SIST EN ISO 5114-1:2024

SLOVENSKI STANDARD
01-september-2024
Akustika - Določanje negotovosti, povezane z meritvami zvočnih emisij - 1. del:
Ravni zvočne moči, določene na podlagi meritev zvočnega tlaka (ISO 5114-1:2024)
Acoustics - Determination of uncertainties associated with sound emission measures -
Part 1: Sound power levels determined from sound pressure measurements (ISO 5114-
1:2024)
Akustik - Bestimmung der Unsicherheiten von Schallemissionsmessgrößen - Teil 1:
Bestimmung von Schallleistungspegeln aus Schalldruckmessungen (ISO 5114-1:2024)
Acoustique - Détermination des incertitudes associées aux mesurages de l’émission
sonore - Partie 1: Niveaux de puissance acoustique déterminés à partir des mesurages
de pression acoustique (ISO 5114-1:2024)
Ta slovenski standard je istoveten z: EN ISO 5114-1:2024
ICS:
17.140.01 Akustična merjenja in Acoustic measurements and
blaženje hrupa na splošno noise abatement in general
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 5114-1
EUROPEAN STANDARD
NORME EUROPÉENNE
June 2024
EUROPÄISCHE NORM
ICS 17.140.01
English Version
Acoustics - Determination of uncertainties associated with
sound emission measures - Part 1: Sound power levels
determined from sound pressure measurements (ISO
5114-1:2024)
Acoustique - Détermination des incertitudes associées Akustik - Bestimmung der Unsicherheiten von
aux mesurages de l'émission sonore - Partie 1: Niveaux Schallemissionsmessgrößen - Teil 1: Bestimmung von
de puissance acoustique déterminés à partir des Schallleistungspegeln aus Schalldruckmessungen (ISO
mesurages de pression acoustique (ISO 5114-1:2024) 5114-1:2024)
This European Standard was approved by CEN on 14 June 2024.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2024 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 5114-1:2024 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 5114-1:2024) has been prepared by Technical Committee ISO/TC 43
"Acoustics" in collaboration with Technical Committee CEN/TC 211 “Acoustics” the secretariat of which
is held by DIN.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by December 2024, and conflicting national standards
shall be withdrawn at the latest by December 2024.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and the
United Kingdom.
Endorsement notice
The text of ISO 5114-1:2024 has been approved by CEN as EN ISO 5114-1:2024 without any
modification.
International
Standard
ISO 5114-1
First edition
Acoustics — Determination of
2024-06
uncertainties associated with sound
emission measures —
Part 1:
Sound power levels determined
from sound pressure measurements
Acoustique — Détermination des incertitudes associées aux
mesurages de l’émission sonore —
Partie 1: Niveaux de puissance acoustique déterminés à partir des
mesurages de pression acoustique
Reference number
ISO 5114-1:2024(en) © ISO 2024

ISO 5114-1:2024(en)
© ISO 2024
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
ISO 5114-1:2024(en)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 General concept to describe the uncertainty of measured sound power levels . 2
5 Determination of σ .3
omc
Determination of σ by round robin tests .4
R0
Detailed uncertainty budget to determine σ .6
R0
Determination of σ .7
tot
Annex A (informative) Detailed uncertainty budget for sound power determinations in
(approximated) free fields according to the direct enveloping method . 9
Annex B (informative) Detailed uncertainty budget for sound power determinations in
(approximated) diffuse fields according to the direct method . 17
Annex C (informative) Detailed uncertainty budget for sound power determinations using a
reference sound source .22
Bibliography .26

iii
ISO 5114-1:2024(en)
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
ISO technical committees. Each member body interested in a subject for which a technical committee
has been established has the right to be represented on that committee. International organizations,
governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely
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 documents 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)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 43, Acoustics, Subcommittee SC 1, Noise, in
collaboration with the European Committee for Standardization (CEN) Technical Committee CEN/TC 211,
Acoustics, in accordance with the Agreement on technical cooperation between ISO and CEN (Vienna
Agreement).
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.

