s` and `Y_i` decides how much of the source's capability ever enters the structure (Hopkins 2007, Section 2.8). The mobilities themselves come from the [mechanical-mobility chain](https://jmrplens.github.io/phonometry/reference/api/vibration/mechanical-mobility/): measured per ISO 7626, or from the infinite-plate closed forms of [panel theory](https://jmrplens.github.io/phonometry/guides/panel-sound-insulation/) when no measurement exists. A pump on a concrete slab is the textbook force source: its casing mobility is orders of magnitude above the slab's, so `D_C` collapses to Formula 19c and the injected power no longer depends on the receiver at all. ```python from phonometry import building # A near-force source (Y_s >> Y_i) on a concrete floor: dc = building.coupling_term(2e-4 + 1e-4j, 3e-5 + 1e-5j) print(round(float(dc), 2)) # ~8.5 dB print(round(float(building.installed_structure_borne_power_level(82.0, dc)), 1)) # installed L_Ws ``` ## 2. Transmission to the receiving room EN 12354 parts 1 and 2 handle rooms excited through the air and by the standard tapping machine; part 5 covers the sources that shake the building *directly*: pumps, fans, lifts, whirlpool baths, cisterns and the pipework that ties them into walls and floors. Once the installed power is in the structure, several elements radiate into the receiving room: the excited element itself and every element the vibration reaches across the junctions. Each excited-element/radiating-element pair `i→j` is a transmission path with its own adjustment term and flanking index: Each transmission path `i→j` gives a normalised sound pressure level from the installed power, the structure-to-airborne adjustment term `D_sa`, the flanking sound reduction index `R_ij,ref` (EN 12354-1) and the element area (Formula 18a): $$ L_{n,s,ij} = L_{Ws,\mathrm{inst},i} - D_{sa,i} - R_{ij,\mathrm{ref}} - 10\lg\frac{S_i}{S_0} - 10\lg\frac{A_0}{4}, $$ with `S₀ = A₀ = 10 m²`, and the paths combine energetically (Formula 17): ```python import numpy as np from phonometry import building bands = np.array([250.0, 500.0, 1000.0]) res = building.installed_source_prediction( characteristic_power_level=np.array([80.0, 82.0, 78.0]), coupling_term=np.array([9.0, 10.0, 11.0]), paths=[ {"adjustment_term": 5.0, "flanking_reduction_index": np.array([50.0, 52.0, 55.0]), "element_area": 12.0}, {"adjustment_term": 6.0, "flanking_reduction_index": np.array([52.0, 54.0, 57.0]), "element_area": 8.0}, ], frequencies=bands, ) print(np.round(res.total_level, 1)) # total L_n,s per band print(round(res.overall_level, 1)) # band-summed level [dB] res.plot() # the per-path and total L_n,s cascade, as in the figure above (needs matplotlib) ``` The `InstalledSourceResult` carries the per-path levels, the total per band, the installed power level and `.overall_level`, and its `.plot()` draws the whole cascade. ## 3. The prediction report (`.report()`) A prediction ends as a *document*. `InstalledSourceResult.report(path)` writes a one-page PDF fiche, clearly labelled a prediction and not a measurement: a prediction-basis line naming EN 12354-5:2009, an optional metadata header (client, source equipment, receiving room, instrumentation, climate, date), a per-band table (nominal octave/one-third-octave frequency, the installed structure-borne power level `L_Ws,inst`, each transmission path's normalised SPL `L_n,s,ij` and the combined total `L_n,s`), the per-path and total `L_n,s(f)` spectra, and a boxed band-summed total `L_n,s` (dB) with the installed power total and the path count. The relevant `ReportMetadata` fields are `client`, `specimen` (the source equipment), `test_room` (the receiving room), `instrumentation` and the footer identity `laboratory`, `operator`, `report_id` and `notes`. Supplying `requirement` adds a PASS/FAIL verdict against a declared upper limit on the overall `L_n,s` (lower is better). `verbose=True` adds one column per transmission path (up to five); otherwise only the installed power and the combined total are