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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Sound intensity and sound power in architectural acoustics

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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Sound intensity and sound power in architectural acoustics

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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Sound intensity and sound power in architectural acoustics

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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Sound intensity and sound power in architectural acoustics

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 Real-

Time Sound Analyzers type 2260 with Sound Intensity Probe type 3595 (state-

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Sound intensity and sound power in architectural acoustics

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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Sound intensity and sound power in architectural acoustics

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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Sound intensity and sound power in architectural acoustics

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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Sound intensity and sound power in architectural acoustics

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

measure. The reference sound power in air is normally taken to be 10−12 watt =

0 dB SWL.

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Sound intensity and sound power in architectural acoustics

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

and

sound source

sound power

Pac

watts

sound power

level Lw

dB re 10−12 W

Rocket engine 1,000,000 W 180 dB

Turbojet engine 10,000 W 160 dB

Siren 1,000 W 150 dB

Heavy truck engine or

loudspeaker rock concert100 W 140 dB

Machine gun 10 W 130 dB

Jackhammer 1 W 120 dB

Excavator, trumpet 0.3 W 115 dB

Chain saw 0.1 W 110 dB

Helicopter 0.01 W 100 dB

Loud speech,

vivid children0.001 W 90 dB

Usual talking,

Typewriter10−5 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

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.

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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

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.

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Sound intensity and sound power in architectural acoustics

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.

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.

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Sound intensity and sound power in architectural acoustics

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

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

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Sound intensity and sound power in architectural acoustics

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.

4.0 CONCLUSIONThe 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

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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.

REFERENCES

Acoustical Society of America Digital Library.

Bruel & Kjaer (2008) Sound Power

Egan .D. (1998}. Architectural Acoustics. New York: (MC Graw-Hill).

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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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