Sound intensity and sound power in architectural acoustics
1.0 INTRODUCTION
Architectural acoustics is the science of controlling sound within buildings.
The acoustical environment in and around buildings is influenced by numerous
interrelated and independent factors associated with the building planning
design construction process.
The architect, the engineer, the building technologist, and the constructor all
play a part in the control of acoustical problem.
A particular advantage of sound intensity measurement to manufacturers is that
production test bays may serve to double as sound power check facilities. Other
application of sound intensity measurement which are at present less well
developed than sound power determination are the in-situ evaluation of
acoustic impedance and sound absorption properties of materials; the detection
and evaluation
flanking transmission in buildings; and the in-situ
determination, under operational conditions, of the sound power generated by
fans together with the performance associated with in-duct attenuators.
The advent practical sound intensity measurement may be seen as one of the
most developments in acoustic technology since the introduction of digital
signal processing systems. It is of great value to equipment designer,
manufacturer, supplier and user, and, in particular, to the specialist acoustical
engineer concerned with the control and reduction of noise.
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2.0 SOUND INTENSITY
The sound intensity, I, (acoustic intensity) is defined as the sound power Pac
per unit area A. The usual context is the noise measurement of sound intensity
in the air at a listener's location. For instantaneous acoustic pressure pinst(t) and
particle velocity v(t) the average acoustic intensity during time T is given by
Both v(t) and I are vectors, which means that both have a direction as well as a
magnitude. The direction of the intensity is the average direction in which the
energy is flowing. The SI units of intensity are W/m2 (watts per square metre).
FIG 1: Decrease in sound intensity for an omnidirectional point source.
For a spherical sound source, the intensity in the radial direction as a function
of distance r from the centre of the source is:
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Here Pac (upper case) is the sound power and A the surface area of a sphere of
radius r. Thus the sound intensity decreases with 1/r2 the distance from an
acoustic point source, while the sound pressure decreases only with 1/r from
the distance from an acoustic point source after the 1/r-distance law.
Where p (lower case) is the RMS sound pressure (acoustic pressure).
Hence
The sound intensity I in W/m2 of a plane progressive wave is:
Where:
Sound intensity level, LI, is the magnitude of sound intensity, expressed in
logarithmic units (decibels).
(dB-SIL),
where Io is the reference intensity, 10-12 W/m2
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The term "intensity" is used exclusively for the measurement of sound in watts
per unit area.
To describe the strength of sound in terms, other than strict intensity, one can
use "magnitude" "strength", "amplitude", or "level" instead.
Sound intensity is not the same physical quantity as sound pressure. Hearing is
directly sensitive to sound pressure which is related to sound intensity. In
stereo the level differences have been called "intensity" differences, but sound
intensity is a specifically defined quantity and cannot be sensed by a simple
microphone, nor would it be valuable in music recording if it could.
{wikipedia}
FIG 2: Chart showing different intensities
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2.1 USES OF SOUND INTENSITY IN ARCHITECTURAL ACOUSTICS
{J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S32-S33 (November 1988)
Issue Date: November 1988}
Sound intensity has received significant attention over the past five years
in the fields of noise control and product noise analysis. Yet, at this date, it is an
infrequently used technique in consulting acoustics in general. Standards have
been slow in developing and thus have not increased its use, and the most
fundamental reason for its use is still the utility of its results rather than any
existing standard. The benefit of intensity measurement in architecture is
principally in its ability to indicate source direction, and this benefit is
particularly important in a number of fields now being studied. The first of
these is the open plan office, and the current work in intensity is based on an
interest in the performance of acoustical dividers and absorbers. The second
field, for which intensity seems to be the only measurement technique that is
easily used, is the analysis of compound element building facades. This
analysis is aimed at developing field transmission loss values for facade
elements, such as windows, doors, and wall section.
2.2 MEASUREMENT OF SOUND INTENSITY
The measurements of sound intensity are carried out over a close, imaginary
box (of any shape, e. g. a cuboid or rectangular parallelepiped, as in the
diagram on the next page) surrounding a piece of equipment operating in situ.
Based on these measurements, the sound power level of the piece of equipment
is determined by the sophisticated analyser. It is carried out using sound
intensity measurements with Brüel & Kjær (B&K) Modular Precision RealTime Sound Analyzers type 2260 with Sound Intensity Probe type 3595 (state-
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of-the-art hand-held sound intensity system). Using this system, the sound
power level may be determined according to ISO 9614-2 or ANSI S12.12.