iv
ISO 5114-1:2024(en)
Introduction
An assessment of uncertainties that is comprehensible and close to reality is indispensable for reporting
and using measured sound power levels. Uncertainties are determined following the principles of
ISO/IEC Guide 98-3. This Guide specifies a detailed procedure for uncertainty evaluation that is based upon
a mathematical model of the measurement. The detailedness of the model can vary from the mere analysis
of the statistical spread of measured sound power levels up to an exhaustive characterisation of all relevant
physical phenomena. Different such models are described by this document.

v
International Standard ISO 5114-1:2024(en)
Acoustics — Determination of uncertainties associated with
sound emission measures —
Part 1:
Sound power levels determined from sound pressure
measurements
1 Scope
This document gives guidance on the determination of measurement uncertainties of sound power levels
determined according to ISO 3741, ISO 3743-1, ISO 3743-2, ISO 3744, ISO 3745, ISO 3746, ISO 3747 or
according to a noise test code based on one of these measurement standards.
2 Normative references
There are no normative references in this document.
3 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
measurement result
value attributed to a particular quantity, obtained by following the complete set of instructions given in a
measurement procedure (the measured value), together with measurement uncertainty
Note 1 to entry: The measurement result can be expressed in terms of a sound power level in octave bands, one-third
octave bands or an A-weighted sound power level.
3.2
measurement uncertainty
parameter, associated with the result of a measurement, that characterizes the dispersion of the values that
can reasonably be attributed to the particular quantity subject to measurement
3.3
expanded uncertainty
U
quantity defining an interval about the result of a measurement that is expected to encompass a large
fraction of the distribution of values that can reasonably be attributed to the particular quantity subject to
measurement
ISO 5114-1:2024(en)
3.4
coverage factor
k
numerical factor used as a multiplier of the measurement uncertainty in order to obtain an expanded
uncertainty (3.3)
3.5
repeatability condition
condition of measurement that includes same measurement procedure; same observer; same measuring
instrument; same location; and repetition over a short period of time
3.6
reproducibility condition
condition of measurement that includes different laboratories, operators, measuring systems, and replicate
measurements on the same or similar objects
3.7
standard deviation of reproducibility of the method
σ
R0
standard deviation of measured values obtained under reproducibility conditions (3.6) using a specified method
Note 1 to entry: In statistics, it is usually distinguished between the standard deviation of the basic population σ and
the empirical standard deviation derived from a sample s. Despite this, the symbol σ is used for all standard deviations
in this document to be in line with other standards on sound emission.
3.8
standard deviation for the operating and mounting conditions
σ
omc
standard deviation of measured values caused by variations of operating and mounting conditions
3.9
total standard deviation
σ
tot
standard deviation of measured values obtained under reproducibility conditions (3.6)
4 General concept to describe the uncertainty of measured sound power levels
The uncertainties of sound power levels, uL , in decibels, determined in accordance with the International
()
W
Standard used (ISO 3741, ISO 3743-1, ISO 3743-2, ISO 3744, ISO 3745, ISO 3746 or ISO 3747) are estimated by
the total standard deviation, in decibels, given by Formula (1):
uL() = σ (1)
W tot
This standard deviation is expressed by the standard deviation of reproducibility of the method, σ , in
R0
decibels, and the standard deviation for the operating and mounting conditions, σ , in decibels, describing
omc
the uncertainty due to the instability of the operating and mounting conditions of the noise source under
test in accordance with Formula (2):
σσ=+σ (2)
tot0R omc
Formula (2) shows that variations of operating and mounting conditions expressed by σ should be taken
omc
into account before a measurement procedure with a certain grade of accuracy (characterized by σ ) is
R0
selected for a specific machine family. The standard deviation σ includes all uncertainty due to conditions
R0
and situations allowed by the International Standard used (different radiation characteristics of the noise
source under test, different instrumentation, different implementations of the measurement procedure),

