ISO 18405:2017

Underwater acoustics — Terminology

ISO 18405:2017 defines terms and expressions used in the field of underwater acoustics, including natural, biological and anthropogenic (i.e. man-made) sound. It includes the generation, propagation and reception of underwater sound and its scattering, including reflection, in the underwater environment including the seabed (or sea bottom), sea surface and biological organisms. It also includes all aspects of the effects of underwater sound on the underwater environment, humans and aquatic life. The properties of underwater acoustical systems are excluded.

Acoustique sous-marine — Terminologie

General Information

• Status: Published
• Publication Date: 24-Apr-2017
• ICS: 01.040.17 - Metrology and measurement. Physical phenomena (Vocabularies)
• ICS: 17.140.01 - Acoustic measurements and noise abatement in general
• ICS: 17.140.30 - Noise emitted by means of transport
• Technical Committee: ISO/TC 43/SC 3 - Underwater acoustics
• Drafting Committee: ISO/TC 43/SC 3/WG 2 - Underwater acoustical terminology
• Current Stage: 9093 - International Standard confirmed
• Start Date: 07-Nov-2022
• Completion Date: 13-Dec-2025

Relations

• Consolidated By: ISO 9917-2:2017 - Dentistry — Water-based cements — Part 2: Resin-modified cements
• Effective Date: 06-Jun-2022

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 18405
First edition
2017-04
Underwater acoustics — Terminology
Acoustique sous-marine — Terminologie
Reference number
©
ISO 2017
© ISO 2017, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
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ii © ISO 2017 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 General terms . 1
3.1.1 General. 1
3.1.2 Acoustical field quantities. 2
3.1.3 Acoustical power quantities . 5
3.1.4 Logarithmic frequency intervals .10
3.1.5 Other acoustical quantities .11
3.2 Levels used in underwater acoustics .13
3.2.1 Levels of acoustical power quantities .13
3.2.2 Levels of acoustical field quantities .16
3.3 Terms for properties of underwater sound sources .17
3.3.1 Source waveforms and factors .17
3.3.2 Source levels .21
3.4 Terms related to propagation and scattering of underwater sound.23
3.4.1 Propagation .23
3.4.2 Scattering .24
3.5 Terms for properties of underwater sound signals .27
3.5.1 Sound signals .27
3.6 Terms related to sonar equations .29
3.6.1 General.29
3.6.2 Sonar equations and sonar equation terms .31
3.7 Terms related to underwater bioacoustics .35
3.7.1 Auditory frequency weighting .35
3.7.2 Sound reception.38
3.7.3 Sound production . .42
Annex A (informative) Alphabetical index .43
Bibliography .50
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).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on 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 the following
URL: w w w . i s o .org/ iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 43, Acoustics, Subcommittee SC 3,
Underwater acoustics.
iv © ISO 2017 – All rights reserved

