Source: https://jmrplens.github.io/phonometry/buildings/rooms/workroom-sound-decay/ # Spatial sound decay in workrooms (ISO 14257, ISO 11690-3) A reverberation time says what a room does to a decay in time. It says very little about what a factory hall does to a worker standing 20 m from a press. The question there is about distance: how much quieter does it get as you walk away, and how much louder is it than open air would be? ISO 14257 answers both with one measurement. A calibrated source stands where a machine would, a microphone walks away from it along a straight path, and the curve of level against distance is the room's own signature. ## The curve, and the line it is read against A level on its own cannot be compared between rooms, because it depends on how loud the source was. Equation (1) works with the sound distribution value `D = L_p - L_W`, the level at a position referred to the sound power of the source that produced it. The free field is then known exactly: Equation (2) is `D_ref = 20 lg(r_0/r) - 11 dB` with `r_0 = 1 m`, where the 11 dB is `10 lg(4 pi r_0^2)` rounded. ```python from phonometry import room distances = [2.0, 3.0, 4.0, 5.0, 6.0, 8.0, 12.0, 16.0, 24.0, 32.0, 48.0] levels = [98.9, 95.1, 93.0, 92.0, 91.0, 87.9, 85.8, 83.5, 81.5, 77.0, 75.6] d = room.sound_distribution_value(levels, 110.8) print(d[:3].round(1)) # [-11.9 -15.7 -17.8] print(room.reference_distribution_value([2.0, 4.0]).round(2)) # [-17.02 -23.04] ``` ## Two descriptors, and what each is for DL2, Equation (5), is the slope: the least-squares fit of `D` against `lg r`, converted from a decade to a doubling and signed so a decay is positive. A free field gives 6 dB and any room gives less. DLf, Equations (6) to (8), is the height: how far above open air the room sits. A room can decay steeply and still be loud, so the two do not substitute for each other. ```python res = room.spatial_decay_curve(d, distances, region="middle", far_limit_m=24.0) print(round(res.decay_rate_db, 2)) # 4.73 dB per doubling print(round(res.mean_excess_db, 2)) # 7.33 dB ``` The ranges are clause 6.2: near from 1 m to `d1`, middle from `d1` to `d2`, far beyond `d2`, with 5 m and 16 m the typical pair and the middle range taken to 24 m whenever the room allows. ISO 11690-3, 4.3, says what to expect there: 2 dB to 5 dB per doubling and an excess of 2 dB to 10 dB. ## How the measurement goes Put the source where a machine would stand, with its acoustical centre on the floor or at least 0,5 m above it, and at least 3 m from any wall or other reflecting object. Check the margin over the background at every position and in every one of the six octave bands from 125 Hz to 4 kHz: 10 dB or more needs no correction, between 6 dB and 10 dB takes the ISO 3744 correction, and under 6 dB there is no measurement. Walk the path from the source outwards at 1,55 m for a standing workplace or 1,2 m for a seated one, with no obstacle on the floor below it and nothing large within 1,5 m of either side, taking a band spectrum at each of the distances 5.3.2 recommends, measured from the acoustical centre. Stop the last point 1,5 m short of any wall, then walk a second path at right angles if the room allows it. The source has to qualify first: Annex A asks for a directivity index inside ± 2 dB up to 630 Hz, rising to ± 8 dB at 1 kHz. ```python print(room.omnidirectionality_tolerance_db(800.0)) # 5.0 ``` The margin over the background is a judgement the library will make for you, one octave band at a time, and it says which of the three cases each position falls in rather than correcting anything. A region holding exactly the two positions a regression needs, and a line read outside the distances it was fitted over, both emit `SpatialDecayWarning`. ```python check = room.check_background_margin([80.0, 70.0, 66.0], 60.0) print(check.unusable) # [False False True] ``` ## Taking the source's own curve back out Close to the source, much of what the microphone hears is the source's own directivity and the floor reflection under it. Annex B swaps the measured free-field curve of that source for the theoretical one of Equations (B.2) to (B.4), which for a source on the floor is the flat 3 dB of a half space. ```python free_field = [98.8, 94.7, 92.3, 90.3, 88.7, 86.1, 82.6, 79.8, 75.7, 73.7, 67.8] reference = room.sound_distribution_value(free_field, 110.8) corrected = room.corrected_distribution_value(d, reference, distances) fixed = room.spatial_decay_curve(corrected, distances, region="middle", far_limit_m=24.0) print(round(fixed.decay_rate_db, 2)) # 4.39 dB per doubling print(round(fixed.mean_excess_db, 2)) # 6.73 dB ``` Annex C prints 4,4 dB per doubling, which is the corrected figure, and 7,3 dB of excess, which is the uncorrected one. Applying the correction to one descriptor and not to the other cannot be right, and 28 of the 36 printed results leave their own rounding if the two are swapped; the entry is in [Errata](https://jmrplens.github.io/phonometry/reference/errata/). ## One number, and the design half Equation (3) weights the six bands by the spectrum of the machine that will stand there, and Equation (4) fixes that spectrum as A-weighted pink noise so two rooms can be compared without a machine in mind. ```python by_band = [-11.9, -13.6, -12.5, -11.9, -12.4, -13.6] # 125 Hz to 4 kHz print(round(room.normalized_distribution_value(by_band), 2)) # -12.58 ``` ISO 11690-3 sorts prediction into four categories, one diffuse-field and three geometrical, and pairs each with the detail it has to be fed. Table E.1 reads in both directions: a reader with a volume and one mean absorption coefficient is limited to the diffuse-field method, and ray tracing over the real shape needs a description gathered at that level first. ```python print(room.detail_is_sufficient("1", room_detail=3, fitting_detail=3, source_detail=1).satisfied) # False print(round(room.fitting_density(480.0, 1200.0), 2)) # 0.1 print(round(room.workstation_level(sound_power_level_db=95.0, emission_level_db=85.0, absorption_area_m2=200.0), 2)) # 85.79 ``` ## What this page does not cover Predicting the curve. ISO 11690-3 says what a prediction method must model and how much detail it needs; it prints none, and neither ray tracing nor radiosity is implemented here. Nor the reverberation-room calibration of the source, which is ISO 6926 and ISO 3741, nor the directivity survey of Annex A, which needs a turntable rather than a formula, nor the reporting checklist of clause 7. ## See also - [Open-plan office acoustics (ISO 3382-3)](https://jmrplens.github.io/phonometry/buildings/rooms/open-plan-acoustics/): the same shape of measurement asked about speech rather than machinery. - [Room acoustics](https://jmrplens.github.io/phonometry/buildings/rooms/room-acoustics/): what a room does to a decay in time. - [Image sources and the steady-state room field](https://jmrplens.github.io/phonometry/buildings/rooms/room-image-sources/): the room constant and the critical distance this measurement so often contradicts. - [Suspended ceilings (EN 16487)](https://jmrplens.github.io/phonometry/materials/absorbers/suspended-ceilings/): the product test code behind the absorption a workroom ceiling is sold on. - [Errata in published sources](https://jmrplens.github.io/phonometry/reference/errata/): the Annex C correction defect above, and the two constants of Equations (5) and (8) that differ by 0,3 %. - API reference: [`room.spatial_decay`](https://jmrplens.github.io/phonometry/reference/api/rooms/spatial-decay/) and [`room.workroom_prediction`](https://jmrplens.github.io/phonometry/reference/api/rooms/workroom-prediction/).