Environment and Transport

This page collects the theory behind outdoor and environmental noise: the whole-day rating descriptors and the impulsive-sound adjustment, atmospheric absorption, the general outdoor propagation method, occupational noise exposure with its uncertainty budget, and the sound power determination methods. It is part of the theory reference.

Each section keeps its own standard’s notation, and four letters are reused across them. Read them per section:

Symbol	In the propagation sections	In the sound-power sections
$A$	Octave-band attenuation, in dB (ISO 9613-2)	Equivalent absorption area of the room, in m²
$A_0$	—	Reference absorption area, 1 m²; except in the ISO 3745 air term, where $A_0=a(f)r$ is a dimensionless absorption product
$C_1$, $C_2$	Barrier constants in $D_z$ (ISO 9613-2)	Meteorological corrections (ISO 3745, ISO 3741)
$K$	—	$K_1$ background, $K_2$ reverberant field, $K_I$ impulse adjustment, and plain $K$ the bias-error factor of the intensity methods; $K_{met}$ is the ISO 9613-2 barrier meteorological factor

Environmental descriptors (ISO 1996-1)

The day-evening-night level $L_{den}$ (ISO 1996-1:2016, 3.6.4) is an energy average over the 24 h day with penalty weightings of +5 dB for the evening and +10 dB for the night:

$$L_{den}=10{\log }_{10}\left\{\frac{1}{24}\left[t_{d}10^{0.1L_{day}}+t_{e}10^{0.1(L_{evening}+5)}+t_{n}10^{0.1(L_{night}+10)}\right]\right\}$$

with default period durations $(t_d,t_e,t_n)=(12,4,8)$ h; countries may define the periods differently (3.6.4 Note 1). The day-night level $L_{dn}$ (3.6.5) drops the evening period:

$$L_{dn}=10{\log }_{10}\left\{\frac{1}{24}\left[t_{d}10^{0.1L_{day}}+t_{n}10^{0.1(L_{night}+10)}\right]\right\},(t_d,t_n)=(15,9)\text{h}$$

Both are special cases of the composite whole-day rating level (6.5, generalizing Formulae 5–6), where each period $i$ contributes its rating level $L_i$ plus an adjustment $K_i$, weighted by its share of the day:

$$L_R=10{\log }_{10}\left[\sum _i\frac{h_i}{24}10^{0.1(L_i+K_i)}\right],\sum _i{h}_i=24\text{h}$$

The adjustments $K_i$ cover time-of-day penalties (ISO 1996-1 Table A.1: evening 5 dB, night 10 dB) as well as source-character adjustments (e.g. tonal penalties), which the ECMA-418-1 TNR/PR assessments can justify objectively.

What the penalties are, and what the number means. The +5 and +10 dB are not physics: nothing about the sound changes at 19:00. They encode a dose-response finding — the same acoustic energy is reported as more annoying when it interrupts an evening at home or a night’s sleep — so $L_{den}$ is an annoyance indicator built out of acoustic levels and must never be read back as one. On the scale it lives on, a rural night sits in the 40s, a quiet residential street in the mid-50s and a façade on a busy urban arterial in the high 60s, and the Environmental Noise Directive reports strategic maps in 5 dB $L_{den}$ bands from 55 dB upward. The weighting also decides where a mitigation is worth applying: an hour of night enters with $10\times 8/24$ against the day’s $12/24$, so a decibel bought at night is worth about 6.7 times a decibel bought during the day — but only once the night is loud enough to matter, and the crossover is arithmetic. The night term overtakes the day term when the night level comes within about 8 dB of the day level; in the profile below the night is 14.4 dB below the day, so it contributes only 12.5 % of the total against the day’s 51.3 %, and 3 dB off the day moves $L_{den}$ by 1.3 dB where 3 dB off the night moves it by 0.3 dB. Check the split before choosing where to spend.

See the Environmental Levels guide for usage.

A 24-hour $L_{Aeq}$ profile split into day, evening and night, the +5/+10 dB penalties and the resulting $L_{den}$ of 64.3 dB — an urban arterial façade, squarely inside the range the Directive maps. The day averages 64.4 dB, the evening 62.6 dB and the night 50.0 dB; the penalties lift the evening and night lines above their own levels, and $L_{den}$ still lands within 0.1 dB of the day, because a night that quiet cannot move it.

