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.

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.

See the Levels guide for usage.

A 24-hour LAeq profile split into day, evening and night, the +5/+10 dB penalties and the resulting Lden.

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):

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

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

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

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

See the Impulse Prominence guide for usage.

Outdoor propagation and occupational exposure (ISO 9613-1/2, ISO 9612)

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 $m=\alpha /(10\lg e)$, exposed as air_attenuation_m.

The ISO 9613-1 coefficient for the 20 °C, 50 % relative-humidity reference atmosphere: the f² rise spans two decades from 50 Hz to 10 kHz.

Outdoor propagation, general method (ISO 9613-2)

ISO 9613-2:1996 predicts the octave-band level at a receiver downwind of a point source (or the equivalent moderate temperature inversion) 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 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 long-term average level subtracts the meteorological correction $C_{met}$ (Eq. (6), (21)/(22)). The method’s stated accuracy is $\pm 1$ to $\pm 3$ dB for broadband noise up to 1000 m (Table 5).

Occupational noise exposure and uncertainty (ISO 9612)

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).

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).

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 of methods recover it.

The three routes to LW: 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. The surface area is 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 $a=0.5l_1+d$, $b=0.5l_2+d$, $c=l_3+d$. 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 $L_W={\bar{L}}_p+10\lg (S/S_0)+C_1+C_2+C_3$ (Eq. 14/15) over a full sphere $S=4\pi r^2$ or hemisphere $S=2\pi r^2$, with the background correction $K_{1i}=-10\lg (1-10^{-0.1\Delta L_{pi}})$ 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 $C_1=-10\lg (p_s/p_{s0})+5\lg [(273+\theta )/{\theta }_0]$ and $C_2=-10\lg (p_s/p_{s0})+15\lg [(273+\theta )/{\theta }_1]$ 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. Two normative field indicators gate validity: the surface pressure-intensity indicator $F_{pI}=[L_p]-L_W+10{\log }_{10}(S/S_0)$ (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.

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, $L_{W0}=L_W-15\lg [(B/101325)\cdot 296.15/(273.15+\theta )]$. 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 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. (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.