Introduction
0.1 Overview
Vocabulary is the most basic of subjects for standardization. Without an accepted standard for the
definition of terminology, the production of scientific and engineering publications in a technical
area, including the development of standards for measurement, processing or modelling in that area,
becomes a laborious and time-consuming task that would ultimately result in the inefficient use of time
and a high probability of misinterpretation.
Basic terminology of underwater acoustics is defined in 3.1, followed by levels in 3.2. These are
followed by definitions of terms associated with sources of sound (3.3), propagation and scattering
(3.4), underwater sound signals (3.5), and sonar equations (3.6). Finally, 3.7 defines basic bioacoustical
terminology used in underwater acoustics.
0.2 Approach
The underlying philosophy followed in preparing this document is to define quantities independently of
how they are measured.
0.3 Remark on exceptions to the ISO/IEC 80000 series
In this document, the ISO/IEC 80000 series is followed for the definitions of physical quantities,
including the level of a power quantity and level of a field quantity. Two exceptions are made to this
general rule, as follows.
— Inconsistencies between ISO 80000-1 and ISO 80000-3 make it necessary to choose between them
(for example, the term “field quantity” used in ISO 80000-3 is deprecated by ISO 80000-1:2009,
Annex C, which prefers the term “root-power quantity”). This document follows ISO 80000-3, which
makes it incompatible with ISO 80000-1.
— The term “sound pressure level” is defined by ISO 80000-8 in a way that does not reflect conventional
use of this term to mean the level of the mean-square sound pressure. This convention is reflected
in ISO 80000-8 by the notes in the “Remarks” column alongside the definition. These remarks are
inconsistent with the definition, making it necessary to choose between the definition and the
remarks. This document follows the “Remarks”, which makes it incompatible with the ISO 80000-8
definition of “sound pressure level”.
0.4 Remark on levels and level differences, and their reference values
Levels used in underwater acoustics are defined in 3.2. In its most general form, a level L of a quantity
Q
Q is defined in the International System of Quantities (see ISO 80000-3) as the logarithm of the ratio of
the quantity Q to its reference value, Q . In formula form, this definition can be written as
L = log (Q/Q ).
Q r 0
The nature of the quantity (Q), its reference value (Q ) and the base of the logarithm (r) should all be
specified. Reference values for use in underwater acoustics are specified by ISO 1683.
Two types of level are in widespread use in underwater acoustics, the level of a field quantity (see
ISO 80000-3:2006, 3-21) and the level of a power quantity (see ISO 80000-3:2006, 3-22). In underwater
acoustics, it is conventional to express both types of level in decibels (dB). When expressed in decibels,
the level L of a field quantity F is
F
L = 20 log (F/F ) dB,
F 10 0
where F is the reference value of the field quantity. Similarly, the level L of a power quantity P is
0 P
L = 10 log (P/P ) dB,
P 10 0