Impulsive-sound prominence (NT ACOU 112)

An impulse annoys beyond its energy, so environmental surveys after ISO 1996-2 penalize periods containing prominent impulsive sounds; NT ACOU 112:2002 makes that penalty objective. From the A-weighted, time-weighting-F level history of a single event, the onset rate (dB/s) and the level difference (dB) of the onset (which qualifies when steeper than 10 dB/s, clauses 4.5–4.7) predict the perceived prominence (clause 7, Formula 1):

$$P=3{\log }_{10}(\text{onset rate})+2{\log }_{10}(\text{level difference}),$$

designed to peak around 15 for very sudden, loud impulses.

Both inputs of $P$ are geometry on this trace, which is why the method needs a level history and not a level. The onset rate is the slope of the fitted line through the rise, in dB/s, and the qualifying threshold of 10 dB/s is a steepness on this axis; the level difference is the height of the same rise. Three strikes are detected here and only the steepest-and-tallest one governs the adjustment.

The adjustment to the measurement-period level takes the governing (highest-$P$) impulse (clause 8, Formula 2):

$$K_I=1.8(P-5)\text{dB}(P>5;\text{else }{K}_I=0),$$

and the whole-day rating level combines the adjusted periods energetically (clause 8, Note 1):

$$L_{Ar,T}=10{\log }_{10}\left[\frac{1}{T}\sum _N\Delta t_{N}10^{(L_{Aeq,N}+K_{I,N})/10}\right].$$

$K_I$ is exactly the kind of source-character adjustment that enters the ISO 1996-1 composite rating level above. The anchors $P(1000\text{dB/s},30\text{dB})=9+2{\log }_{10}30=11.95$ and $K_I(P=10)=9.0$ dB are reproduced exactly.

Which document to cite. ISO has since published the same construction as ISO/PAS 1996-3:2022, so a survey report may cite either; the prominence $P$ and the adjustment $K_I$ implemented here follow the NT ACOU 112 formulation that the PAS reproduces. What requires an adjustment at all is ISO 1996-2:2017, the measurement part — the objective procedure only decides how large the adjustment is, and it is ISO 1996-1 that then combines the adjusted periods into a rating level.

See the Impulse Prominence guide for usage.

Outdoor propagation (ISO 9613-1/2)

Atmospheric absorption (ISO 9613-1)

Air is a lossy medium: a propagating tone loses energy to shear viscosity and heat conduction (classical and rotational losses, growing as $f^2$) and to the vibrational relaxation of the oxygen and nitrogen molecules, each an energy reservoir that resonates near a humidity- and temperature-dependent relaxation frequency. ISO 9613-1:1993, Eq. (5) gives the pure-tone attenuation coefficient $\alpha$ in decibels per metre:

$$\alpha =8.686f^2[1.84\times 10^{-11}(p_a/p_r{)}^{-1}(T/T_0{)}^{1/2}+(T/T_0{)}^{-5/2}(0.01275\frac{e^{-2239.1/T}}{f_{rO}+f^2/f_{rO}}+0.1068\frac{e^{-3352.0/T}}{f_{rN}+f^2/f_{rN}})],$$

with the oxygen and nitrogen relaxation frequencies $f_{rO}$, $f_{rN}$ of Eq. (3)/(4), the reference conditions $T_0=293.15$ K, $p_r=101.325$ kPa (Clause 4.2) and the molar water-vapour concentration $h$ from the relative humidity (Annex B). At low frequency $\alpha \propto f^2$; near each relaxation frequency the corresponding term peaks and rolls off, which is why $\alpha$ rises by two decades from 50 Hz to 10 kHz and why raising the humidity sweeps a peak across the band. The library reproduces Table 1 to under 0.4 % (the standard’s own printed precision), well inside its stated $\pm 10$ %; passing exact_midband=True snaps each frequency onto the exact midbands $f_m=1000\cdot 10^{k/10}$ (Note 5) used to compute that table. The same $\alpha$ is the only route to the ISO 354 power attenuation coefficient $m=\alpha /(10{\log }_{10}e)$, exposed as air_attenuation_m.