Fig3: Equipment used for sound intensity measurement
2.2.1 APPLICATION OF SOUND INTENSITY MEASUREMENT
The application of sound intensity measurement may be broadly classified as
follows:
1. Determination of the sound power sources.
2. Measurement of sound energy transmission through partitions
{transmission loss}
3. Measurement of the sound absorption properties of materials and
structures.
4. Identification and rank ordering of source regions {source location and
identification}
5. Measurement of sound energy flow in fluid transport ducts.
A factor which is common to all these applications is the determination
of the sound power passing through some selected surface within a fluid.
Even in the process of source location, it is essentially the sound power
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of source regions, and not the sound intensity {sound power flux
density} which is of significance. For example, a small leak in a
partition may produce local intensities far in excess of the average over
the remainder of the partition surface, but the area of leak may be so
small as to render negligible its contribution to the total transmitted
power. An implication of considerable practical importance is that, in
cases where the normal sound intensity on a surface varies widely with
position, errors incurred in estimating local intensity must be considered
in relation to the associated area-weighted surface. It is therefore just as
important to minimize errors in the measurement of low intensities
distributed over relatively small areas.
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3.0 SOUND POWER
Sound power or acoustic power Pac is a measure of sonic energy E per time t
unit. The symbol for sound power is W and its unit is the watt. (Named after
the Scottish mechanical engineer James Watt, 1736-1819, of steam engine
fame.) A source that emits power equally in all directions is called an
omnidirectional source. Any other source is called a directional source.
For an omnidirectional point source, the sound wave spreads out from the
source in all directions. The sound power, W, of the source is hence spread
over the surface of a sphere.
SoS=4 r2
And
It is measured in watts, or sound intensity I times area A:
The measure of a ratio of two sound powers is
where
P1, P0 are the sound powers.
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3.1 THE SOUND POWER LEVEL
Sound power level or acoustic power level is a logarithmic measure of the
sound power in comparison to a specified reference level.
The sound power level of a signal with sound power W is [1] [2]
Where W0 is the 0 dB SWL reference level:
The sound power level is given the symbol LW or SWL. This is not to be
confused with dBW, which uses 1W as a reference level.
In the case of a free field sound source in air at ambient temperature, the sound
power level is approximately related to sound pressure level (SPL) at distance r
of the source by the equation
Where S0 = 1m2.
This is only valid assuming the acoustic impedance of the medium equals 400
Pa*s/m.
The sound power level PWL, LW, or LPac of a source is expressed in decibels
(dB) and is equal to 10 times the logarithm to the base 10 of the ratio of the
sound power of the source to a reference sound power. It is thus a logarithmic
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measure. The reference sound power in air is normally taken to be 10−12 watt =
0 dB SWL.
Sound power is neither room dependent nor distance dependent. Sound power
belongs strictly to the sound source.
Table 1: Sound power and sound power level of some sound sources
Situation
sound power sound power
and
Pac
level Lw
sound source
watts
dB re 10−12 W
Rocket engine
1,000,000 W
180 dB
10,000 W
160 dB
1,000 W
150 dB
100 W
140 dB
Machine gun
10 W
130 dB
Jackhammer
1W
120 dB
Excavator, trumpet
0.3 W
115 dB
Chain saw
0.1 W
110 dB
Helicopter
0.01 W
100 dB
0.001 W
90 dB
10−5 W
70 dB
Refrigerator
10−7 W
50 dB
(Auditory threshold at 2.8 m)
10-10 W
20 dB
(Auditory threshold at 28 cm)
10-12 W
0 dB
Turbojet engine
Siren
Heavy truck engine or
loudspeaker rock concert
Loud speech,
vivid children
Usual talking,
Typewriter
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Usable music sound (trumpet) and noise sound (excavator) both have the same
sound power of 0.3 watts, but will be judged psycho acoustically to be different
levels.
3.2 SOUND POWER WITH PLAIN SOUND WAVES
Between sound power and other important acoustic values there is the
following relationship:
Where:
Table 2: List of some symbols, units and their meanings
Symbol
Units
Meaning
p
Pa
sound pressure
f
Hz
frequency
Ξ
m
particle displacement
c
m/s
speed of sound
v
m/s
particle velocity
ω = 2πf
rad/s
angular frequency
ρ
kg/m3
density of air
Z=c·ρ
N·s/m³
acoustic impedance
a
m/s²
particle acceleration
I
W/m²
sound intensity
E
W·s/m³
sound energy density
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3.3 SOUND POWER MEASUREMENT
Noise emission values are increasingly becoming the subject of regulations for
a safer and healthier working place and for the protection of the environment.