where P is the reference value of the power quantity. This definition of L is a product of the three
0 P
factors 10, log (P/P ) and 1 dB. In words, this product is written in this document as “ten times the
10 0
logarithm to the base 10 of the ratio P/P , in decibels”. For levels of both field and power quantities,
the nature of the quantity (F or P) is implied by the name of the level, while the base of the logarithm is
implied by the use of decibel as the unit. For all levels, the reference value is stated explicitly. The use
by this document of the definitions of “level” and “decibel” from ISO 80000-3 results in inconsistencies
between this document and ISO 80000-1 because of inconsistencies between ISO 80000-3 and
ISO 80000-1:2009, Annex C.
Level differences [i.e. differences between levels of like quantities (see ANSI/ASA S1.1-2013, 10.44)] are
also expressed in decibels. For example, if P and P are power quantities of the same kind, and L and
1 2 P,1
L are their respective levels, the corresponding level difference is
P,2
ΔL = L – L = 10 log (P /P ) dB – 10 log (P /P ) dB = 10 log (P /P ) dB.
P P,1 P,2 10 1 0 10 2 0 10 1 2
Similarly, for like field quantities F and F , with respective levels, L and L ,
1 2 F,1 F,2
ΔL = L – L = 20 log (F /F ) dB – 20 log (F /F ) dB = 20 log (F /F ) dB.
F F,1 F,2 10 1 0 10 2 0 10 1 2
Examples of level difference are transmission loss, array gain, and hearing threshold shift.
Differences between levels of power quantities of different kinds are encountered in 3.6 and 3.7 in
connection with the response of underwater systems, and are also expressed in decibels. For example,
if A and B are two power quantities, with A being a measure of the response signal (output) of a system
and B a measure of the forcing signal (input), such that the system sensitivity is S = A/B, the sensitivity
level of that system is
N = L – L = 10 log (A/A ) dB – 10 log (B/B ) dB = 10log (S/S ) dB
S A B 10 0 10 0 10 0
where S , the reference value of the sensitivity, is equal to A /B .
0 0 0
An example of sensitivity level in underwater acoustics is target strength (reference value = 1 m ). If
this quantity were expressed instead as the difference between levels of field quantities, defined as the
square root of the respective power quantities, the reference value would then become 1 m.
0.5 Remark on reference values of root-power quantities
For every real, positive power quantity, P, there exists a root-power quantity, F , equal to the square
rp
1/2
root of P (see ISO 80000-1:2009), that is, F = P . The level of this root-power quantity is
rp
L = 20 log (F /F ) dB.
F,rp 10 rp 0
1/2
This level is equal to L if the reference value F is given by F = P . Selected power quantities and
P 0 0 0
their respective reference values are listed in columns 1 and 2 of Table 1. The corresponding root-
power quantities and their respective reference values are listed in columns 3 and 4 of Table 1. A field
quantity is “a quantity whose square is proportional to power when it acts on a linear system” (see
ISO 80000-3), so all root-power quantities are also field quantities. For example, the level of mean-
square sound pressure, with reference value 1 μPa , is equal to that of root-mean-square sound
vi © ISO 2017 – All rights reserved