That $\pm 10$ % is not unconditional. Table 1 is tabulated from 50 Hz to 10 kHz, −20 to +50 °C and 10 to 100 % relative humidity at one atmosphere, and the $\pm 10$ % accuracy is claimed only for molar water-vapour concentrations between 0.05 % and 5 % with the temperature between 253 and 323 K (Clause 7.1); outside that humidity window it degrades to about $\pm 20$ % (7.2) and below $h=0.005$ % to about $\pm 50$ % (7.3). Because $\alpha$ multiplies path length, that percentage becomes a level error that grows with distance: the same $\pm 20$ % on a coefficient of 30 dB/km is $\pm 0.2$ dB at 30 m and $\pm 6$ dB at a kilometre, which is why atmospheric absorption is usually the largest single uncertainty in a long-range prediction and why a measured humidity is worth more than a carefully measured temperature — the relaxation frequencies move with humidity, so the attenuation in a given band is far more sensitive to it. Interpolating the printed table is expressly discouraged (Clause 6.4); the equations, which is what the library evaluates, are the intended route.

The ISO 9613-1 coefficient for the 20 °C, 50 % relative-humidity reference atmosphere: the $f^2$ rise spans two decades from 50 Hz to 10 kHz.

The humidity claim of the paragraph above, drawn: four atmospheres, and a spread far wider than the $\pm 10$ % claimed for any one of them. At 2 kHz the coefficient is 9.9 dB/km at the 20 °C / 50 % reference and 45.5 dB/km at the same temperature and 10 % humidity — a factor 4.6 from humidity alone, worth 36 dB over a kilometre. Note which way it goes: drying the air increases the mid-band attenuation, because the oxygen relaxation frequency falls with humidity and drags its peak down into the band. Temperature moves the curves far less: 0 °C at 70 % and 20 °C at 50 % differ by 0.02 dB/km at 1 kHz.

Outdoor propagation, general method (ISO 9613-2)

ISO 9613-2:1996 predicts the octave-band level at a receiver under downwind propagation — a light wind blowing from source to receiver, or the moderate ground-based temperature inversion that bends rays the same way (clause 5) — as $L_{fT}(DW)=L_W+D_c-A$ (Eq. (3)), where $D_c$ is the directivity correction and $A$ is the octave-band attenuation, a sum of independent physical mechanisms (Eq. (4)):

$$A=A_{div}+A_{atm}+A_{gr}+A_{bar}+A_{misc}.$$

The four terms at their true relative sizes, band by band, for a 200 m path over porous ground with a 4 m barrier. $A_{div}$ is 57 dB in every band because it is pure geometry. $A_{atm}$ is nothing at 63 Hz and 18.7 dB at 8 kHz, so it is the term that decides how far high frequencies travel and no other. $A_{gr}$ is where the low bands live and is negative at 63 Hz (−4.6 dB: the ground reflection adds energy rather than removing it). $A_{bar}$ is at its 20 dB cap from 2 kHz up but falls to zero at 250 Hz, because the top-edge form subtracts the ground effect the screened path gives away, $A_{bar}=D_z-A_{gr}\ge 0$, and 250 Hz is exactly where $A_{gr}$ peaks. Which term is worth refining depends entirely on the band and the geometry.

The library implements the four general terms of Clause 7; the informative $A_{misc}$ (foliage, industrial sites, housing) and reflections are left to the caller. Geometrical divergence is spherical spreading from a point source, $A_{div}=20{\log }_{10}(d/d_0)+11$ dB with $d_0=1$ m (Eq. (7)): exactly 51 dB at 100 m, +6 dB per distance doubling. Atmospheric absorption is $A_{atm}=\alpha d$ (Eq. (8)) with $\alpha$ the ISO 9613-1 coefficient above. Ground effect $A_{gr}=A_s+A_r+A_m$ (Eq. (9)) sums a source, receiver and middle region, each evaluated from the Table 3 functions $a^{\prime }/b^{\prime }/c^{\prime }/d^{\prime }$ and its ground factor $G$ (0 hard, 1 porous); a negative $A_{gr}$ denotes a net gain from the ground reflection. An alternative A-weighted-only form $A_{gr}=4.8-(2h_m/d)[17+300/d]\ge 0$ (Eq. (10)) is offered for porous ground when only the A-weighted level matters, paired with the solid-angle index $D_{\Omega }$ (Eq. (11)). Screening by a barrier is the diffraction insertion loss

