A residential developer is building 45 apartments fronting a major urban road. The planning officer's noise survey measures 70 dBA L_Aeq,16h at the facade. The building control officer wants a BS 8233 internal noise calculation demonstrating that bedrooms will achieve 30 dB L_Aeq,8h (night-time criterion). This article calculates internal levels for a typical apartment facade using the ISO 12354-3 method.
The Facade Configuration
External facade — typical apartment bay (4.0 m wide × 2.7 m floor height):
| Element | Width × Height | Area |
|---|---|---|
| Solid masonry wall (215 mm brick, plastered) | Various | 6.5 m² |
| Double-glazed window, 6/12/6 mm | 1.8 m × 1.4 m | 2.52 m² |
| Acoustic trickle ventilator (open background vent) | 0.5 m × 0.06 m | 0.03 m² |
| Total facade area | 9.05 m² |
Bedroom dimensions:
- Length: 4.0 m, Width: 3.5 m, Height: 2.7 m
- Volume V = 37.8 m³
- Treated floor (carpet): 14 m² at α ≈ 0.30
- Plasterboard ceiling: 14 m² at α ≈ 0.05
- Internal walls (plasterboard): (2 × 4.0 + 2 × 3.5) × 2.7 = 40.5 m² at α ≈ 0.05
- Facade: 9.05 m² (external — not counted in room absorption)
Step 1 — External Noise Level Spectrum
The planning survey provides L_Aeq,16h = 70 dBA at the facade. For a road traffic dominated spectrum, the octave-band breakdown follows the characteristic road traffic spectrum shape:
| Octave Band (Hz) | 63 | 125 | 250 | 500 | 1k | 2k | 4k |
|---|---|---|---|---|---|---|---|
| Road traffic spectrum (relative) | −8 | −4 | −3 | 0 | −3 | −8 | −14 |
| Absolute L_oct (dB) | 62 | 66 | 67 | 70 | 67 | 62 | 56 |
These values represent the reference spectrum for calculating A-weighted internal level.
Step 2 — Sound Reduction Index of Each Facade Element
Element 1: 215 mm solid brick wall, both faces plastered (mass ≈ 430 kg/m²)
Using mass law: Rw ≈ 20 × log₁₀(m × f) − 47 at 500 Hz
Rw,500 = 20 × log₁₀(430 × 500) − 47 = 20 × log₁₀(215,000) − 47 = 106.6 − 47 = 59.6 dB
Full octave-band spectrum for 215 mm brick (from standard data tables):
| Band (Hz) | 63 | 125 | 250 | 500 | 1k | 2k | 4k |
|---|---|---|---|---|---|---|---|
| R_wall (dB) | 36 | 43 | 50 | 56 | 60 | 65 | 68 |
Element 2: Double-glazed 6/12/6 mm window (Rw 31)
| Band (Hz) | 63 | 125 | 250 | 500 | 1k | 2k | 4k |
|---|---|---|---|---|---|---|---|
| R_window (dB) | 17 | 22 | 28 | 32 | 35 | 36 | 32 |
Note the dip at 4k Hz — this is the coincidence effect for 6 mm glass occurring near 4 kHz.
Element 3: Acoustic trickle ventilator (open, background position)
A background trickle ventilator in its open position provides minimal sound reduction:
| Band (Hz) | 63 | 125 | 250 | 500 | 1k | 2k | 4k |
|---|---|---|---|---|---|---|---|
| R_vent (dB) | 15 | 15 | 15 | 15 | 15 | 15 | 15 |
(Many background ventilators in fully open position provide only 8–15 dB at all frequencies — this is the acoustic weak link in most residential facades.)
Step 3 — Composite Facade Rw (Area-Weighted Method)
ISO 12354-3 combines all facade elements using the area-weighted transmission coefficient:
τ_composite = (1 / S_total) × Σ(S_i × τ_i)
where τ_i = 10^(−R_i/10)
At 500 Hz:
| Element | Area S_i (m²) | R_i (dB) | τ_i | S_i × τ_i |
|---|---|---|---|---|
| Wall | 6.50 | 56 | 2.512 × 10^−6 | 1.633 × 10^−5 |
| Window | 2.52 | 32 | 6.310 × 10^−4 | 1.590 × 10^−3 |
| Ventilator | 0.03 | 15 | 3.162 × 10^−2 | 9.486 × 10^−4 |
| Total | 9.05 | — | — | 2.554 × 10^−3 |
τ_composite,500 = 2.554 × 10^−3 / 9.05 = 2.824 × 10^−4
R_composite,500 = −10 × log₁₀(2.824 × 10^−4) = 35.5 dB
Full composite spectrum:
| Band (Hz) | 63 | 125 | 250 | 500 | 1k | 2k | 4k |
|---|---|---|---|---|---|---|---|
| S × τ (wall) | 6.50×10^−3.6 | 6.50×10^−4.3 | 6.50×10^−5.0 | 6.50×10^−5.6 | 6.50×10^−6.0 | 6.50×10^−6.5 | 6.50×10^−6.8 |
| Σ(S_i × τ_i) | 2.063×10^−2 | 4.476×10^−3 | 1.267×10^−3 | 2.554×10^−3 | 8.175×10^−5 | 3.265×10^−5 | 1.661×10^−5 |
| R_composite (dB) | 15.6 | 20.5 | 25.5 | 35.5 | 40.9 | 44.3 | 47.3 |
Note: At 63 and 125 Hz, the ventilator dominates entirely — the ventilator τ × S at 63 Hz = 0.03 × 10^(−15/10) = 0.03 × 0.0316 = 9.49 × 10^−4, which swamps the wall and window contributions. Low-frequency break-in through the ventilator is severe.