ISO 5114-1:2024(en)
except that due to instability of the sound power of the noise source under test. The latter is considered
separately by σ .
omc
Values for the standard deviation σ may be derived from dedicated round robin tests (see Clause 6) or by
R0
using the mathematical modelling approach (see Clause 7). They should be given in noise test codes specific
to machinery families.
NOTE 1 If different measurement procedures offered by ISO 3741, ISO 3743-1, ISO 3743-2, ISO 3744, ISO 3745,
ISO 3746 or ISO 3747 are used, systematic numerical deviations (biases) can additionally occur.
Derived from σ , the expanded measurement uncertainty, UL , in decibels, shall be calculated from
()
tot W
Formula (3):
UL()=kσ (3)
W tot
The expanded measurement uncertainty depends on the confidence level that is desired. For a normal
distribution of measured values, there is a 95 % confidence level that the true value lies within the range
LU+ to LU− . This corresponds to a coverage factor of k= 2 . If the purpose of determining the
() ()
W W
sound power level is to compare the result with a limit value, it can be more appropriate to apply the coverage
factor for a one-sided normal distribution. In that case, the coverage factor k=16, corresponds to a 95 %
confidence level.
NOTE 2 The expanded uncertainty, as described in this document, does not include the standard deviation of
[18]
production which is used in ISO 4871 for the purpose of making a noise declaration for batches of machines.
5 Determination of σ
omc
The standard deviation for the operating and mounting conditions σ which describes the uncertainty
omc
associated with the instability of the operating and mounting conditions for the particular noise source
under test shall be taken into account when determining the measurement uncertainty. It is determined
from repeated measurements carried out on the same source at the same location by the same persons,
using the same measuring instruments and the same measurement position(s). To determine σ , sound
omc
pressure level measurements are repeated either at the single microphone position associated with the
highest sound pressure level, or at multiple microphone positions. These positions shall be distributed on an
enveloping surface in approximated hemi-free fields or in a volume in approximated diffuse fields.
Measurements are then corrected for background noise. Background noise measurements should be taken
at the same location, and as close as possible in time to the measurement when the machine is operating.
Further, if background sound levels are within 10 dB of the total measured level, then the uncertainty
associated with the variation in background sound level should be considered.
For each of these repeated measurements, the mounting of the machine and its operating conditions shall be
′
readjusted. For the individual noise source under test, σ is designated as σ . It is possible that a noise
omc omc
test code provides a value of σ which is representative for the machine family concerned. This value
omc
should take into account all possible variations of operating and mounting conditions specified in the noise
test code.
′
The standard deviation σ is calculated by Formula (4):
omc
1 N 2
′
σ = LL− (4)
()
omca∑ pj, p v
j=1
N−1
ISO 5114-1:2024(en)
where
L
is the sound pressure level measured at a prescribed position or averaged over the surface or
pj,
th
volume and corrected for background noise for the j repetition of the prescribed operating
and mounting conditions, in decibels;
L
is its arithmetic mean level calculated for all these repetitions, in decibels;
pav
is the number of repeated measurements under variation of the prescribed operating and
N
mounting conditions.
In general, the mounting and operating conditions to be used for noise emission measurements are
prescribed by machinery specific noise test codes. Otherwise, these conditions shall be defined precisely
and described in the test report.
Some recommendations for defining these conditions and consequences for the expected values of σ are
omc
given hereafter.
The test conditions shall represent normal usage and conform to manufacturersʼ and usersʼ recommended
practice. However, even in normal usage, variations within a specified operation mode, variations in material
flow, and other conditions varying between different phases of operation can occur. This uncertainty
covers both the uncertainty due to variation in long-term operating conditions (e.g. from day to day) and
fluctuations of noise emission measurements repeated immediately after readjusting mounting and
operating conditions.
Machines that stand exclusively on soft springs or on heavy concrete floors do not normally exhibit any
effect of mounting. However, there can be large discrepancies between measurements on heavy concrete
floors and those made in situ. The uncertainty due to mounting can be highest for machinery that is
connected to auxiliary equipment. Hand-held machines can also cause problems. This parameter should be
investigated if movement of the machine or mounts causes changes in noise. If there is a range of possible
mounting conditions to be included in a single declaration, then σ is estimated from the standard
omc
deviation of the sound levels for these mounting conditions. If there is any known effect due to mounting,
recommended mounting conditions should be documented in the relevant noise test code or manufacturersʼ
recommended practice.
With respect to the main uncertainty quantity, σ , investigations on σ have a higher priority compared
tot omc
to those on the other uncertainty components leading to σ [see Formula (2)]. This is because σ can be
R0 omc
significantly larger in practice than e.g. σ =2 dB for accuracy grade 2 measurements as given in Table 1.
R0
If σσ> , the application of measurement procedures with a high accuracy, i.e. a low value of σ
omc0R R0
makes no sense economically because this is not going to result in a lower value of the total uncertainty.
NOTE If the sound power has only a small variation with time and the measurement procedure is defined properly,
a value of 0,5 dB for σ can apply. In other cases, e.g. a large influence of the material flow into and out of the
omc
machine or material flow that varies in an unpredictable manner, a value of 2 dB is appropriate. However, in extreme
cases such as strongly varying noise generated by the processed material (stone-breaking machines, metal-cutting
machines and presses operating under load) a value of 4 dB results.
6 Determination of σ by round robin tests
R0
The standard deviation σ includes uncertainty due to all conditions and situations allowed by ISO 3741,
R0
ISO 3743-1, ISO 3743-2, ISO 3744, ISO 3745, ISO 3746 and ISO 3747 (different radiation characteristics of the
source under test, different instrumentation, different implementations of the measurement procedure) except
that due to instability of the sound power of the source under test. The latter is considered separately by σ .
omc
Typical values of σ are given in Table 1. They reflect the knowledge at the time of publication taking into
R0
consideration the great variety of machines and equipment covered by these standards (see References [2],
[3], [7], [8]). In special cases or if certain requirements of the standards are not met for a machine family or

