ISO 9613-2:2024

International
Standard
ISO 9613-2
Second edition
Acoustics — Attenuation of sound
2024-01
during propagation outdoors —
Part 2:
Engineering method for the
prediction of sound pressure levels
outdoors
Acoustique — Atténuation du son lors de sa propagation à l'air
libre —
Partie 2: Méthode d'ingénierie pour la prédiction des niveaux de
pression acoustique en extérieur
Reference number
© ISO 2024
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ii
Contents Page
Foreword .iv
Introduction .vi
1 Scope . 1
2 Normative references . 2
3 Terms, definitions, symbols and units . 2
3.1 Terms and definitions .2
3.2 Symbols and units .3
4 Source description . 4
5 Meteorological conditions . 6
6 Basic formulae . 7
7 Calculation of the attenuation terms . 8
7.1 Geometric divergence, A .8
div
7.2 Atmospheric absorption, A .9
atm
7.3 Ground attenuation, A .9
gr
7.3.1 General method of calculation .9
7.3.2 Simplified method of calculation for A-weighted sound pressure levels . 12
7.4 Screening, A . 13
bar
7.4.1 General method of calculation . 13
7.4.2 Alternative method to calculate the path length difference z with one edge or
with more parallel edges .17
7.4.3 Lateral diffraction around vertical edges .19
7.4.4 Combining vertical and lateral diffractions and limitations . 20
7.5 Reflections . 20
7.5.1 General . 20
7.5.2 Single reflection at a flat surface – conditions and calculation . 20
7.5.3 Multi-reflection up to higher orders .21
7.5.4 Reflections at cylindrical surfaces . 22
8 Meteorological correction, C .23
met
9 Accuracy and limitations of the method .25
Annex A (informative) Additional types of attenuation, A .27
misc
Annex B (informative) Directivity correction, D, for chimney stacks .34
c
Annex C (informative) Meteorological correction due to the dependency of C from the angular
wind distribution .38
Annex D (informative) Calculation of sound pressure levels caused by wind turbines .42
Bibliography .45

iii
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
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with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO document should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
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This document was prepared by Technical Committee ISO/TC 43, Acoustics, Subcommittee SC 1, Noise.
This second edition cancels and replaces the first edition (ISO 9613-2:1996), which has been technically
revised.
The main changes are as follows:
— subdivision of extended sources improved (more detailed to decrease uncertainty with software
implementations);
— improved classification of the source-directivity;
— improved and more detail specified in the determination of the ground factor G (projection to horizontal
plane);
— integration of a correction for A to account for the decreasing ground effect for small values of distance/
gr
height – harmonizing the General method 7.3.1 and the Simplified method 7.3.2;
— modified definition of the mean height h for the application of the Simplified method 7.3.2;
m
— integration of the strategy to calculate screening as it was developed with ISO/TR 17534-3;
— modified specification of the barrier attenuation D and the correction for meteorological effects K to
z met
eliminate well known shortcomings with low barriers and large source-to-receiver distances;
— inclusion of clear specifications on how to combine vertical and lateral diffraction (from ISO/TR 17534-3);
— improved specification of the minimal extension (width or height) of a reflecting surface;
— multi-reflections up to higher orders (in accordance with ISO/TR 17534-3);
— reflections at vertical cylindrical surfaces;

iv
— additional to the simple method for the attenuation of foliage without any parameter dependencies of the
old version ISO 9613-2:1996, A.2.2, a new and more detailed method including the influence of forestal
parameters (see A.2.3);
— the directivity correction D for chimney stacks (see Annex B);
c
— proposal for a meteorological correction derived from the local wind-climatology (see Annex C);
— calculation of sound pressure levels caused by wind turbines (see Annex D).
A list of all parts in the ISO 9613 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

v
Introduction
[1][2][3]
The ISO 1996 series of standards specifies methods for the description of noise outdoors in community
environments. Other standards specify methods for determining the sound power levels emitted by
[4]
various noise sources, such as machinery and specified equipment (ISO 3740 series ), or industrial plants
[5]
(ISO 8297 ). This document is intended to bridge the gap between these two types of standards, to enable
noise levels in the community to be predicted from sources of known sound emission. The method described
in this document is general in the sense that it may be applied to a wide variety of noise sources and covers
most of the major mechanisms of attenuation. There are, however, constraints on its use, which arise
principally from the description of environmental noise in the ISO 1996 series.
This version includes the modifications developed for reasons of quality assurance if the method is
[6] [7]
implemented in software as described in ISO 17534-1 and ISO/TR 17534-3 and some improvements to
make the applied strategy fit for broad software-based application.