$$D_z=10{\log }_{10}[3+(C_2/\lambda )C_{3}z{K}_{met}]\text{dB},$$

(Eq. (14)) with $C_2=20$ (or 40 when ground reflections are handled by image sources), $C_3=1$ for a single edge or Eq. (15) for a double edge, the path-length difference $z=d_{ss}+d_{sr}-d$ (Eq. (16)/(17)), wavelength $\lambda =340/f$ and the meteorological factor $K_{met}$ (Eq. (18)); $D_z$ is capped at 20 dB (single) or 25 dB (double). For a top-edge barrier the ground effect of the screened path is folded into the screening term, $A_{bar}=D_z-A_{gr}\ge 0$ (Eq. (12), Note 13); for a lateral (vertical-edge) barrier $A_{bar}=D_z$ and the ground term is kept (Eq. (13)). (The standard fixes $\lambda =340/f$ inside the screening term rather than deriving $c$ from the temperature, so the barrier attenuation is temperature-independent by construction; the atmospheric-absorption term above is not.) The long-term average level subtracts the meteorological correction $C_{met}$ (Eq. (6), (21)/(22)).

Where the method applies, and what counts as a barrier. It is defined for the eight nominal octave midbands from 63 Hz to 8 kHz and for point sources, an extended source being decomposed into point sub-sources (clauses 4–5), so a one-third-octave chain or a 31.5 Hz band is outside it. It predicts the downwind level; an upwind or crosswind situation is reached only through the long-term correction $C_{met}$, never by evaluating Eq. (3) directly. The A-weighted-only ground form of Eq. (10) carries two further conditions of its own: porous or mostly porous ground, and a sound that is not a pure tone. And an object earns a $D_z$ only if it qualifies as a barrier under clause 7.4 — a surface density of at least 10 kg/m², a closed surface with no large gaps, and a horizontal dimension normal to the source-receiver line greater than the wavelength — so a slatted fence, a hedge or a wall the sound simply passes around is modelled as no barrier at all, not as a weak one. Crediting one is worth many decibels of error in the wrong direction. Finally, Table 5 gives the accuracy by geometry rather than as one range: about $\pm 1$ dB only for a mean source-receiver height between 5 and 30 m at distances under 100 m, and about $\pm 3$ dB in every other case within 1000 m, with no accuracy stated beyond 1000 m, where the method is an extrapolation.

Occupational noise exposure (ISO 9612)

The quantity itself, $L_{EX,8h}$, is defined from sound exposure in Signal Analysis; this section is about measuring it in a workplace and bounding its uncertainty.

ISO 9612:2009 is the engineering method (accuracy grade 2) for a worker’s daily noise exposure level $L_{EX,8h}$, normalised to a nominal 8 h day. Three measurement strategies trade effort for representativeness. The task-based method (Clause 9) splits the day into tasks, energy-averages $I\ge 3$ samples per task (Eq. 7) and sums the task contributions $L_{EX,8h,m}=L_{p,A,eqT,m}+10{\log }_{10}(T_m/T_0)$ energetically (Eq. 9/10). The job-based method (Clause 10) energy-averages $N\ge 5$ random samples over a homogeneous exposure group (Eq. 11) and normalises the effective-day duration (Eq. 12); the full-day method (Clause 11) does the same arithmetic on whole-day measurements (Eq. 13).

Where the microphone goes. With a sound level meter the preferred position is the worker’s head position with the worker absent — in the centre plane of the head, on a line with the eyes and with the microphone axis parallel to the direction of view — and where the worker must be present, at 0.1 m to 0.4 m from the entrance of the external ear canal on the side of the more exposed ear (clause 12.4). A body-worn personal sound exposure meter has its microphone on top of the shoulder, at least 0.1 m from the ear-canal entrance on the more exposed side and about 0.04 m above the shoulder, with microphone and cable fastened so that clothing and handling cannot fake a result (12.3). A field calibration is performed before and after each series, and a drift above 0.5 dB discards the series (12.2). That geometry is what the $u_3=1.0$ dB below buys: it is not a property of the instrument but the price of the position, and in the job and full-day budgets it is usually the second-largest term after the sampling spread — so a position taken loosely does not merely widen the interval, it quietly voids the grade-2 claim.