ISO 5114-1:2024(en)
if it is anticipated that actual values of σ for a given family of machines are smaller than those given in the
R0
standards respectively, a round robin test is recommended to obtain machine-specific values of σ .
R0
Table 1 — Typical values for the standard deviation of reproducibility, σ
R0
ISO 3741
Frequency bandwidth One-third-octave
One-third-octave 100 - 200 - 400 -
6 300 -
A-weighted
10 000
mid-band frequency Hz 160 315 5 000
Standard deviation of
3,0 2,0 1,5 3,0 0,5
reproducibility, σ dB
R0
ISO 3743-1
Frequency bandwidth Octave
Octave 500 -
125 250 8 000 A-weighted
mid-band frequency Hz 5 000
Standard deviation of
3,0 2,0 1,5 2,5 1,5
reproducibility, σ dB
R0
ISO 3743-2
Frequency bandwidth Octave
Octave 500 -
125 250 8 000 A-weighted
mid-band frequency Hz 4 000
Standard deviation of
5,0 3,0 2,0 3,0 2,0
reproducibility, σ dB
R0
ISO 3744
Frequency bandwidth One-third-octave
One-third-octave 100 - 200 - 400 -
6 300 -
A-weighted
10 000
mid-band frequency Hz 160 315 5 000
Standard deviation of
3,0 2,0 1,5 2,5 1,5
reproducibility, σ dB
R0
ISO 3745
Frequency bandwidth One-third-octave
One-third-octave 50- 100 - 800 -
6 300 - 12 500 -
A-weighted
10 000 20 000
mid-band frequency Hz 80 630 5 000
Hemi-anechoic room
Standard deviation of
2,0 1,5 1,0 1,5 2,0 0,5
reproducibility, σ dB
R0
Anechoic room
Standard deviation of
2,0 1,0 0,5 1,0 2,0 0,5
reproducibility, σ dB
R0
ISO 3746
A-weighted
For a noise source which emits sound without significant tones 3,0
Standard deviation of
For a noise source which emits sound that contains predominant discrete
reproducibility, σ dB
4,0
R0
tones
ISO 3747
Grade of accuracy A-weighted
ISO 5114-1:2024(en)
TTabablele 1 1 ((ccoonnttiinnueuedd))
ΔL ≥7 at all microphone positions and
fA
Engineering (grade 2) 1,5
source directivity range ≤±7 dB
Standard deviation of
ΔL <7 or not determined and
fA
Survey (grade 3) 4,0
reproducibility, σ dB
R0 source directivity range ≤±7 dB
ΔL ≥7 at all microphone positions and
fA
Survey (grade 3) 4,0
source directivity range >±7 dB
The round robin test for determining σ shall be carried out in accordance with ISO 5725 (all parts), where
R0
the sound power level of the noise source under test is determined under reproducibility conditions, i.e.
different persons carrying out measurements at different testing locations with different measuring
instruments. Such a test provides the total standard deviation σ′ relevant for the individual noise source
tot
which has been used for the round robin test.
′
This total standard deviation σ , in decibels, obtained with a round robin test includes the standard
tot
′ ′
deviation σ and allows σ to be determined by using Formula (5):
omc R0
′ ′ ′
σσ= − σ (5)
() ()
R0 totomc
′
If σ values obtained from many different pieces of machinery belonging to the same family deviate within
R0
a small range only, their mean value may be regarded as typical for the application of this document to this
particular family and used as σ . Whenever available, such a value should be given in the noise test code
R0
specific to the machine family concerned (together with σ ) and used in particular for the purpose of
omc
declaring noise emission values.
If no round robin test has been carried out, the existing knowledge about the sound power measurement
from a particular family of machines may be used to estimate realistic values of σ .
R0
For certain applications, the effort involved in a round robin test may be reduced by omitting measurements
for different locations, e.g. if machines under test are usually installed under conditions with a small
background noise correction K or if the noise emission of a machine is rechecked at the same location.
Results of such delimited tests should be denoted by σ , and this designation should also be used for
R0,DL
tests on large machines being not movable in space.
Values for σ can be expected to be lower than those given in in ISO 3741, ISO 3743-1, ISO 3743-2,
R0,DL
ISO 3744, ISO 3745, ISO 3746 and ISO 3747.
The determination of σ using Formula (5) is imprecise if σ is only slightly higher than σ . In this
R0 tot omc
case, Formula (5) provides a small value of σ but with a low accuracy. To limit this inaccuracy, σ
R0 omc
should not exceed σ /2 .
tot
It is advised to develop a detailed uncertainty budget (see Clause 7) for the design of a new round robin to
ensure that the main uncertainty components are covered by the round robin test.
7 Detailed uncertainty budget to determine σ
R0
Generally σ , in decibels, is dependent upon several partial uncertainty components, cu , associated with
R0 ii
the different measurement parameters such as uncertainties of instruments, environmental corrections,