pressure, with reference value 1 μPa. These two reference values are therefore used interchangeably
for sound pressure level.
Table 1 — Power quantities, their corresponding root-power quantities, and their reference
values, based on Reference [21]
Power quantity Reference value Corresponding root-power Reference value
1/2
(P) (P ) quantity (F = P )
0 0 0
1/2
(F = P )
rp
Mean-square sound pressure 1 μPa Root-mean-square sound 1 μPa
pressure
Mean-square sound particle 1 pm Root-mean-square sound 1 pm
displacement particle displacement
2 2
Mean-square sound particle 1 nm /s Root-mean-square sound 1 nm/s
velocity particle velocity
2 4 2
Mean-square sound particle 1 μm /s Root-mean-square sound 1 μm/s
acceleration particle acceleration
2 1/2
Sound exposure 1 μPa s Root sound exposure 1 μPa s
1/2
Sound power 1 pW Root sound power 1 pW
1/2
Sound energy 1 pJ Root sound energy 1 pJ
2 2
Source factor 1 μPa m Root source factor 1 μPa m
Propagation factor 1 m Root propagation factor 1 m
0.6 Remark on the usage of “acoustic” and “sound” in this document
This document recognizes the interchangeability of the words “acoustic” and “sound” when the word
“sound” is used as part of a compound noun, and not otherwise.
INTERNATIONAL STANDARD ISO 18405:2017(E)
Underwater acoustics — Terminology
1 Scope
This document defines terms and expressions used in the field of underwater acoustics, including
natural, biological and anthropogenic (i.e. man-made) sound. It includes the generation, propagation and
reception of underwater sound and its scattering, including reflection, in the underwater environment
including the seabed (or sea bottom), sea surface and biological organisms. It also includes all aspects
of the effects of underwater sound on the underwater environment, humans and aquatic life. The
properties of underwater acoustical systems are excluded.
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 terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http:// www .electropedia .org/
— ISO Online browsing platform: available at http:// www .iso .org/ obp
3.1 General terms
3.1.1 General
3.1.1.1
sound
alteration in pressure, stress or material displacement propagated via the action of elastic stresses in an
elastic medium and that involves local compression and expansion of the medium, or the superposition
of such propagated alterations
Note 1 to entry: The medium in which the sound exists is often indicated by an appropriate adjective, e.g.
airborne, water-borne, or structure-borne.
Note 2 to entry: In the remainder of this document, the medium is assumed to be a compressible fluid.
Note 3 to entry: A sound wave is a realization of sound.
Note 4 to entry: The word “sound” may also be used as part of a compound noun, in which case, it is a synonym of
“acoustic”. For example, “acoustic pressure” and “acoustic power”’ are synonyms of sound pressure (3.1.2.1) and
sound power (3.1.3.14).
[SOURCE: Reference [23] and Reference [35]]
3.1.1.2
ambient sound
sound (3.1.1.1) that would be present in the absence of a specified activity
Note 1 to entry: Ambient sound is location-specific and time-specific.
Note 2 to entry: In the absence of a specified activity, all sound is ambient sound.
Note 3 to entry: Ambient sound includes ambient noise (3.1.5.11).
Note 4 to entry: Examples of specified activity include the act of measuring the underwater sound and the
radiation of sound by specified sound sources.
Note 5 to entry: Ambient sound can be anthropogenic (e.g. shipping) or natural (e.g. wind, biota).
3.1.1.3
soundscape
characterization of the ambient sound (3.1.1.2) in terms of its spatial, temporal
and frequency attributes, and the types of sources contributing to the sound field
3.1.1.4
reverberation
sound (3.1.1.1) resulting from cumulative scattering of sound by an aggregation, or ensemble, of
scatterers
Note 1 to entry: Reverberation commonly arises from scatterers in a volume or on a surface.
3.1.1.5
material element
sound particle
smallest element of the medium that represents the medium’s mean density
Note 1 to entry: The characteristic length scale of this element is of the order of several times the mean free
molecular path (see Reference [22]).
3.1.2 Acoustical field quantities
3.1.2.1
sound pressure
p
contribution to total pressure caused by the action of sound (3.1.1.1)
Note 1 to entry: Sound pressure is a function of time, which may be indicated by means of an argument t, as in
p(t), where p is sound pressure and t is time.
Note 2 to entry: Sound pressure is expressed in pascals (Pa).
Note 3 to entry: The term “sound pressure” is sometimes used as a synonym of “root-mean-square sound
pressure”. This use is deprecated.
Note 4 to entry: The term “sound pressure” is defined by IEC 60050 as the root-mean-square value of p(t). While
this IEC definition is not compatible with the present (ISO) definition, users of ISO standards might nevertheless
encounter the IEC definition, for example, in hydrophone calibration standards developed by the IEC.
Note 5 to entry: Weighted sound pressure is defined in 3.7.1.1.
[SOURCE: ISO 80000-8:2007, 8-9.1 and 8-9.2, modified]
3.1.2.2
sound pressure spectrum
P
Fourier transform of the sound pressure (3.1.2.1)
Note 1 to entry: Sound pressure spectrum is a function of frequency, which may be indicated by means of an
argument f, as in P( f ), where P is sound pressure spectrum and f is frequency.
+∞
Note 2 to entry: In formula form, Pf =−expi2π ft p(t) dt, where p(t) is the sound pressure as a function
() ()
∫
−∞
+∞
of time, t. If P( f) is known, p(t) can be calculated using the inverse Fourier transform pt =+expi2π ft
() ()
∫
−∞
P( f ) df. See ISO 80000-2:2009.
2 © ISO 2017 – All rights reserved