The Annex C uncertainty budget is normative. The combined standard uncertainty is $u^2=\sum c_i^2{u}_i^2$ (C.1) and the expanded uncertainty is $U=ku$ with $k=1.65$ for a one-sided 95 % interval (Clause 14), so the reported upper limit is $L_{EX,8h}+U$. The task and job methods differ in an instructive way: the task noise-sampling uncertainty $u_{1a}$ divides the summed squared deviations by $I(I-1)$ (the standard error of the mean, Eq. C.6) whereas the job/full-day sampling uncertainty $u_1$ is the plain sample standard deviation with denominator $N-1$ (Eq. C.12), so the same spread contributes more in the job method (fewer, coarser samples). The task budget (Eq. C.3) adds the sensitivity coefficients $c_{1a}$ (Eq. C.4) and $c_{1b}$ (Eq. C.5) and an optional task-duration uncertainty $u_{1b}$ (Eq. C.7); the job/full-day budget (Eq. C.9) reads $c_1{u}_1$ from Table C.4 as a function of $(N,u_1)$ and adds the instrument uncertainty $u_2$ (Table C.5) and microphone-position uncertainty $u_3=1.0$ dB in quadrature. Peak levels $L_{p,Cpeak}$ are reported without an uncertainty: Annex C provides no method for them (Table C.5, Note 1). The three worked examples of Annexes D (task, $L_{EX,8h}=84.3$ dB, $U=2.7$ dB), E (job, $88.1$ dB, $3.8$ dB) and F (full-day, $90.1$ dB, $3.4$ dB) are reproduced to the standard’s printed precision: every intermediate of Annex E is digit-exact, and its final level differs only by the standard’s own pre-rounding of the effective-day level (see the Occupational Noise Exposure guide).

What the budget buys: the Annex D worked day, its three task contributions, the energy-summed $L_{EX,8h}$ and the band up to $L_{EX,8h}+U$ that the one-sided 95 % interval adds on top. The reported result is the pair, not the line — and with $U=2.7$ dB the upper limit sits 2.7 dB above the number, which is enough to cross an action value on its own.

See the Outdoor Propagation guide and the Occupational Noise Exposure guide for usage.

Sound power determination (ISO 3744/3745/3746, ISO 3741, ISO 9614-2/3)

The sound power level $L_W=10{\log }_{10}(P/P_0)$ ($P_0=1$ pW) is an emission quantity: unlike a pressure level it does not depend on the receiver distance or the room. Three families recover it, and the choice is dictated by the room available. Pressure over an enveloping surface in a free field above a reflecting plane assumes the intensity normal to that surface is the mean-square pressure divided by $\rho c$: ISO 3744 (engineering) and ISO 3746 (survey) below, and ISO 3745 (precision) when the room is anechoic. Pressure in a diffuse field turns the room’s own absorption into the calibration instead: ISO 3741. Intensity scanning measures the flux directly and needs no qualified room at all, at the price of a two-channel probe and the field indicators that police it: ISO 9614-2 (engineering) and ISO 9614-3 (precision).

The three routes to $L_W$: enveloping pressure surface, reverberation room and intensity scan.

Enveloping-surface pressure (ISO 3744/3746)

Over a reflecting plane the free-field relation is simply $L_W={\bar{L}}_p+10{\log }_{10}(S/S_0)$: the mean-square pressure averaged over an enveloping surface of area $S$, multiplied by $S$, is the radiated power. Two corrections restore that idealisation. Uncorrelated background noise adds its mean square to the source’s, so with the margin $\Delta L_p=L_{ST}-L_{bg}$ the source-only level is recovered by subtracting $K_1=-10{\log }_{10}(1-10^{-\Delta L_p/10})$ (from $p_{src}^2=p_{ST}^2(1-10^{-\Delta L_p/10})$). The reverberant field of a non-anechoic room adds a near-uniform energy density $4P/(Ac)$ to the direct $P/(Sc)$, so the surface level exceeds the free-field value by their ratio, $K_2=10{\log }_{10}(1+4S/A)$, with $A$ the room’s equivalent absorption area.

Neither correction is unconditional, and both gate the result. For $K_1$, ISO 3744 clause 8.2.3 sets a ladder on the margin: above 15 dB the correction is taken as zero, between 6 and 15 dB the formula applies, and below 6 dB it is capped at the value it reaches at 6 dB — 1.3 dB — and the reported power becomes an upper bound rather than a determination. (ISO 3746 uses the same shape with coarser A-weighted thresholds: 10 dB, 3 dB and a 3 dB cap.) The honest response to a 2 dB margin is a quieter time of day or a measurement surface closer to the source, not a larger correction. For $K_2$, it may be neglected below 0.5 dB, and the engineering method is valid only while $K_{2A}\le 4$ dB (7 dB for the ISO 3746 survey method, clause 4.3), so a room that returns 6 dB is not a correction to apply but a room to reject. And read the direction of $K_2$ carefully: it grows with $4S/A$, so enlarging the measurement surface makes the room correction worse, which is the opposite of the intuition most operators bring to it.

