The method, typeset.
Every level the studio prints is one outdoor propagation calculation, run nine times — once per octave band from 31.5 Hz to 8 kHz — then summed in energy and A-weighted at the receptor. This page draws the equation, the bands, the source model, the four classes of source data, and the ±3 dB the method itself states. All numbers below are from the engine's worked example, the site near Marl in North Rhine-Westphalia.
ISO 9613-2, in eight symbols.
The studio runs the long equation once per octave band. The nine bands are summed in energy, then A-weighted at the receptor to give LAeq in dB(A). Dc is zero for an omnidirectional source — every unit on this site is one.
| Symbol | Meaning | Unit |
|---|---|---|
| Lp(f) | Sound pressure level at the receptor in octave band f | dB re 20 µPa |
| Lw(f) | Sound power level of the source in octave band f | dB re 1 pW |
| Dc | Directivity correction (zero for an omnidirectional source) | dB |
| Adiv | Geometric divergence — spherical spreading with distance | dB |
| Aatm(f) | Air absorption in band f, from ISO 9613-1 | dB |
| Agr | Ground effect, from ground factor G ∈ [0, 1] | dB |
| Abar | Barrier screening (≤ 20 dB single edge, ≤ 25 dB double) | dB |
| Amisc | Miscellaneous — foliage and housings; off by default | dB |
| d | Propagation distance from source to receptor | m |
| α(f) | Air absorption coefficient in octave band f | dB/km |
| f | Octave band centre frequency | Hz |
Distance, and only distance.
Geometric divergence is the only term in equation (1) that has no knob. Double the distance, lose 6 dB. At 100 m the term alone is 42 dB; at 300 m it is 51.5 dB.
Why nearest is not loudest.
The curve is exact — equation (2) has no parameters. The dots show the eight homes at their yard-centre distances, from An der Tränke 1 (114 m, nearest) to Zur Freiheit 41 (191 m, farthest). Wasserwerksweg 7, the worst home, at 117 m loses 52.4 dB of sound power to distance alone.
The band-dependent part.
Air absorption comes from ISO 9613-1 and is the only term that depends on temperature, humidity and pressure. The coefficient rises sharply with frequency; at 8 kHz it is more than a hundred times larger than at 31.5 Hz.
134 metres of air, band by band.
Aatm(f) = α(f) · d / 1000. At 134 m the air strips more from the top bands than the bottom — at 8 kHz it removes 15.9 dB; at 31.5 Hz it removes 0.004 dB.
| Band | α (dB/km) | A_atm (dB) |
|---|
Nine bands. A-weighting at the receptor.
ISO 9613-2 runs once per octave band; the band levels are summed in energy and then A-weighted at the receptor. The A-weighting correction is the same at every site and never changes.
Low-frequency content still matters at night. The A-weighting cuts 31.5 Hz by 39.4 dB and 63 Hz by 26.2 dB, but transformer hum at 100 Hz and its harmonics at 200, 300 and 400 Hz can dominate the inside of a bedroom even when the broadband level on the facade looks small. The studio carries the nine-band spectrum at every receptor for that reason.
Sound power, per face, never as a point.
A 40-foot enclosure radiates from five faces: two long sides, two ends and the roof. Each face carries its own sound power and is split into cells no larger than 2 m, with one sub-source at the centre of each cell, set 2 cm outside the face so the enclosure screens only what lies behind it. A large enclosure is never one point.
The example enclosure's source data is one dB(A) figure per face, a Class C input (±4 dB). Each long side and each end carries 78 dB(A) of sound power, the roof 74 dB(A). The 12.19 m long sides split into 7 × 2 cells, the ends into 2 × 2 and the roof into 7 × 2: 50 sub-sources per enclosure, 600 for the twelve in the example, each carried to every receptor through equation (1).
| Rank | Unit | LAeq at apartment block |
|---|
The method states its own accuracy: ±3 dB.
A margin is only as good as the uncertainty under it. Four of the eight homes that meet the limit do so by 2.4 dB or less, while the method's own stated accuracy is ±3 dB. One headline number would call them fine. dBCAD shows the margin next to the uncertainty.