Note 3 to entry: Sound pressure spectrum is expressed in units of pascal per hertz (Pa/Hz).
Note 4 to entry: In general, P( f ) is a complex function of frequency.
Note 5 to entry: The definition of sound pressure spectrum applies to a single-event or transient sound pressure
signal, in which case, for the purpose of the integral over time in the formula for P( f), the sound pressure p(t)
is set to zero at all times before the signal starts and after it ends. It can also be applied to a finite segment of a
continuous sound pressure signal, in which case, the start and end times of the segment shall be specified.
3.1.2.3
zero-to-peak sound pressure
peak sound pressure
p
0-pk
p
pk
greatest magnitude of the sound pressure (3.1.2.1) during a specified time interval, for a specified
frequency range
Note 1 to entry: Zero-to-peak sound pressure is expressed in pascals (Pa).
Note 2 to entry: A zero-to-peak sound pressure can arise from a positive or negative sound pressure.
[SOURCE: ISO/TR 25417:2007, 2.4, modified]
3.1.2.4
compressional pressure
p
c
sound pressure (3.1.2.1), p(t), when p(t) > 0, where t is time
Note 1 to entry: Compressional pressure is expressed in pascals (Pa).
Note 2 to entry: For shock waves, compressional pressure may be referred to as “blast overpressure”. See
Reference [33].
3.1.2.5
peak compressional pressure
p
pk,c
greatest compressional pressure (3.1.2.4) during a specified time interval, for a specified frequency range
Note 1 to entry: Peak compressional pressure is expressed in pascals (Pa).
Note 2 to entry: A peak compressional pressure can only arise from a positive sound pressure.
Note 3 to entry: For shock waves, peak compressional pressure may be referred to as “peak blast overpressure”.
3.1.2.6
rarefactional pressure
p
r
magnitude of sound pressure (3.1.2.1), |p(t)|, when p(t) < 0, where p is sound pressure and t is time
Note 1 to entry: Rarefactional pressure is expressed in pascals (Pa).
3.1.2.7
peak rarefactional pressure
p
pk,r
greatest rarefactional pressure (3.1.2.6) during a specified time interval, for a specified frequency range
Note 1 to entry: Peak rarefactional pressure is expressed in pascals (Pa).
Note 2 to entry: A peak rarefactional pressure can only arise from a negative sound pressure.
Note 3 to entry: Peak rarefactional pressure is always positive.
3.1.2.8
peak-to-peak sound pressure
p
pk-pk
sum of the peak compressional pressure (3.1.2.5) and the peak rarefactional pressure (3.1.2.7) during a
specified time interval, for a specified frequency range
Note 1 to entry: Peak-to-peak sound pressure is expressed in pascals (Pa).
Note 2 to entry: The start and end times used to determine the time interval for the peak compressional pressure
shall be the same as those used to determine the time interval for the peak rarefactional pressure.
3.1.2.9
sound particle displacement
δ
displacement of a material element (3.1.1.5) caused by the action of sound (3.1.1.1)
Note 1 to entry: Sound particle displacement is a function of time, t, which may be indicated by means of an
argument t, as in δ(t).
Note 2 to entry: Sound particle displacement is expressed in metres (m).
Note 3 to entry: Sound particle displacement is a vector quantity. Spatial components of the sound particle
displacement may be indicated by assigning subscripts to the symbol. For example, in Cartesian coordinates,
δ = (δ , δ , δ ). By convention in underwater acoustics, the z axis is usually chosen to point vertically down from
x y z
the sea surface, with x and y axes in the horizontal plane.
[SOURCE: ISO 80000-8:2007, 8-10, modified]
3.1.2.10
sound particle velocity
u
contribution to velocity of a material element (3.1.1.5) caused by the action of sound (3.1.1.1)
Note 1 to entry: Sound particle velocity is a function of time, t, which may be indicated by means of an argument
t, as in u(t).
Note 2 to entry: For small-amplitude sound waves in an otherwise stationary medium, the sound particle velocity
and sound particle displacement (3.1.2.9) are related by
∂δδ
u =
∂t
where δ(t) is the sound particle displacement at time, t, and the partial derivative is evaluated at a fixed position. The
formula above is an approximation, with relative error of order |u/c|, where c is the speed of sound in the medium.
Note 3 to entry: Sound particle velocity is expressed in units of metre per second (m/s).
Note 4 to entry: Sound particle velocity is a vector quantity. Spatial components of the sound particle velocity
may be indicated by assigning subscripts to the symbol. For example, in Cartesian coordinates, u = (u , u , u ). By
x y z
convention in underwater acoustics, the z axis is usually chosen to point vertically down from the sea surface,
with x and y axes in the horizontal plane.
[SOURCE: ISO 80000-8:2007, 8-11, modified]
3.1.2.11
sound particle acceleration
a
contribution to acceleration of a material element (3.1.1.5) caused by the action of sound (3.1.1.1)
Note 1 to entry: Sound particle acceleration is a function of time, t, which may be indicated by means of an
argument t, as in a(t).
4 © ISO 2017 – All rights reserved