The surface is built on the reference box, the smallest right parallelepiped that just encloses the source, whose sides are $l_1$, $l_2$ and $l_3$; over one reflecting plane the characteristic dimension is $d_0=\sqrt{(l_1/2{)}^2+(l_2/2{)}^2+l_3^2}$ (clause 7.1). A hemispherical surface needs a radius $r\ge 2d_0$, at least 1 m (0.5 m for small products) and at most 16 m (7.2.3); a box surface needs a measurement distance $d\ge 0.25$ m, preferably 1 m (7.2.4) — that $d$ is the one in the formulas below. The area is then the closed form of the geometry: a hemisphere $S=2\pi r^2$ over one reflecting plane (halved and quartered for two and three planes), a one-plane box $S=4(ab+bc+ca)$ with $a=0.5l_1+d$, $b=0.5l_2+d$, $c=l_3+d$. The microphone positions are normative rather than free: Annex B tabulates equal-area coordinates on the hemisphere — Table B.1 for sources that may emit discrete tones, Table B.2 for broadband ones — of which the engineering grade uses 10 key positions over one reflecting plane (5 over two, 3 over three), with the survey method taking a reduced subset. measurement_positions() returns them scaled to the chosen radius, and plot_microphone_positions() draws the array before anything is measured. ISO 3746 (survey) shares the maths with looser criteria. The expanded uncertainty is $U=2\sqrt{{\sigma }_{R0}^2+{\sigma }_{omc}^2}$.

Precision grade in anechoic rooms (ISO 3745)

ISO 3745:2012 is the grade-1 (precision) sibling: a qualified anechoic or hemi-anechoic room removes the reverberant field, so there is no $K_2$ term and the corrections become meteorological. The power level is $L_W={\bar{L}}_p+10{\log }_{10}(S/S_0)+C_1+C_2+C_3$ (Eq. 14/15) over a full sphere $S=4\pi r^2$ or hemisphere $S=2\pi r^2$, with the background correction $K_{1i}=-10{\log }_{10}(1-10^{-0.1\Delta L_{pi}})$ applied per microphone position before the energy average (Eq. 11); no correction is needed above a 15 dB margin, and below 10 dB (250 Hz – 5 kHz) or 6 dB (edge bands) the correction is clamped and the result flagged as an upper bound (clause 9.4.2). The meteorological terms are $C_1=-10{\log }_{10}(p_s/p_{s0})+5{\log }_{10}[(273+\theta )/{\theta }_0]$ and $C_2=-10{\log }_{10}(p_s/p_{s0})+15{\log }_{10}[(273+\theta )/{\theta }_1]$ with ${\theta }_0=314$ K, ${\theta }_1=296$ K: at the 23 °C / 101.325 kPa reference $C_2=0$ exactly and $C_1=-0.128$ dB; and $C_3=A_0(1.0053-0.0012A_0{)}^{1.6}$ with $A_0=a(f)r$ restores the ISO 9613-1 air absorption over the measurement radius. The Annex D/E microphone arrays are built in as digit-exact coordinate tables (40 equal-area positions; the mirror set 21–40 is added when the band-SPL spread exceeds $N_M/2$, clause 9.3.2), and the same positions yield the directivity index $D{I}_i=L_{pi}-{\bar{L}}_p$ (Eq. 21). The clause 10.5 uncertainty example, $U=2\sqrt{0.5^2+2.0^2}=4.12$ dB, is reproduced, along with the Table 2/3 per-band ${\sigma }_{R0}$ values.

Reverberation room (ISO 3741)

In a qualified diffuse field the steady energy density $w=4P/(Ac)$ ties the power to the room absorption, giving $L_W={\bar{L}}_p+10{\log }_{10}(A/A_0)-6$ plus higher-order corrections, with $A=(55.26/c)(V/T_{60})$ and $c=20.05\sqrt{273+\theta }$. The Waterhouse correction $10{\log }_{10}(1+Sc/(8Vf))$ compensates the extra energy stored in the boundary layer that interior microphones miss ($Sc/(8Vf)=S\lambda /(8V)$, so it fades as frequency rises); the $4.34A/S$ term is the mean-free-path air correction, and $C_1$, $C_2$ carry the result to the reference meteorological conditions (23 °C, 101.325 kPa). The comparison method subtracts a reference source of known power measured in the same room, $L_W=L_{W(\text{RSS})}+({\bar{L}}_p-{\bar{L}}_{p,\text{RSS}}+C_2)$, so the absorption-area, Waterhouse and $C_1$ terms cancel and the room need not be characterised.