vi
International Standard ISO 9613-2:2024(en)
Acoustics — Attenuation of sound during propagation
outdoors —
Part 2:
Engineering method for the prediction of sound pressure
levels outdoors
1 Scope
This document specifies an engineering method for calculating the attenuation of sound during propagation
outdoors in order to predict the levels of environmental noise at a distance from a variety of sources. The
method predicts the equivalent continuous A-weighted sound pressure level (as described in ISO 1996-series)
under meteorological conditions favourable to propagation from sources of known sound emission.
These conditions are for downwind propagation or, equivalently, propagation under a well-developed
moderate ground-based temperature inversion, such as commonly occurs in clear, calm nights. Inversion
conditions over extended water surfaces are not covered and may result in higher sound pressure levels
than predicted from this document (see e.g. References [11] and [12]).
The method also predicts a long-term average A-weighted sound pressure level as specified in ISO 1996-1
and ISO 1996-2. The long-term average A-weighted sound pressure level encompasses levels for a wide
variety of meteorological conditions.
Guidance has been provided to derive a meteorological correction based on the angular wind distribution
relevant for the reference or long-term time interval as specified in ISO 1996-1:2016, 3.2.1 and 3.2.2.
Examples for reference time intervals are day, night, or the hour of the night with the largest value of the
sound pressure level. Long-term time intervals over which the sound of a series of reference time intervals is
averaged or assessed representing a significant fraction of a year (e.g. 3 months, 6 months or 1 year).
The method specified in this document consists specifically of octave band algorithms (with nominal mid-
band frequencies from 63 Hz to 8 kHz) for calculating the attenuation of sound which originates from a point
sound source, or an assembly of point sources. The source (or sources) may be moving or stationary. Specific
terms are provided in the algorithms for the following physical effects:
— geometrical divergence;
— atmospheric absorption;
— ground effect;
— reflection from surfaces;
— screening by obstacles.
Additional information concerning propagation through foliage, industrial sites and housing is given in
Annex A. The directivity of chimney-stacks to support the sound predictions for industrial sites has been
included with Annex B. An example how the far-distance meteorological correction C can be determined
from the local wind-climatology is given in Annex C. Experiences of the last decades how to predict the
sound pressure levels caused by wind turbines is summarized in Annex D.
The method is applicable in practice to a great variety of noise sources and environments. It is applicable,
directly, or indirectly, to most situations concerning road or rail traffic, industrial noise sources, construction

activities, and many other ground-based noise sources. It does not apply to sound from aircraft in flight, or
to blast waves from mining, military, or similar operations.
To apply the method of this document, several parameters need to be known with respect to the geometry of
the source and of the environment, the ground surface characteristics, and the source strength in terms of
octave band sound power levels for directions relevant to the propagation.
If only A-weighted sound power levels of the sources are known, the attenuation terms for 500 Hz may be
used to estimate the resulting attenuation.
The accuracy of the method and the limitations to its use in practice are described in Clause 9.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 9613-1:1993, Acoustics — Attenuation of sound during propagation outdoors — Part 1: Calculation of the
absorption of sound by the atmosphere
3 Terms, definitions, symbols and units
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1.1
A-weighted equivalent continuous sound pressure level
L
AT
sound pressure level defined by Formula (1):
T
  
   
2 2
 
L =10lg pt()ddtp/ B (1)
   
AAT 0
∫
T  
 
 0  
where
p (t) is the instantaneous A-weighted sound pressure, expressed in pascals;
A
-6
p is the reference sound pressure (= 20 × 10 Pa);
T is a specified time interval, expressed in seconds
[10]
Note 1 to entry: The A-frequency weighting is that specified for sound level meters in IEC 61672-1 .
Note 2 to entry: The time interval T should be long enough to average the effects of varying meteorological parameters.
Two different situations are considered in this document, namely short-term downwind and long-term overall
averages.
3.1.2
equivalent continuous downwind octave band sound pressure level
L (DW)
fT
sound pressure level is given as follows:
T
  