Note 2 to entry: For small-amplitude sound waves in an otherwise stationary medium, the sound particle
acceleration and sound particle velocity (3.1.2.10) are related by
∂u
a =
∂t
where u(t) is the sound particle velocity at time, t, and the partial derivative is evaluated at a fixed position. The
formula above is an approximation, with relative error of order |u/c|, where c is the speed of sound in the medium.
Note 3 to entry: Sound particle acceleration is expressed in units of metre per second squared (m/s ).
Note 4 to entry: Sound particle acceleration is a vector quantity. Spatial components of the sound particle
acceleration may be indicated by assigning subscripts to the symbol. For example, in Cartesian coordinates,
a = (a , a , a ). By convention in underwater acoustics, the z axis is usually chosen to point vertically down from
x y z
the sea surface, with x and y axes in the horizontal plane.
[SOURCE: ISO 80000-8:2007, 8-12, modified]
3.1.3 Acoustical power quantities
3.1.3.1
mean-square sound pressure
p
integral over a specified time interval of squared sound pressure (3.1.2.1), divided by the duration of the
time interval, for a specified frequency range
t
2 2 2
Note 1 to entry: In formula form, p = pt dt , where p(t) is the sound pressure, and t and t are
1 2
()
∫
t
tt−
the start and end times, respectively. For a transient sound, the start and end times are sometimes chosen to
correspond to the start and end of the percentage energy signal duration (3.5.1.5).
Note 2 to entry: Mean-square sound pressure is expressed in units of pascal squared (Pa ).
Note 3 to entry: The square root of the mean-square sound pressure is a field quantity known as the root-mean-
square sound pressure. This field quantity may be denoted p .
rms
3.1.3.2
mean-square sound particle displacement
δ
integral over a specified time interval of squared magnitude of the sound particle displacement (3.1.2.9),
divided by the duration of the time interval, for a specified frequency range
t
2 2 2
Note 1 to entry: In formula form, δδ= ttd , where δ(t) is the magnitude of the sound particle
()
∫
t
tt−
displacement, and t and t are the start and end times, respectively.
1 2
Note 2 to entry: Mean-square sound particle displacement is expressed in units of metre squared (m ).
Note 3 to entry: The square root of the mean-square sound displacement is a field quantity known as the root-
mean-square sound displacement. This field quantity may be denoted δ .
rms
3.1.3.3
mean-square sound particle velocity
u
integral over a specified time interval of squared magnitude of the sound particle velocity (3.1.2.10),
divided by the duration of the time interval, for a specified frequency range
t
2 2 2
Note 1 to entry: In formula form, u = ut dt , where u(t) is the magnitude of the sound particle
()
∫
t
tt−
velocity, and t and t are the start and end times, respectively.
1 2
Note 2 to entry: Mean-square sound particle velocity is expressed in units of (metre per second) squared [(m/s) ].
Note 3 to entry: The square root of the mean-square sound velocity is a field quantity known as the root-mean-
square sound velocity. This field quantity may be denoted u .
rms
3.1.3.4
mean-square sound particle acceleration
a
integral over a specified time interval of squared magnitude of the sound particle acceleration (3.1.2.11),
divided by the duration of the time interval, for a specified frequency range
t
2 2 2
Note 1 to entry: In formula form, a = at dt , where a(t) is the magnitude of the sound particle
()
∫
t
tt−
acceleration, and t and t are the start and end times, respectively.
1 2
Note 2 to entry: Mean-square sound particle acceleration is expressed in units of (metre per second squared)
2 2
squared [(m/s ) ].
Note 3 to entry: The square root of the mean-square sound acceleration is a field quantity known as the root-
mean-square sound acceleration. This field quantity may be denoted a .
rms
3.1.3.5
time-integrated squared sound pressure
sound pressure exposure
sound exposure
E
p,T
integral of the square of the sound pressure (3.1.2.1), p, over a specified time
interval or event, for a specified frequency range
t
2 2
Note 1 to entry: In formula form, Ep= ttd , where t and t are the start and end times of the time
() 1 2
pT,
∫
t
interval or event, respectively, and T = t – t is the duration of the signal.
2 1
Note 2 to entry: Time-integrated squared sound pressure is expressed in units of pascal squared second (Pa s).
Note 3 to entry: According to the continuous form of Parseval’s theorem (also known as Plancherel’s theorem),
the time-integrated squared sound pressure can be written as the frequency-integrated sound exposure spectral
+∞ +∞ 2 +∞
density (3.1.3.9). In formula form, Ep= ttdd= Pf fE= ffd , where p (t) is equal to
() () () T
pT, ∫∫Tf∫
−∞ −∞ 0
p(t) for t < t < t and is otherwise zero, P( f) is the Fourier transform (see ISO 80000-2) of p (t) and E is the
1 2 T f
sound exposure spectral density of the pressure time series p (t).
T
Note 4 to entry: In the far field the time-integrated squared sound pressure is equal to the product of the
characteristic acoustic impedance (3.1.5.6) of the medium and the magnitude of the time-integrated sound
intensity (3.1.3.10). In the near field this equality does not hold in general.
Note 5 to entry: See also weighted time-integrated squared sound pressure (3.7.1.2).
6 © ISO 2017 – All rights reserved