ISO 5114-1:2024(en)
and microphone positions. Using the modelling approach presented in ISO/IEC Guide 98-3, σ can be
R0
described by Formula (6):
N−1 N
2 22
σ ≈ cu + cu +…+ cu +2 cc ux ,x (6)
() () ()
()
Rn01 1 22 ni∑ ∑ ji j
i=1 jj=+1
th th
where ux ,x is the covariance associated with the i and j uncertainty components.
()
ij
If the contributions in Formula (6) are assumed to be not correlated, σ can be given by Formula (7):
R0
2 22
σ ≈ cu + cu +…+ cu (7)
() () ()
Rn01 1 22 n
For consistency with Formula (5), in Formulae (6) and (7) the uncertainty components due to the instability
of the sound emission of the source are not included. These components are covered by σ .
omc
NOTE The modelling approach requires detailed knowledge to determine the individual terms in Formulae (6)
and (7).
By contrast, the estimation of σ based on a round robin test does not require assumptions about possible
R0
correlations between the individual terms of Formulae (6) and (7). A round robin test is currently more
realistic than determining possible correlations between the single terms of Formulae (6) and (7) and their
dependencies on all other influencing parameters using the modelling approach. However, round robin tests
are not always possible and are often replaced by experience from earlier measurements.
The modelling approach, however, implies both statistically independent components c , u and especially
i i
the existence of Formulae which allow assessment of these uncertainty components by considering either
measurement parameters and environmental conditions or a reasonably large body of practical experience.
However, relevant well-founded data for this part of this document were not available at the time of
publication. However, Annex A, Annex B and Annex C give a rough outline of the relevant quantities without
being definitive. It is recommended to validate the results from detailed uncertainty budgets by round robin
testing (see Clause 6).
8 Determination of σ
tot
The total standard deviation and the expanded measurement uncertainty shall be determined using
Formula (2) and Formula (3), respectively. Examples are given in Table 2.
Table 2 — Examples of calculated total standard deviations σ for three different cases
tot
Operating and mounting conditions
stable unstable very unstable
Standard deviation of reproduci-
Standard deviation, σ , dB
omc
bility of the method, σ , dB
R0
0,5 2,0 4,0
Total standard deviation, σ , dB
tot
0,5
0,7 2,1 4,0
(Accuracy grade 1)
1,5
2,1 2,8 4,5
(Accuracy grade 2)
3,0 3,6 5,0
(Accuracy grade 3)
The examples show that it might be superfluous to extend the measuring effort to ensure a measurement of
accuracy grade 1 if the uncertainty associated with the mounting and operating conditions is large.