Intensity scanning (ISO 9614-2)

Sound intensity is the net energy flux $\vec{I}=\overline{p\vec{u}}$, so by the divergence theorem the power through a closed surface is $P={\sum }_i⟨I_{n,i}⟩S_i$. A steady source outside the surface contributes zero net flux (its energy enters and leaves), which is why intensity rejects stationary background noise, but it can still drive a band’s $P$ negative, in which case that band is not determinable.

What the indicators are judging. The surface is divided into at least four contiguous segments (clause 8.2) and each is swept continuously along parallel lines whose mean spacing does not exceed the mean distance from that segment to the source surface, with the probe axis held normal to the surface throughout (8.1). A manual sweep runs at 0.1 to 0.5 m/s (0 to 1 m/s mechanically) and lasts at least 20 s per segment; the segment stands at least 200 mm off an extended vibrating surface, or 100 mm off a small compact one (8.2). The engineering grade takes two sweeps per segment along orthogonal paths and records each separately (8.3.1), and it is the agreement between those two that the Table 2 repeatability criterion tests — which is why a failing band is far more often a scanning problem than an instrument problem. Two checks belong on site rather than in the calculation: a windscreen wherever a mean flow above 4 m/s cannot be ruled out (5.3), and the probe-reversal check of 6.2.2 — rotate the probe 180°, and the two indicated intensities must have opposite signs and differ by less than 1.5 dB in the maximum band, or the phase match has not survived the environment.

Two normative field indicators then gate validity: the surface pressure-intensity indicator $F_{pI}={\bar{L}}_p-L_W+10{\log }_{10}(S/S_0)$ (reactivity) and the negative-partial-power indicator $F_{+/-}=10{\log }_{10}({\sum }_i|P_i|/|{\sum }_i{P}_i|)$ (recirculation), together with the probe’s dynamic capability $L_d={\delta }_{pI0}-K$ ($K=10$ dB grade 2, 7 dB grade 3), which must exceed $F_{pI}$. A band earns the engineering grade when $L_d>F_{pI}$, $F_{+/-}\le 3$ dB and the two repeated sweeps agree within the Table 2 limit.

The same two indicators carry three sets of names across the ISO 9614 family: ISO 9614-1 calls them $F_2$ (pressure-intensity), $F_3$ (negative partial power) and $F_4$ (field non-uniformity); Part 2 writes $F_{pI}$ and $F_{+/-}$; Part 3 writes $F_{pIn}$ and $F_S$. Each subsection here uses its own part’s symbols. The $F_2$-to-$F_4$ naming is the one used in Sound intensity.

The gate as a picture rather than an inequality — drawn here in the ISO 9614-1 naming, $F_2$ for what Part 2 calls $F_{pI}$. The reactivity indicator climbs towards low frequency and crosses the dynamic-capability line at 125 Hz: that band fails, and no amount of averaging will rescue it, because the cause is the field near the surface and not the analyser. $F_3$ rising above $F_2$ in the same band reveals inward-flowing partial intensity, and the $F_4$ bars set how many positions the surface needs.

Precision intensity scanning (ISO 9614-3)

ISO 9614-3:2002 upgrades the scanning method to precision grade with a tighter indicator machinery. The partial powers $P_i=I_{n,i}{S}_i$ (Eq. 5) sum as before, but validity now rests on the signed and unsigned pressure-intensity indicators $F_{pIn}={\bar{L}}_p-L_{In}$ (Eqs. B.3/B.6, the F2/F3 of ISO 9614-1) and the normalized intensity non-uniformity $F_S$ (Eq. B.8), through five acceptance criteria (Annex C): scan repeatability $|L_{In}(1)-L_{In}(2)|\le s/2$ (C.1), dynamic capability $L_d={\delta }_{pI0}-K\ge F_{pIn}(\text{signed})$ with the precision bias-error factor $K=10$ dB (C.2), $F_{pIn}(\text{signed})-F_{pIn}(\text{unsigned})\le 3$ dB (C.3), $F_S\le 2$ (C.4) and the scan-density convergence $0.83\le F_S(1)/F_S(2)\le 1.2$ (C.5). Eq. 10 normalizes the result to the reference meteorological conditions, $L_{W0}=L_W-15{\log }_{10}[(B/101325)\cdot 296.15/(273.15+\theta )]$. Bands whose net power is negative are not determinable (clause 9.2) and are flagged. A uniform normal intensity recovers the power exactly (100 µW over 3.75 m² → 80.0 dB re 1 pW), independent of how the surface is segmented.