3.1.3.6
time-integrated squared sound particle displacement
E
δ,T
integral of the square of the magnitude of the sound particle displacement (3.1.2.9), δ, over a specified
time interval or event, for a specified frequency range
t
2 2
Note 1 to entry: In formula form, Et= δ dt , where t and t are the start and end times of the time
() 1 2
δ ,T
∫
t
interval or event, respectively, and T = t – t is the duration of the signal.
2 1
Note 2 to entry: Time-integrated squared sound particle displacement is expressed in units of metre squared
second (m s).
3.1.3.7
time-integrated squared sound particle velocity
E
u,T
integral of the square of the magnitude of the sound particle velocity (3.1.2.10), u, over a specified time
interval or event, for a specified frequency range
t
2 2
Note 1 to entry: In formula form, Eu= ttd , where t and t are the start and end times of the time
() 1 2
uT,
∫
t
interval or event, respectively, and T = t – t is the duration of the signal.
2 1
Note 2 to entry: Time-integrated squared sound particle velocity is expressed in units of (metre per second)
squared second [(m/s) s].
3.1.3.8
time-integrated squared sound particle acceleration
E
a,T
integral of the square of the magnitude of the sound particle acceleration (3.1.2.11), a, over a specified
time interval or event, for a specified frequency range
t
2 2
Note 1 to entry: In formula form, Ea= ttd , where t and t are the start and end times of the time
() 1 2
aT,
∫
t
interval or event, respectively, and T = t – t is the duration of the signal.
2 1
Note 2 to entry: Time-integrated squared sound particle acceleration is expressed in units of (metre per second
2 2
squared) squared second [(m/s ) s].
3.1.3.9
sound exposure spectral density
sound pressure exposure spectral density
E
f
distribution as a function of non-negative frequency of the time-integrated
squared sound pressure (3.1.3.5) per unit bandwidth of a sound having a continuous spectrum
Note 1 to entry: Sound exposure spectral density is expressed in units of pascal squared second per hertz
(Pa s/Hz).
Note 2 to entry: In its idealized form, sound exposure spectral density is evaluated as the limit, as the bandwidth
tends to zero, of the time-integrated squared sound pressure in a finite frequency band divided by the frequency
bandwidth.
Note 3 to entry: For operational purposes, sound exposure spectral density is estimated as the time-integrated
squared sound pressure in a finite frequency band divided by the frequency bandwidth. The result is equal to the
mean value of the sound exposure spectral density, averaged across the band. The time duration and frequency
band shall be specified.
Note 4 to entry: According to the continuous form of Parseval’s theorem (also known as Plancherel’s theorem),
the sound pressure spectrum (3.1.2.2), P( f), is related to the sound pressure p(t) via the formula
+∞ 2 +∞
Pf ddfp= tt . Here, |P( f )| is a function of both positive and negative frequencies and is known
() ()
∫∫
−∞ −∞
as a “double-sided” spectral density. By contrast, E ( f ) is known as a “single-sided” spectral density because it is
f
+∞ +∞
a function of non-negative frequencies only, and satisfies the formula Ef ddfp= tt . It follows
() ()
f
∫∫
0 −∞
2 2
from these formulae that for any positive non-zero frequency, E ( f ) = 2|P( f )| . For zero frequency, E (0) = |P(0)| .
f f
Note 5 to entry: The integral over positive frequencies of the sound exposure spectral density is equal to the
+∞
time-integrated squared sound pressure Ef dfE= .
()
fp,T
∫
3.1.3.10
sound intensity
instantaneous sound intensity
I
product of the sound pressure (3.1.2.1), p, and the sound particle velocity (3.1.2.10), u
Note 1 to entry: Sound intensity is a function of time, t, which may be indicated by means of an argument t, as in I(t).
Note 2 to entry: In formula form, I(t) = p(t) u(t).
Note 3 to entry: Sound intensity is expressed in units of watt per metre squared (W/m ).
Note 4 to entry: Sound intensity is a vector quantity. Spatial components of the sound intensity may be indicated
by assigning subscripts to the symbol. For example, in Cartesian coordinates, I = (I , I , I ). By convention in
x y z
underwater acoustics, the z axis is usually chosen to point vertically down from the sea surface, with x and y axes
in the horizontal plane.
Note 5 to entry: Sound intensity is also known as the “Umov vector”, “Poynting vector” or “Umov-Poynting
vector”.
Note 6 to entry: Sound pressure is a real scalar quantity and sound particle velocity is a real vector quantity.
Sound intensity is therefore a real vector quantity.
Note 7 to entry: In the International System of Quantities (ISQ), sound pressure and sound particle velocity are
instantaneous quantities. Their product, sound intensity, is therefore also an instantaneous quantity in the ISQ.
The upper case symbol I, without a subscript, is used to denote this instantaneous quantity to distinguish it from
the time-averaged sound intensity, I .
av
Note 8 to entry: The term “sound intensity” is in widespread use as a synonym of “time-averaged sound intensity”,
I . This use is not compatible with the ISQ.
av
Note 9 to entry: This definition could become inapplicable in situations with a high mean fluid flow.
Note 10 to entry: This definition is in accordance with ISO 80000-8:2007, 8-17.1.
[SOURCE: ISO/TR 25417:2007, 2.12, modified]
3.1.3.11
time-averaged sound intensity
I
av
integral over a specified time interval of sound intensity (3.1.3.10), I, divided by the duration of the time
interval, for a specified frequency range
t
Note 1 to entry: In formula form, II= ttd , where t and t are the start and end times,
1 2
()
av ∫
t
tt−
respectively.
Note 2 to entry: Time-averaged sound intensity is expressed in units of watt per metre squared (W/m ).
8 © ISO 2017 – All rights reserved