Moreover,
awareness
among consumers
regarding
noise issues has
substantially increased and voluntary awards for companies who meet
acoustical criteria are becoming a product differentiator.
In cases where the noise emissions of products have been significantly reduced
(e.g., within the information technology industry) customer acceptability of the
product is mostly related to absence/minimal presence of tonal components.
Two quantities which complement each other can be used to describe noise
emissions. One is the sound power which has become the preferred quantity as
it is independent of the particular circumstances of the measuring environment.
The other is the emission sound pressure at specified positions in the vicinity of
the machinery (e.g., operator's position).
Measuring Sound Power
Sound Power can be determined according to three main methods:
1. Measure the sound pressure due to the source in a free (or essentially
free) sound field, and then determine its sound power from the sound
pressure measurements.
2. As 1, but in a diffuse sound field.
3. Direct measurements of sound intensity in any sound field to determine
the sound power of the source.
The pressure-based methods are most often used for production audits and
high-volume testing (with specific standards for information technology
equipment), while the intensity-based methods are generally used for
engineering and in-situ measurements.
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3.3.1 PULSE SOUND POWER TYPE 7799
It is a software application for determining noise emission quantities of
machinery, equipment and their sub-assemblies.
It includes the determination of sound power levels as described in
international standards, as well as the measurement of emission sound pressure
levels at specified positions in the vicinity of a machine.
Moreover, to evaluate the annoyance of tonal components in noise emissions,
the calculation of two complementary parameters, Tone-to-Noise Ratio and
Prominence Ratio, is seamlessly integrated in the solution.
Uses

To determine whether a product complies with noise specifications
(legislation, voluntary awards)

To compare the noise emissions of machinery and equipment of the
same and different types (for example, when benchmarking, or in
engineering work, when developing quieter products)

To analyze product sound in terms of identification and evaluation of
prominent discrete tones and impulsive noise
3.4 RELATIONSHIP BETWEEN SOUND INTENSITY AND
SOUND POWER
As most measurements of sound are in terms of sound power (p), it is useful to
know the relationship between sound intensity and sound Power:
Where:
I
= P2
C
I is the sound intensity in watts/m2
p is the sound pressure in Pa
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Is the density of medium in kg/m3
C is the speed of sound in m/s
For air at 21°C , = 1.2 kg/m3
and following the equation above:
c = 344 m/s
Therefore, I = = 0.0024 p2
Strictly speaking, this equation is for plane waves (i.e. waves propagating with
parallel wave fronts). However, away from a point source, the spherical waves
approximate plane waves.
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4.0 CONCLUSION
The rapid acceleration of our technological age has given us the ability to make
increasingly detailed analyses of our architectural acoustic environment. In turn
it is providing the tools for modelling building designs in order to predict the
greater accuracy than in the recent past their acoustic performance in advance
of any construction.
There is this prospect that these tools will continue to be improved and,
thereby, permit better and more economic processes for use in architectural
acoustics design. The architectural profession should keep abreast of this
increasing ability of the architectural acoustics profession to provide significant
service in the process of building design and it to contribute to an excellent
creative effort.
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REFERENCES
Acoustical Society of America Digital Library.
Bruel & Kjaer (2008) Sound Power
Egan .D. (1998}. Architectural Acoustics. New York: (MC Graw-Hill).
F.J. Fahy sound intensity
Georgia State University. Physics Department- Tutorial on Sound
intensity.
Metha, M. , Et al. (1999) Architectural Acoustics: Principle and Design.
Upple saddle River, MJ: Prentice Hall.
Ogunsote, O.O. Lecture note on Acoustic and Noise Control.
{Department of architecture, Federal University of Technology Akure,
Ondo State}
Stein, B & Reynolds, J. (2000). Mechanical & Electrical Equipment for
buildings, 9th edition. New York: John Willey & Sons.
Williams, J. Cavanaugh Joseph, A. Wilkes Principles and practice of
architectural acoustic
www.engineeringtoolbox.com
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