shown. `language="es"` renders the Spanish fiche. The basis strip states Formulae 18a/17 and the prediction disclaimer. Rendering needs the optional `phonometry[report]` extra (reportlab), plus matplotlib for the plot. ```python import numpy as np from phonometry import ReportMetadata, installed_source_prediction bands = np.array([63, 125, 250, 500, 1000, 2000], float) lwc = np.array([84.4, 82.5, 69.9, 67.6, 61.6, 49.9]) # characteristic power [dB] dsa = np.array([-13.6, -17.3, -17.4, -20.0, -26.9, -32.9]) paths = [ {"adjustment_term": dsa, "flanking_reduction_index": np.array([43.0, 46, 50.2, 54.7, 64.6, 73]), "element_area": 12.8}, {"adjustment_term": dsa, "flanking_reduction_index": np.array([37.0, 41.2, 35.9, 37.7, 49, 57.8]), "element_area": 12.8}, ] res = installed_source_prediction(lwc, 16.2, paths, frequencies=bands) res.report( "installed_structure_borne.pdf", metadata=ReportMetadata( client="Example dwelling refurbishment", specimen="WC flushing cistern (wall-fixed)", test_room="Receiving room: adjacent bedroom", report_id="EXAMPLE-12354-5", requirement=45.0, ), ) # overall L_n,s ~ 43 dB -> declared limit 45 dB: PASS ``` The rendered example fiche, regenerated with `make reports`, is kept in the repository. Click the preview to open the PDF: [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/en12354_5_installed_structure_borne_example.pdf) *Installed structure-borne prediction fiche (`InstalledSourceResult.report`), an EN 12354-5 estimate of the normalised structure-borne SPL in the receiving room.* ## See also - [Structure-borne sound power of equipment (EN 15657)](https://jmrplens.github.io/phonometry/reference/api/building/structure-borne-power/): the reception-plate characterisation that supplies `L_Ws,c` and the source mobility this prediction consumes. - [Mechanical mobility and the FRF family (ISO 7626-1)](https://jmrplens.github.io/phonometry/reference/api/vibration/mechanical-mobility/): the measured `Y_s` and `Y_i` behind the coupling term. - [Bending-wave transmission at plate junctions](https://jmrplens.github.io/phonometry/reference/api/vibration/junction-transmission/): the junction physics that carries the installed power to the flanking radiators. - [Predicting Sound Insulation (EN 12354)](https://jmrplens.github.io/phonometry/guides/insulation-prediction/): the airborne and impact members of the same prediction family. ## References - Cremer, L., Heckl, M., & Petersson, B. A. T. (2005). *Structure-borne sound: Structural vibrations and sound radiation at audio frequencies* (3rd ed.). Springer. ISBN 978-3-540-22696-3. [doi:10.1007/b137728](https://doi.org/10.1007/b137728). The source-receiver mobility coupling and the structure-borne transmission across junctions behind the coupling term and the path model. - Hopkins, C. (2007). *Sound insulation*. Butterworth-Heinemann. ISBN 978-0-7506-6526-1. [doi:10.4324/9780080550473](https://doi.org/10.4324/9780080550473). Section 2.8 (driving-point impedance and mobility): the power a mechanical source injects into a plate through the source and receiver mobilities. ## Standards EN 12354-5:2009, *Building acoustics — Estimation of acoustic performance of buildings from the performance of elements — Part 5: Sound levels due to service equipment*: the coupling term (clause 4.4.3, Formulae 19a-19e), the installed structure-borne power level (Formula 18b), the structure-to- airborne adjustment term (clause 4.4.4, Formulae 20a/20b), and the normalised sound pressure level per path and its energetic combination (Formulae 18a, 17). Conformance is anchored on the coupling-term force-source limit and the standard's own Annex I worked examples: the whirlpool bath of I.2 (Table I.6a: mobility correction and path 11) and the flushing cistern of I.3 (Tables I.8/I.9: source conversion, all four transmission paths, the Formula 17 total and its 29 dB(A) closure), within the ±0.15 dB rounding of the printed one-decimal intermediates. `D_sa` and `R_ij,ref` are inputs (from measurement / EN 12354-1 / Annexes D and F).