See the Sound Power guide for the choice of method, and the pressure, reverberation-room and intensity-scanning guides for usage.

References

• Attenborough, K., & Van Renterghem, T. (2021). Predicting outdoor sound (2nd ed.). CRC Press. https://doi.org/10.1201/9780429470806The ground impedance and meteorological effects underlying the ground-effect and barrier terms.
• Fahy, F. J. (1995). Sound intensity (2nd ed.). E&FN Spon. https://doi.org/10.4324/9780203475386ISBN 978-0-419-19810-9. The intensity physics behind the scanning methods: active intensity and the p-p error budget.
• International Organization for Standardization. (1993). Acoustics — Attenuation of sound during propagation outdoors — Part 1: Calculation of the absorption of sound by the atmosphere (ISO 9613-1:1993). The pure-tone attenuation coefficient and its relaxation physics.
• International Organization for Standardization. (1993). Acoustics — Determination of sound power levels of noise sources using sound intensity — Part 1: Measurement at discrete points (ISO 9614-1:1993). The field indicators and dynamic-capability criterion shared by the intensity-scanning methods.
• International Organization for Standardization. (1996). Acoustics — Attenuation of sound during propagation outdoors — Part 2: General method of calculation (ISO 9613-2:1996). The attenuation chain (divergence, air, ground, barrier) of the general-method section. Revised in 2024; the 1996 method is the implemented one.
• International Organization for Standardization. (2009). Acoustics — Determination of occupational noise exposure — Engineering method (ISO 9612:2009). The three measurement strategies and the Annex C uncertainty budget of the occupational section.
• International Organization for Standardization. (2010). Acoustics — Determination of sound power levels and sound energy levels of noise sources using sound pressure — Engineering methods for an essentially free field over a reflecting plane (ISO 3744:2010). The enveloping-surface method with its background and reverberant-field corrections.
• International Organization for Standardization. (2010). Acoustics — Determination of sound power levels and sound energy levels of noise sources using sound pressure — Precision methods for reverberation test rooms (ISO 3741:2010). The diffuse-field method with the Waterhouse correction and the comparison method.
• International Organization for Standardization. (2012). Acoustics — Determination of sound power levels and sound energy levels of noise sources using sound pressure — Precision methods for anechoic rooms and hemi-anechoic rooms (ISO 3745:2012). The precision anechoic method with its meteorological corrections and microphone arrays.
• International Organization for Standardization. (2016). Acoustics — Description, measurement and assessment of environmental noise — Part 1: Basic quantities and assessment procedures (ISO 1996-1:2016). The composite rating level and Table A.1 adjustments of the descriptors section.
• International Organization for Standardization. (2017). Acoustics — Description, measurement and assessment of environmental noise — Part 2: Determination of sound pressure levels (ISO 1996-2:2017). The survey standard that requires an adjustment for prominent impulsive sounds in the first place; the objective procedure only decides how large it is.
• International Organization for Standardization. (2022). Acoustics — Description, measurement and assessment of environmental noise — Part 3: Objective method for the measurement of prominence of impulsive sounds and for adjustment of LAeq (ISO/PAS 1996-3:2022). The ISO successor built on the NT ACOU 112 prominence.
• Maekawa, Z. (1968). Noise reduction by screens. Applied Acoustics, 1(3), 157-173. https://doi.org/10.1016/0003-682X(68)90020-0The screen-attenuation chart that the barrier insertion-loss formulas descend from.
• Nordtest. (2002). Acoustics: Prominence of impulsive sounds and for adjustment of LAeq (NT ACOU 112:2002). The onset-rate prominence and LAeq adjustment of the impulsive-sound section.
• Salomons, E. M. (2001). Computational atmospheric acoustics. Kluwer Academic Publishers. https://doi.org/10.1007/978-94-010-0660-6ISBN 978-1-4020-0390-5. The wave-based outdoor propagation theory behind the engineering approximations of the ISO 9613-2 section.