 
  2 2
 
L ()DW =10lg pt()ddtp/ B (2)
   
fT f 0
∫
T 
 
 
 0  
where p (t) is the instantaneous octave band sound pressure downwind, in pascals, and the subscript f
f
represents a nominal mid-band frequency of an octave band filter
Note 1 to entry: The electrical characteristics of the octave band filters should comply at least with the class 2
[8]
requirements of IEC 61260-1 .
3.1.3
insertion loss (of a barrier)
difference between the sound pressure levels in decibels at a receiver in a specified position under two
conditions:
a) with the barrier removed; and
b) with the barrier present (inserted);
and no other significant changes that affect the propagation of sound
Note 1 to entry: The insertion loss is expressed in decibels.
3.2 Symbols and units
Table 1 provides a summary of symbols and units.
Table 1 — Symbols and units
Symbol Definition Unit
a component distance parallel to the barrier edge between source and receiver m
A octave band attenuation dB
A attenuation due to atmospheric absorption dB
atm
A attenuation due to a barrier, including possible correction dB
bar
A attenuation due to geometrical divergence dB
div
A attenuation due to reflection at a cylindrical surface dB
curv
A attenuation due to the ground effect dB
gr
A middle region —
m
A attenuation due to miscellaneous other effects dB
misc
C meteorological correction dB
met
C factor, which depends on local meteorological statistics for wind speed and direction, and dB
temperature gradients
d distance from point source to receiver projected onto the ground plane (see Figure 3) m
p
d distance between source and point of reflection on the reflecting obstacle (see Figure 13) m
S,O
d distance between point of reflection on the reflecting obstacle and receiver (see Figure 13) m
O,R
D directivity correction dB
c
D barrier attenuation dB
z
D apparent large-distance directivity dB
wd
e distance between the first and last diffraction edge m
G ground factor —
TTaabbllee 11 ((ccoonnttiinnueuedd))
Symbol Definition Unit
h height of point source above ground m
S
h height of receiver above ground m
R
h mean height of the propagation path above the ground m
m
k raster factor —
K correction factor for geometry —
geo
L sound pressure level dB
p
L (DW) equivalent continuous A-weighted downwind sound pressure level dB
AT
L (LT) long-term average A-weighted sound pressure level dB
AT
L (DW) equivalent continuous downwind octave band sound pressure level dB
fT
at a receiver location
L sound power level dB
W
α atmospheric attenuation coefficient dB/km
atm
α absorption coefficient —
β angle of incidence rad
β angle of incidence projected to the horizontal plane rad
b
β angle of incidence projected to a vertical plane rectangular to the reflecting surface rad
h
λ wavelength of sound m
4 Source description
Formulae to be used are for the attenuation of sound from point sources.
Extended noise sources, therefore, such as road and rail traffic or an industrial site (which may include
several installations or plants, together with traffic moving on the site) shall be broken down into small
sections that can be replaced by a central point source as starting point for the calculation of sound
propagation, see Figure 1. This subdivision shall be chosen in such a way that the propagation conditions
from each point of a section to the receiver can be considered representative. If no acoustically opaque
objects block the direct path between any point of a section and the receiver, the propagation conditions
shall be considered representative if no extent of the section is larger than the distance of its centre from the
receiver multiplied by the raster factor k. A well proven value for the factor k is 0,5.
Key
R receiver
Figure 1 — Principle of subdivision for a line source
If buildings, barriers or other screening objects are located between the extended source and the receiver,
the subdivision of the source is made in such a way that all points of a section are either screened or not
screened. The subsections can be separated by lines connecting the receiver with the edges of all facades or
with the two edges of each object forming the largest possible angle between them in 2D top view.