ISO 5114-1:2024(en)
Furthermore σσ> might create substantial misunderstandings with respect to the true relevant
omc0R
total standard deviation, σ , because the different grades of accuracy are, at the time of publication,
tot
specified by the value of σ only.
R0
ISO 5114-1:2024(en)
Annex A
(informative)
Detailed uncertainty budget for sound power determinations in
(approximated) free fields according to the direct enveloping method
A.1 Model formula
Preliminary estimations show that when corrected for meteorological conditions, the sound power level,
L , determined in (approximated) free field according to ISO 3744, ISO 3745 or ISO 3746, is a function of a
W
[20]
number of parameters, indicated by Formula (A.1) (see ISO/IEC Guide 98-3 ):
 S 
′
LL= +10lg dB−−KK ++CC ++C δδ++δ +++δδ +δ (A.1)
W p()ST   12 12 3 anglemic slm tone method omc
S
 
Formula (A.1) is a general formulation for all direct free-field methods. Not all quantities are explicitly
mentioned in all standardised procedures, e.g. K is omitted in ISO 3745, and C is omitted in ISO 3744 and
2 3
ISO 3746.
The parameters included in Formula (A.1) are explained in Table A.1.
Table A.1 — Explanation for quantities used in Formula (A.1)
is the mean (in octave band or one-third-octave band) sound pressure level of the noise source under
′
L
p()ST
test, before background corrections are applied, in decibels;
S is the total surface area, in square metres, of the measurement surface;
S =1 m ;
is the background noise correction, in decibels;
K
is the environmental correction, in decibels;
K
C is a meteorological correction to account for the different decibel reference quantities used in sound
pressure level and in sound power level, in decibels
p
273,/15+°θ C
s
C =−10lg dB+5lg dB ;
1  
p θ /K
 
s,00
C is a source order correction to account for changes in sound power with temperature and pressure,
the value shall be obtained from the appropriate noise test code. In the absence of a noise test code,
the following formula may be used. It is valid for a monopole source and also a mean value for other
sources (see References [1] and [4])
p
273,/15+°θ C
s
C =−10lg dB+15lg dB ;
 
p θ /K
 
s,01
C is the correction for air absorption, in decibels (see Reference [5]);
is the ambient pressure, in pascals, at the time of test;
p
s
p is the reference ambient pressure, 101,325 kPa;
s,0
θ is the air temperature, in degrees Celsius, at the time of test;
θ = 314 K;
= 296 K;
θ
δ is an input quantity to account for any difference of angle between the direction in which the sound is
angle
emitted by the source and the normal to the measurement surface, in decibels;