Note 3 to entry: Time-averaged sound intensity is a vector quantity. Spatial components of the time-averaged
sound intensity may be indicated by assigning subscripts to the symbol. For example, in Cartesian coordinates,
I = (I , I , I ). By convention in underwater acoustics, the z axis is usually chosen to point vertically down
av av,x av,y av,z
from the sea surface, with x and y axes in the horizontal plane.
Note 4 to entry: This definition is in accordance with ISO 80000-8:2007, 8.
[SOURCE: ISO/TR 25417:2007, 2.13, modified]
3.1.3.12
equivalent plane wave sound intensity
I
eq
mean-square sound pressure (3.1.3.1), p , divided by the product of the density, ρ, and sound speed, c, of
the undisturbed fluid
Note 1 to entry: In formula form, Ic= p /ρ .
eq
Note 2 to entry: Equivalent plane wave sound intensity is expressed in units of watt per metre squared (W/m ).
Note 3 to entry: The averaging time and frequency band shall be specified.
Note 4 to entry: The equivalent plane wave sound intensity is a scalar quantity, equal to the component of time-
averaged sound intensity (3.1.3.11) in the direction of propagation of a plane progressive sound wave having the
specified mean-square sound pressure.
3.1.3.13
mean-square sound pressure spectral density
 
p
 
 
f
distribution as a function of non-negative frequency of the mean-square sound pressure (3.1.3.1) per unit
bandwidth of a sound having a continuous spectrum
Note 1 to entry: Mean-square sound pressure spectral density is expressed in units of pascal squared per hertz
(Pa /Hz).
Note 2 to entry: In its idealized form, mean-square sound pressure spectral density is evaluated as the limit,
as the bandwidth tends to zero, of the mean-square sound pressure in a finite frequency band divided by the
frequency bandwidth.
Note 3 to entry: For operational purposes, mean-square sound pressure spectral density is estimated as the
mean-square sound pressure in a finite frequency band divided by the frequency bandwidth. The averaging time
and frequency band shall be specified.
Note 4 to entry: According to the continuous form of Parseval’s theorem (also known as Plancherel’s theorem),
the sound pressure spectrum (3.1.2.2), P( f), is related to the sound pressure, p(t), via the formula
+∞ +∞
Pf ddfp= tt . Here, |P( f )| is a function of both positive and negative frequencies and is known
() ()
∫∫
−∞ −∞
 
as a “double-sided” spectral density. By contrast, p is known as a “single-sided” spectral density because it
 
 
f
+∞
 
is a function of non-negative frequencies only and satisfies the formula ppdf = .
 
∫
 
f
Note 5 to entry: As a consequence of the Wiener-Khinchin theorem, the mean-square sound pressure spectral
density of a sound pressure signal is also equal to twice the Fourier transform (see ISO 80000-2) of the
autocorrelation function of that signal.
Note 6 to entry: Mean-square sound pressure spectral density is one of several related quantities known
generically as “power spectral density”. The generic term is used with a descriptor (in this case, mean-square
sound pressure) to indicate the type of power-like quantity whose spectral density is being described.
3.1.3.14
sound power
W
integral over a specified surface of the product of the sound pressure (3.1.2.1), p, and the component of
the sound particle velocity (3.1.2.10) in the direction normal to that surface, u
n
Note 1 to entry: Sound power is a function of time, t, which may be indicated by means of an argument t, as in W(t).
Note 2 to entry: Sound power is expressed in watts (W).
Note 3 to entry: This definition could become inapplicable in situations with a high mean fluid flow.
[SOURCE: ISO 80000-8:2007, 8-16, modified]
3.1.3.15
time-averaged sound power
W
av
integral over a specified time interval of sound power (3.1.3.14), W, divided by the duration of the time
interval, for a specified frequency range
Note 1 to entry: If the surface completely encloses a sound source, and in the absence of absorption, the time-
averaged sound power is equal to the average rate per unit time at which sound energy is radiated from the source.
3.1.4 Logarithmic frequency intervals
3.1.4.1
one-third octave
one-third octave (base 2)
one third of an octave
1/3
Note 1 to entry: The frequency ratio corresponding to a one-third octave is 2 , or approximately 1,259 9.
Note 2 to entry: One-third octave (base 2) bands are defined in ISO 13261-1.
Note 3 to entry: From the definition 1 oct ≡ log (2) = 1 (see ISO 80000-8:2007, 8-3.a), it follows that one one-third
octave (base 2) (1/3 oct) is equal to 1/3, or approximately 0,333 33.
[SOURCE: DIN 13320]
3.1.4.2
one-third octave (base 10)
decidecade
ddec
one tenth of a decade
0,1
Note 1 to entry: The frequency ratio corresponding to a decidecade (1 ddec) is 10 , or approximately 1,258 9,
which is smaller than a one-third octave (base 2) by approximately 0,08 %.
Note 2 to entry: The use of “one-third octave” to mean 1 ddec is permitted by IEC 61260-1 and ANSI/ASA S1.6-2016.
Note 3 to entry: From the definition 1 dec ≡ log (10) (see ISO 80000-8:2007, 8-3 b), it follows that one decidecade
(0,1 dec) is equal to 0,1 log (10), or approximately 0,332 19.
Note 4 to entry: The symbol for one-third octave (base 10) is ddec. This symbol is not intended to be used as an
abbreviation.
10 © ISO 2017 – All rights reserved

3.1.5 Other acoustical quantities
3.1.5.1
force impulse
J
F
integral of a transient force, over a specified time interval or event, for a specified frequency range
+∞ t
Note 1 to entry: In formula form, J = F ttd  or J = F ttd , where F(t) is the force, and the integral is
F () F ()
∫ ∫
−∞ t
taken either over the entire time-history, or between specified limits (as in th
...