a) Line source
b) Area source
c) Area source (dark grey), partitioned in 5 sub-parts (light grey)
Key
1 projection lines
2 barriers
3 area source
Figure 2 — Projection method for line source and area source
The principle is shown with Figure 2 a) for a line source and Figures 2 b) and 2 c) for an area source. A
further subdivision is made if a sloping edge of a screening object is only partially blocking the direct view.
This subdivision caused by screening objects is called "projection method".
For line sources that are geometrically defined by successive polygon points the subdivision is performed in
three steps:
a) each polygon point is the edge point of one or two polygon elements;
b) if the direct propagation path is blocked by a screening object, a further subdivision is carried out by
applying the projection method;

c) finally, these resulting parts are further subdivided according to the distance criterion applying the
raster factor k.
Area sources are subdivided applying a similar strategy.
The area source is separated in convex shaped parts. These parts are subdivided further depending on the
receiver position and all screening objects (walls, buildings, and other objects). This is carried out by cutting
the subsections obtained in the first step by straight lines between receiver and edge-points of all screening
objects (producing smaller subsections of second order). Then it is checked if the individual sources of
each subsection meet the distance criterion. If not, they are subdivided further till the distance criterion is
fulfilled.
Similar as with extended sources, a group of point sources may be described by an equivalent point sound
source situated in the middle of the group, in particular if
a) the sources have approximately the same strength and height above the local ground, and
b) the same propagation conditions exist from the sources to the receiver, and
c) no extent of the group of point sources is larger than the distance of its centre from the receiver
multiplied by the raster factor k. A well proven value for the factor k is 0,5.
If the distance d is smaller (as expressed in c)) or if the propagation conditions for the component point
sources are different (e.g. due to screening), the total sound source shall be divided into its component point
sources.
NOTE In addition to the real sources described above, image sources will be introduced to describe the reflection
of sound from walls and ceilings (but not by the ground) as described in 7.5. Images of extended sources are
constructed taking into account the extension of all relevant reflectors between original source and receiver.
5 Meteorological conditions
Downwind propagation conditions for the method specified in this document are namely:
— wind direction within an angle of ±45° of the direction connecting the centre of the dominant sound
source and the centre of the specified receiver region, with the wind blowing from source to receiver,
and
— wind speed between approximately 1 m/s and 5 m/s, measured at a height of 3 m to 11 m above the
ground.
When applying this standard to wind turbines, higher wind speeds may be considered (see Annex D).
The formulae for calculating the equivalent continuous A-weighted downwind sound pressure level L (DW)
AT
in this document, including the formulae for attenuation given in Clause 7, are the average for meteorological
conditions within these limits. The term average here means the average over a short time interval.
These formulae also hold, equivalently, for average propagation under a well-developed moderate
ground-based temperature inversion, such as commonly occurs on clear, calm nights.
The long-term averaged A-weighted sound pressure level L (LT) can be determined by applying the
AT
meteorological correction described in Clause 8. It depends generally on the long-term variation of the
angular distribution of the horizontal wind speed and the effective vertical sound speed gradient. Owing to
this influence of the sound speed gradient the vertical gradients of the wind speed and the air temperature
may be important and should generally be considered.

6 Basic formulae
The equivalent continuous downwind octave band sound pressure level at a receiver location, L (DW), shall
fT
be calculated for each point source, and its image sources, and for the eight octave bands with nominal mid-
band frequencies from 63 Hz to 8 kHz from Formula (3):
LLDW =+DA− (3)
()
fT W c
where
L is the octave band sound power level produced by the point sound source relative to a reference
W
sound power of one picowatt (1 pW), expressed in decibels;
D is the directivity correction, in decibels, that describes the extent by which the equivalent continuous
c
sound pressure level from the point sound source deviates in a specified direction from the level of
an omnidirectional point sound source producing the sound power level L , expressed in decibels;
W
A is the octave band attenuation that occurs during propagation from the point sound source to the
receiver, expressed in decibels.
Sound power levels in Formula (3) can be determined from measurements, for example as described in the
ISO 3740 series (for machinery) or in ISO 8297 (for industrial plants).
NOTE 1 The letter symbol A (in italic type) signifies attenuation in this document except in subscripts, where it
designates the A-frequency weighting (in roman type).
The directivity correction D in connection with the sound power level L describes
c W
— the direction-dependent emission of the real source (case 1), or
— an apparent direction-dependent emission, resulting from reflecting structures near the source that
reduce the solid angle available for radiation (case 2).
In case 1 D is a necessary part of the source emission data for all directions relevant for the calculation at
c
receiver positions.
In case 2 the directivity D with an omnidirectional point source due to nearby reflecting surfaces is given
c
by Formula (4):
4π
 