ISO 5114-1:2024(en)
TTabablele A A.11 ((ccoonnttiinnueuedd))
is an input quantity to allow for any uncertainty due to the finite number of microphone positions, in
δ
mic
decibels;
is an input quantity to allow for any uncertainty in the measuring instrumentation, in decibels;
δ
slm
δ is an input quantity to allow for any uncertainty due to spectral shape and the presence of tones, in
tone
decibels;
is an input quantity to allow for any uncertainty due to the measurement method applied including
δ
method
the derivation of results and associated uncertainties, in decibels;
is an input quantity to allow for any uncertainty due to operating and mounting conditions, in
δ
omc
decibels — this quantity is not included in the calculation of σ [see Formula (2)].
R0
NOTE 1 The input quantities included in Formula (A.1) to allow for uncertainties are those thought to be applicable
at the state of knowledge current at the time of publication of this document, but further research could reveal that
there are others.
NOTE 2 Similar expressions as Formula (A.1) apply with respect to sound power levels determined in frequency
bands and with A-weighting applied.
NOTE 3 A similar expression as Formula (A.1) applies to sound energy levels.
A probability distribution (normal, rectangular, Student-t, etc.) is associated with each of the input quantities.
Its expectation (mean value) is the best estimate for the value of the input quantity and its standard deviation
is a measure of the dispersion of values, termed uncertainty.
The uncertainty components related to mounting and operating conditions are already covered by σ
omc
whereas σ includes the remaining uncertainty components.
R0
NOTE 4 In case of specific families of noise sources, e. g. for a certain type of machinery, the values in this annex can
be explicitly checked. Smaller values can be expected. For purposes where the sound power levels are compared with
limit values, the measured variation in δ can be reduced when the noise test code specifies a single measurement
angle
surface shape and a measurement distance related to the source dimensions. In practice, this allows a smaller value of
the total standard deviation σ to be declared.
tot
The standard uncertainties from some contributions remain to be established by research.
A.2 Explanation and numerical example for the uncertainty parameters
An explanation and numerical example for the uncertainty parameters are given in Table A.2. Formulae to
calculate uncertainties are given with examples to show the expected range of measurement uncertainties.
Table A.2 — Uncertainty budget for determination of σ for sound power level using the direct method
R0
Quantity Estimate Probability
Standard uncertainty, u Sensitivity coefficient, c
i i
distribution
dB
u
mean sound
L′
p ST
′ ′ () 1+
L L
Normal
p()ST p()ST
01,/ΔL dB
pressure level
p
N 10 −1
 S   S  Δr
measurement
10lg 10lg
87, dB Rectangular 1
   
surface area
S S
    3 r
0 0
background
s
K noise K
L Normal
1 1 p(B)
01,/ΔL dB
p
10 −1
correction
environmen-
22*
K K   Normal 1
uL +uL
2 2 ()
W W()RSS
tal correction  
decibel
C reference C 0 Triangular 1
1 1
correction
ISO 5114-1:2024(en)
Table A.2 (continued)
Quantity Estimate Probability
Standard uncertainty, u Sensitivity coefficient, c
i i
distribution
dB
source order
C C 0,2 dB Triangular 1
2 2
correction
air absorption
C C 0,1 C to 0,3 C
Rectangular 1
3 3 3 3
correction
Box:
S
00,,50dB+ 6lg dB
()2
d
Hemisphere:
δ
angle 0 Rectangular 1
angle
−11, dB
r
11− ,3
()
d
u
′
L
p()ST
δ sampling 0 Normal 1
mic
N
M
Class 1: 0,3 dB
sound level
δ 0 Normal 1
slm
meter
Class 2: 1,0 dB
Audible tones: 3 dB
spectral
δ 0 Normal 1
tone
shape
Otherwise: 0
δ method 0 0,3 dB Normal 1
method
A.3 Uncertainty of the mean sound pressure level
The uncertainty of the mean sound pressure level may be obtained from the standard deviation of
repeatability, using N measurements of the decibel sound pressure levels at a single microphone position
(without correction for background noise), as given in Formula (A.2):
 