The four classes of source data
| Class | σ | What the data is |
|---|---|---|
| A · per-face sound power | ±1.5 dBper face | Manufacturer test report at every octave band, with the measurement surface and the geometry. Used when the data sheet is full. |
| B · octave-band sound power | ±2.5 dBper band | Octave-band sound power without the per-face split. dBCAD distributes the power uniformly across the radiating faces. |
| C · one dB(A) at a distance | ±4.0 dBoverall | A single dB(A) figure at a stated distance. dBCAD converts it to sound power over the measurement surface and uses the library's octave shape. This is the example's class. |
| U · nothing usable | +3.0 dB pad | No usable source data. The library default applies, with an extra 3 dB added and the unit marked as unverified. |
Nearest is not loudest. An der Tränke 1 is the nearest home (114 m) and still reads 3.1 dB below Wasserwerksweg 7 (117 m, 42.6 dB(A)). The yard's long front row faces Wasserwerksweg 7; the engine models each enclosure face by face; distance, screening and which face points where all count.
Why the verdict follows the night.
Night is the longest, the strictest, and the one the receptor is asleep for. The day carries the headline number; the night carries the binding one.
| Zone | Day 06:00 – 22:00 | Night 22:00 – 06:00 | Gap | Notes |
|---|---|---|---|---|
| Industrial | 70 dB(A) | 70 dB(A) | 0 dB | No day / night split |
| Commercial | 65 dB(A) | 50 dB(A) | 15 dB | |
| Core and mixed | 60 dB(A) | 45 dB(A) | 15 dB | |
| WA · general residential | 55 dB(A) | 40 dB(A) | 15 dB | The example site. 40 dB(A) is the binding number. |
| Pure residential | 50 dB(A) | 35 dB(A) | 15 dB | Strictest German limit |
| Spa areas | 45 dB(A) | 35 dB(A) | 10 dB |
What the method does not do. What this example does not show.
Every limit below is stated in the product. The example is a worked example, not a site assessment; its inputs are assumptions.
- Downwind propagation
- ISO 9613-2 is a downwind method. Upwind or crosswind gives lower levels than the engine prints.
- Source heights < 30 m, 100–1,000 m
- The method's stated accuracy window. Outside it, the ±3 dB band widens.
- One meteorological condition
- Downwind, 10 °C, 70 % humidity, 101.325 kPa. Other conditions need an alternative method.
- A_bar caps at 20 dB / 25 dB
- Single edge / double edge per ISO 9613-2 §7.4. Higher attenuation is not claimed.
- No reflection model
- for tall facades opposite the yard. The example site has no such facades.
- No screens, no barriers
- A_bar is zero for every receptor; the example does not show the screening cap.
- No reflections
- from neighbouring buildings.
- Zone WA is assumed
- (general residential). The local plan was not checked.
- Receptor height 4.0 m
- (upper-floor window) is assumed for all eight homes.
- Class C source data
- The example enclosure uses ±4 dB sound-power data, the broadest class. Class A or B would tighten every margin.
- Launch-country rules
- TA Lärm (Germany) was checked against the primary text on 2026-10-13; the other four are shown as unverified until each has been checked against the official text.
- Source data
- every unit in the example runs on the generic library entry: assumed, no manufacturer measurement.
- French results
- would be PRELIMINARY until a background survey is entered. The example uses Germany / TA Lärm, so this flag does not apply here.
Standards cited.
The standards and the rule this page relies on, by number and title.
- ISO 9613-1Acoustics — Attenuation of sound during propagation outdoors — Part 1: Calculation of the absorption of sound by the atmosphere. International Organization for Standardization.
- ISO 9613-2Acoustics — Attenuation of sound during propagation outdoors — Part 2: General method of calculation. International Organization for Standardization.
- IEC 61672-1Electroacoustics — Sound level meters — Part 1: Specifications. International Electrotechnical Commission.
- TA Lärm 2017Technische Anleitung zum Schutz gegen Lärm. Bundesministerium für Umwelt, Naturschutz und Reaktorsicherheit, Germany, as amended 2017.
Run this on your own site.
ISO 9613-2, the nine bands, the four uncertainty classes, the night verdict — all of it runs inside the studio you design in.