D =10lg dB (4)
c  
Ω
 
where Ω is the solid angle remaining for radiation.
Table 2 gives values for the resulting directivity of an omnidirectional point source near reflecting surfaces.
Table 2 — Resulting directivity D of an omnidirectional point source near reflecting surfaces
c
Reflecting surface Solid angle Ω D
c
Configuration Number rad dB
Surface 1 4π/2 3
Edge 2 4π/4 6
Corner 3 4π/8 9
NOTE 2 Formula (4) and the values of D in Table 2 are based on the premise of the superposition of sound energies.
c
In case of distances of source-to-reflector smaller λ/4 coherent superposition will occur, the factor 10 in Formula (4)
and the values of D in Table 2 will increase up to twice the values given. However, an increase over the values shown is
c
only possible if the source can produce and radiate the additional sound power.

NOTE 3 In software-based calculations of the increase of sound pressure levels from an omnidirectional point
source caused by reflecting surfaces nearby a directivity D with Formula (4) or with values from Table 2 replaces the
c
calculation of reflections at these surfaces with image sources (see 7.5).
The attenuation term A in Formula (3) is given by Formula (5):
AA=+ AA++ AA+ (5)
divatm gr barmisc
where
A is the attenuation due to geometrical divergence, expressed in decibels (see 7.1);
div
A is the attenuation due to atmospheric absorption, expressed in decibels (see 7.2);
atm
A is the attenuation due to the ground effect, expressed in decibels (see 7.3);
gr
A is the attenuation due to a barrier, expressed in decibels (see 7.4);
bar
A is the attenuation due to miscellaneous other effects, expressed in decibels (see 7.5.4 and Annex A).
misc
General methods for calculating the first four terms in Formula (5) are specified in this document.
Information on four contributions to the last term A is given in Annex A (the attenuation due to the
misc
curvature of reflecting surfaces in 7.5.4, the attenuation due to propagation through foliage, industrial sites
and through regions built up of houses).
The equivalent continuous A-weighted downwind sound pressure level shall be obtained by summing the
contributing time-mean-square sound pressures calculated according to Formulae (3) and (5) for each point
sound source, for each of their image sources, and for each octave band, as specified by Formula (6):
n 8
  
01,,Li jA+ j 
 () () 
fT f
 
L DW =10lg  10  dB (6)
()
 
AT ∑ ∑
 
 
i=1 j=1
  
where
n is the number of contributions i (sources and paths);
j is an index indicating the eight standard octave mid-band frequencies from 63 Hz to 8 kHz;
A denotes the standard A-weighting (see IEC 61672-1).
f
The long-term average A-weighted sound pressure level L (LT) shall be calculated according to Formula (7).
AT
LL()LT = ()DW −C (7)
AATT met
where C is the meteorological correction described in Clause 8.
met
The calculation and significance of the various terms in Formulae (1) to (7) are explained in Clauses 7 and 8.
7 Calculation of the attenuation terms
7.1 Geometric divergence, A
div
The geometrical divergence accounts for spherical spreading in the free field from a point sound source,
making the attenuation, in decibels, equal to Formula (8):
Ad= 20lg /d +11 dB (8)
[]()
div 0
where
d is the distance from the source to receiver, expressed in metres;
d is the reference distance (= 1 m).
NOTE 1 The constant in Formula (8) relates the sound power level to the sound pressure level at a reference
distance d which is 1 m from an omnidirectional point sound source.
7.2 Atmospheric absorption, A
atm
The attenuation due to atmospheric absorption A , expressed in decibels, during propagation through a
atm
distance d, in metres, is given by Formula (9):
Ad=α /1000 (9)
atmatm
where α is the atmospheric attenuation coefficient for each octave band at the mid-band frequency,
atm
expressed in decibels per kilometre.
It shall be calculated with ISO 9613-1:1993, Formulae (2) to (6) in connection with ISO 9613-1:1993, B.1
to B.3. With ISO 9613-1:1993, Formula (6) the exact octave band related centre-frequencies are applied
(different to all other frequency dependent calculations based on the nominal and rounded octave band
centre-frequencies).
If no specific requirements are defined, default values should be defined related to representative conditions
for the investigated area.
NOTE For example, a temperature of 10 °C and a relative humidity of 70 % are typical default parameters applied
in some countries in Mid-Europe. The atmospheric attenuation coefficient depends strongly on the frequency of the
sound, the ambient temperature and relative humidity of the air, but only weakly on the ambient pressure.
For calculation of environmental noise levels, the atmospheric attenuation coefficient should be based on
average values determined by the range of ambient weather, which is relevant to the locality.
7.3 Ground attenuation, A
gr
7.3.1 General method of calculation
Ground attenuation, A , is mainly the result of sound reflected by the ground surface interfering with the
gr
sound propagating directly from source to receiver.
The downward-curving propagation path (downwind) ensures that this attenuation is determined primarily
by the ground surfaces near the source and near the receiver. This method of calculating the ground effect
is based on a scenario with ground, which is approximately flat, either horizontally or with a constant slope.
Three distinct regions for ground attenuation are specified (see Figure 3):
a) the source region, stretching over a distance from the source towards the receiver of 30 h , with a
S
maximum distance of d (h is the source height, and d the distance from source to receiver, as projected
p S p
on the ground plane);
b) the receiver region, stretching over a distance from the receiver back towards the source of 30 h , with
R
a maximum distance of d (h is the receiver height);
p R
c) a middle region, stretching over the distance between the source and receiver regions. If
d < (30 h + 30 h ), the source and receiver regions will overlap, and there is no middle region.
p S R
According to this scheme, the ground attenuation does not increase with the size of the middle region but is
mostly dependent on the properties of source and receiver regions.
The acoustical properties of each ground region are taken into account through a ground factor G.