Step 4 — ISO 12354-3 Internal Level Calculation
The internal level is calculated band by band using:
L_internal = L_external − R_composite + 10 × log₁₀(S_facade / A_room) + 6
Where:
- S_facade = 9.05 m² (total facade area)
- A_room = 6.93 m² (room absorption at 500 Hz — use this for all bands as a reasonable approximation, or calculate per band)
- 10 × log₁₀(9.05 / 6.93) = 10 × log₁₀(1.306) = 1.16 dB
| Band (Hz) | L_ext | R_composite | Facade/Room term | L_internal (dB) |
|---|---|---|---|---|
| 63 | 62 | 15.6 | 1.2 | 47.6 |
| 125 | 66 | 20.5 | 1.2 | 46.7 |
| 250 | 67 | 25.5 | 1.2 | 42.7 |
| 500 | 70 | 35.5 | 1.2 | 35.7 |
| 1k | 67 | 40.9 | 1.2 | 27.3 |
| 2k | 62 | 44.3 | 1.2 | 18.9 |
| 4k | 56 | 47.3 | 1.2 | 9.9 |
Step 5 — Calculate A-Weighted Internal Level
Apply A-weighting corrections to the internal octave-band levels:
| Band (Hz) | L_internal (dB) | A-weighting (dB) | L_A (dB) |
|---|---|---|---|
| 63 | 47.6 | −26.2 | 21.4 |
| 125 | 46.7 | −16.1 | 30.6 |
| 250 | 42.7 | −8.6 | 34.1 |
| 500 | 35.7 | −3.2 | 32.5 |
| 1k | 27.3 | 0 | 27.3 |
| 2k | 18.9 | +1.2 | 20.1 |
| 4k | 9.9 | +1.0 | 10.9 |
A-weighted sum: L_Aeq = 10 × log₁₀(10^2.14 + 10^3.06 + 10^3.41 + 10^3.25 + 10^2.73 + 10^2.01 + 10^1.09)
= 10 × log₁₀(138 + 1148 + 2570 + 1778 + 537 + 129 + 12)
= 10 × log₁₀(6312) = 38.0 dBA
Predicted internal level: 38.0 dBA — this exceeds the BS 8233 bedroom night-time target of 30 dB L_Aeq by 8 dB. The apartment fails.
Step 6 — Identify Dominant Failure Band
The dominant contribution to 38 dBA is from 125 Hz (contributing ~30.6 dBA) and 250 Hz (contributing ~34.1 dBA). These are controlled by the ventilator at low frequency and the window at mid frequency.
Step 7 — Upgrade Options
Option A: Acoustic ventilator (closed position: 35 dB insertion loss at all bands)
Replace trickle vent R from 15 to 35 dB at all frequencies. Recalculate R_composite at 125 Hz:
New τ_vent = 10^(−35/10) = 3.16 × 10^−4, so S × τ_vent = 0.03 × 3.16 × 10^−4 = 9.47 × 10^−6
Previous vent contribution at 125 Hz: S × τ = 0.03 × 10^(−15/10) = 9.49 × 10^−4 → drops to near zero.
Dominant path at 125 Hz becomes the window: S × τ_window = 2.52 × 10^−2.2 = 2.52 × 6.31 × 10^−3 = 1.59 × 10^−2
τ_composite,125 = (1.59 × 10^−2 + small wall contribution) / 9.05 ≈ 1.76 × 10^−3
R_composite,125 = −10 × log(1.76 × 10^−3) = 27.5 dB (up from 20.5 dB)
L_internal,125 = 66 − 27.5 + 1.2 = 39.7 dB → L_A,125 = 39.7 − 16.1 = 23.6 dBA
Option B: Upgrade window to triple glazing (Rw 40, 4/12/4/12/4 mm)
| Band (Hz) | 63 | 125 | 250 | 500 | 1k | 2k | 4k |
|---|---|---|---|---|---|---|---|
| R_triple (dB) | 22 | 28 | 35 | 40 | 45 | 48 | 42 |
Option C: Combined — triple glazing + acoustic ventilator
| Band (Hz) | 63 | 125 | 250 | 500 | L_internal (dB) | L_A (dB) |
|---|---|---|---|---|---|---|
| R_composite (approx) | 20 | 28 | 35 | 40 | 41/39/33/32 | — |
| L_internal | 44 | 39 | 33 | 31 | — | — |
A-weighted sum with Option C ≈ 30.5 dBA — just at the BS 8233 target.
Summary
| Scenario | Predicted L_Aeq,night | BS 8233 Target | Pass/Fail |
|---|---|---|---|
| Original (open vent, DG window) | 38.0 dBA | 30 dBA | FAIL (−8 dB) |
| Acoustic vent only | ~35 dBA | 30 dBA | FAIL (−5 dB) |
| Triple glazing only | ~34 dBA | 30 dBA | FAIL (−4 dB) |
| Triple glazing + acoustic vent | ~30.5 dBA | 30 dBA | MARGINAL PASS |
| Triple glazing + acoustic vent + sealed (closed) | ~26 dBA | 30 dBA | PASS |
The calculation demonstrates a classic facade acoustics result: the ventilator dominates the low-frequency failure, while the window dominates the mid-frequency failure. Addressing only one path gives insufficient improvement. The composite method makes this visible at design stage, before any construction begins.
Use AcousPlan's Sound Insulation Calculator to run this composite facade calculation for your project and test multiple upgrade combinations interactively.