LL′ − ′
N pjST , p ST av
1 () ()
 
u = (A.2)
∑
L′
j=1
p()ST
N−1
N
These measurements are made under repeatability conditions.
Measurement repeatability can also be strongly influenced by averaging time. High background noise level
can cause high values of u due solely to the fluctuations in background noise. If the averaging time
′
L
p()ST
does not cover a sufficient number of machinery cycles, the total uncertainty can be unacceptably large for
any grade standard. This component of uncertainty can often be made negligible with a sufficiently long
averaging time consisting of an integer number of work cycles. For extremely low noise sources, reduction of
background noise can reduce the sensitivity coefficient and hence total uncertainty by up to a factor of 2.
The sensitivity coefficient is given by Formula (A.3):
c =+1 (A.3)
′
L
p()ST 01,/ΔL dB
p
10 −1
A.4 Uncertainty of the measurement surface area, S
For a hemispherical measurement surface, the estimate for Sr= 2π is calculated for a given value of the
radius of the hemisphere. The standard uncertainty depends on the uncertainty of the realisation of the
defined microphone positions on this surface. If the uncertainty in the measurement surface dimensions is

ISO 5114-1:2024(en)
assumed to have a rectangular distribution with a range of ±Δr , the standard deviation results in
Formula (A.4):
Δr
u = (A.4)
S
Similar results apply for a box surface. If the uncertainty in the measurement surface dimensions is assumed
to have a rectangular distribution with a range of ±Δd , the standard deviation is given by Formula (A.5):
Δd
u = (A.5)
S
where d is the distance from the reference box to a parallelepiped measurement surface.
The sensitivity coefficient, c , is obtained from the derivative of L from Formula (A.1) with respect to r .
S W
After substitution for the surface area Sr= 2π , the sensitivity coefficient is cr= 87,/ dB for a hemisphere
S
or cd= 87,/ dB for a box surface, where d is the characteristic source dimension.
S 0 0
In an extreme scenario, the range for Δr is 7 % of r , resulting in an uncertainty contribution, cu of 0,4 dB.
Ss
Typically, an uncertainty contribution of 0,1 dB is achievable with very careful microphone positioning.
A.5 Uncertainty of the background noise correction, K
The uncertainty, u , due to the background noise correction, K , is obtained from the standard deviation,
K 1
s , of the decibel values from repeated measurements of background noise at a single microphone
L
p()B
position.
The sensitivity coefficient, c , due to the background noise level, L , is obtained from the derivative of
K p()B
L from Formula (A.1) with respect to L . The parameters inL that are related to the source
W p()B W
−01, ΔL
p
′ ′
measurement are given by LL= +−10lg 110 dB , where ΔLL= −L . In this
pp()ST ()ST ( ) p p()ST p(B)
example, the sign of the sensitivity coefficient is unimportant, and reduces to Formula (A.6):
c = (A.6)
K
1 01,/ΔL dB
p
10 −1
Lowering the fluctuations in background noise can reduce this uncertainty component. Significant
reductions in the sensitivity coefficient are obtained by reducing background noise by systematically
tracking down and blocking and/or absorbing noise from unwanted sources (through proper grounding,
lead wrapping, vibration isolation, adding mass, adding absorptive materials, etc., as appropriate).
Furthermore, the uncertainty, u , is typically halved each time the averaging time is increased by a factor
K
of four. In large rooms, the sound pressure caused by the noise source under test is higher near noise sources,
and background noise can be reduced by measuring closer to the noise source under test. The influence of
background noise is reduced by 3 dB when the measurement surface area is reduced by a factor of 2
...