If a region is characterized by N sections with length d and ground factor G for section n the ground factor
n n
of the region is given by Formula (10):
N N
GG()region = dd/ (10)
∑∑nn n
n==11n
The source, middle and receiver regions are projections to the horizontal reference plane.
Key
1 source region
2 middle region
3 receiver region
h height of point source above ground
S
h height of receiver above ground
R
Figure 3 — Three distinct regions for determination of ground attenuation
Three categories of reflecting surface are specified as follows:
a) Hard ground, which includes paving, water, ice, concrete, and all other ground surfaces having a low
porosity. Tamped ground, for example, as often occurs around industrial sites, can be considered hard.
For hard ground G = 0.
b) Porous ground, which includes ground covered by grass, trees or other vegetation, and all other ground
surfaces suitable for the growth of vegetation, such as farming land. For porous ground G = 1. For more
information, see e.g Reference [19].
c) Mixed ground, if the surface consists of both hard and porous ground, then G takes on values ranging
from 0 to 1, the value being the fraction of the region that is porous.
NOTE 1 Instead of the term “porous ground,” the term “absorbing ground” is used in some countries.
To calculate the ground attenuation for a specific octave band, first calculate the component attenuations A
S
for the source region specified by the ground factor G (for that region). Then calculate A for the receiver
S R
region specified by the ground factor G , and A for the middle region specified by the ground factor G ,
R m m
using the expressions in Table 3. (The functions a', b', c' and d' in Table 3 are shown as curves in Figure 4.)
The total ground attenuation for that octave band shall be obtained from Formulae (11), (12) and (13):
−A′
gr
   
AK=−10lg11+− 01⋅ dB (11)
gr geo
 
 
   
where
′
AA=+ AA+ (12)
gr SR m
dh+−()h
pS R
K = (13)
geo
dh++()h
pS R
h the height of the source above ground, expressed in metres;
S
h the height of the receiver above ground, expressed in metres;
R
d the distance source-to-receiver projected on the horizontal plane, expressed in metres
p
NOTE 2 Formula (10) characterizes the 2D-projected surface between source and receiver independent of screening
by elevated terrain or objects like buildings.
NOTE 3 Formula (11) with Formula (12) and (13) accounts for the vanishing ground influence if the distance d < h
p S
and/or d < h .
p R
Table 3 — Expressions to be used for calculating ground attenuation contributions A , A and A in
S R m
octave bands
a
Nominal midband frequency A or A A
S R m
Hz dB dB
b
63 −1,5 −3q
125 −1,5 + G × a'(h)
250 −1,5 + G × b'(h)
500 −1,5 + G × c'(h)
1 000 −1,5 + G × d’(h) −3q(1-G )
m
2 000
4 000 −1,5(1 - G)
8 000
NOTE
−d
p
 
−62
 −×28, 10 ×d 
−−01, 25()h −00, 9h
  p
′
ah()=+15,,30×−ee15+×,e71−−e
 
 
 
 
 
−d
p
 
−00, 9h
 
′
bh()=+15,,86×−ee1
 
 
 
−d
p
 
−04, 6h
 
′
ch()=+15,,14 01×−ee
 
 
 
−d
p
 
−09, h
 
′
dh()=+15,,50×−ee1
 
 
 
a
For calculating A , take G = G and h = h . For calculating A , take G =G and h = h . See 7.3.1 for values of G for various ground
S S S R R R
surfaces.
b
q= 0 when d ≤ 30(h + h )
p S R
30()hh+
SR
q =−1 when dh>+30()h
pS R
d
p
where d is the source-to-receiver distance, in metres, projected onto the ground plane.
p
Key
d distance source-to-receiver projected on the horizontal plane, expressed in metres
p
Figure 4 — Functions a', b', c' and d' representing the influence of the source-to-receiver distance d
p
and the source or receiver height h, respectively, on the ground attenuation A (computed from
gr
Formulae in Table 3)
7.3.2 Simplified method of calculation for A-weighted sound pressure levels
The ground influence calculated with the simplified method is independent from the observable ground
cover and its acoustic properties.
Under the following specific conditions and for ground surfaces of any shape, the ground attenuation can be
calculated from Formula (14):
— only the A-weighted sound pressure level at the receiver position is of interest;
— the sound propagation occurs over porous ground or mixed ground most of which is porous (see 7.3.1);
— the sound is not a pure tone.
2h
   
m
A =−48, 17+ ≥0dB (14)
 
gr  
 
dd
  
 
where
h is the mean height of the propagation path above the ground, expressed in metres;
m
d is the distance from the source to receiver, expressed in metres.
The mean height h is evaluated by h = F/d , applying the method shown in Figure 5. Negative values for
m m g
A from Formula (14) shall be replaced by zeros.
gr
Key
1 ground profile
S source
R receiver
F is the area limited by the ground profile and the straight line from the source to the receiver;
d distance between source and receiver;
d is the distance between the base points of source and receiver;
g
h the height of the source above ground, expressed in metres;
S
h the height of the receiver above ground, expressed in metres;
R
Figure 5 — Method for evaluating the mean height h
m
When the ground attenuation is calculated using Formula (14), the directivity correction D in Formula (3)
c
shall include a term D in decibels, to account for the apparent increase in sound power level of the source
Ω
due to reflection from the ground without any reflection-loss.
DK=+10lg 1 dB (15)
()
Ω geo
K defined in Formula (13) is the correction for geometry due to distance-height relations.
geo
NOTE The influence of the ground relative to free-field propagation calculated with this simplified method is
comparable to that calculated with the “General method” described in 7.3.1 with reflecting ground (G = 0) near the
source and porous or vegetated ground (G = 1) in larger distances.
7.4 Screening, A
bar
7.4.1 General method of calculation
An object shall be taken into account as a screening obstacle (often called a barrier), if it meets the following
requirements:
— the surface density is at least 10 kg/m ;

— the object has a closed surface without large cracks or gaps (consequently process installations in
chemical plants, for example, are ignored);
— the horizontal dimension of the object normal to the source-to-receiver line is larger than the acoustic
wavelength, λ, at the nominal midband frequency for the octave band of interest (based on a reference
sound speed of 340 m/s); in other words, l + l > λ (see Figure 6).
l r
Each object that fulfils these requirements shall be represented by a barrier with vertical edges. The top
edge of the barrier is a straight line that may be sloping.
Key
S source
R receiver
l , l extention of the object to the left/right in the direction of propagation
l r
Figure 6 — Plan view of an obstacle between the source (S) and the receiver (R)
For the purposes of this document, the attenuation by a barrier, A , shall be given by the insertion loss.
bar
Diffraction over the top edge and around vertical edges of a barrier may both be important (see Figure 7).
For downwind sound propagation, the effect of diffraction (expressed in decibels) over top edges when
A > 0 shall be calculated by Formula (16):
gr
AD=−A >0 (16)
barz gr
and for diffraction around vertical edges or over top with A < 0 by Formula (17):
gr
AD=>0 (17)
barz
where
D is the barrier attenuation for each octave band;
z
A is the ground attenuation in the absence of the barrier (i.e. with the screening obstacle removed)
gr
(see 7.3).
...