Department of Mechanical EngineeringUniversity of AdelaideSouth Australia 5005AUSTRALIAchansen@mecheng.adelaide.edu.au Fundamental aspects of… [622551]

1
FUNDAMENTALS OF ACOUSTICS
Professor Colin H Hansen
Department of Mechanical EngineeringUniversity of AdelaideSouth Australia [anonimizat]
Fundamental aspects of acoustics are presented, as they relate to the understanding andapplication of a methodology for the recognition, evaluation and prevention or control of noiseas an occupational hazard. Further information can be found in the specialised literature listedat the end of the chapter.
1.1. PHYSICS OF SOUND
To provide the necessary background for the understanding of the topics covered in this
document, basic definitions and other aspects related to the physics of sound and noise arepresented. Most definitions have been internationally standardised and are listed in standardspublications such as IEC 60050-801(1994).
Noise can be defined as "disagreeable or undesired sound" or other disturbance. From the
acoustics point of view, sound and noise constitute the same phenomenon of atmospheric
pressure fluctuations about the mean atmospheric pressure; the differentiation is greatly
subjective. What is sound to one person can very well be noise to somebody else. The
recognition of noise as a serious health hazard is a development of modern times. With modernindustry the multitude of sources has accelerated noise-induced hearing loss; amplified musicalso takes its toll. While amplified music may be considered as sound (not noise) and to givepleasure to many, the excessive noise of much of modern industry probably gives pleasure tovery few, or none at all.
Sound (or noise) is the result of pressure variations, or oscillations, in an elastic medium
(e.g., air, water, solids), generated by a vibrating surface, or turbulent fluid flow. Soundpropagates in the form of longitudinal (as opposed to transverse) waves, involving a successionof compressions and rarefactions in the elastic medium, as illustrated by Figure 1.1(a). Whena sound wave propagates in air (which is the medium considered in this document), theoscillations in pressure are above and below the ambient atmospheric pressure.
1.1.1. Amplitude, Frequency, Wavelength And Velocity
Sound waves which consist of a pure tone only are characterised by:
/G04the amplitude of pressure changes , which can be described by the maximum pressure
amplitude, p
M, or the root-mean-square (RMS) amplitude, prms, and is expressed in Pascal
(Pa). Root-mean-square means that the instantaneous sound pressures (which can be positive

Fundamentals of acoustics 24
Figure 1.1. Representation of a sound wave.
(a) compressions and rarefactions caused in air by the sound wave.(b) graphic representation of pressure variations above and below
atmospheric pressure.or negative) are squared, averaged and the square root of the average is taken. The quantity,p
rms = 0.707 pM;
/G04the wavelength (/G1B), which is the distance travelled by the pressure wave during one cycle;
/G04the frequency (f), which is the number of pressure variation cycles in the medium per unit
time, or simply, the number of cycles per second, and is expressed in Hertz (Hz). Noise isusually composed of many frequencies combined together. The relation between
wavelength and frequency can be seen in Figure 1.2.
/G04the period (T), which is the time taken for one cycle of a wave to pass a fixed point. It is
related to frequency by: T = 1/f
Figure 1.2. Wavelength in air versus frequency under normal conditions (after Harris
1991).
The speed of sound propagation, c, the frequency, f, and the wavelength, /G1B, are related by the
following equation:
c = f/G1B
/G04the speed of propagation, c, of sound in air is 343 m/s, at 20 /G28C and 1 atmosphere pressure.
At other temperatures (not too different from 20 /G28C), it may be calculated using:
c = 332 + 0.6 T
c

Fundamentals of acoustics 25
c/G0A/G0BRTk/M(m s/G091) (1)
Figure 1.3. Sound generation illustrated. (a) The piston moves right, compressing air as
in (b). (c) The piston stops and reverses direction, moving left and decompressing air infront of the piston, as in (d). (e) The piston moves cyclically back and forth, producingalternating compressions and rarefactions, as in (f). In all cases disturbances move to theright with the speed of sound. where T
c is the temperature in /G28C . Alternatively the following expression may be used for
any temperature and any gas. Alternatively, making use of the equation of state for gases, thespeed of sound may be written as:
where T
k is the temperature in /G28K, R is the universal gas constant which has the value 8.314
J per mole /G28K, and M is the molecular weight, which for air is 0.029 kg/mole. For air, the
ratio of specific heats, /G0B, is 1.402.
All of the properties just discussed (except the speed of sound) apply only to a pure tone (single
frequency) sound which is described by the oscillations in pressure shown in Figure 1.1.However, sounds usually encountered are not pure tones. In general, sounds are complexmixtures of pressure variations that vary with respect to phase, frequency, and amplitude. Forsuch complex sounds, there is no simple mathematical relation between the differentcharacteristics. However
, any signal may be considered as a combination of a certain number
(possibly infinite) of sinusoidal waves, each of which may be described as outlined above. Thesesinusoidal components constitute the frequency spectrum of the signal.
To illustrate longitudinal wave generation, as well as to provide a model for the discussion
of sound spectra, the example of a vibrating piston at the end of a very long tube filled with airwill be used, as illustrated in Figure 1.3
Let the piston in Figure 1.3 move forward. Since the air has inertia, only the air immediately
next to the face of the piston moves at first; the pressure in the element of air next to the pistonincreases. The element of air under compression next to the piston will expand forward,

Fundamentals of acoustics 26
p
p
ptt
tff f1
f1f2f3
Frequency bands(a)
(c)
(e)(b)
(d)
(f)p2
p2
p2
Figure 1.4. Spectral analysis illustrated. (a) Disturbance p varies sinusoidally with time t
at a single frequency f1, as in (b). (c) Disturbance p varies cyclically with time t as a
combination of three sinusoidal disturbances of fixed relative amplitudes and phases; theassociated spectrum has three single-frequency components f
1, f2 and f3, as in (d).
(e) Disturbance p varies erratically with time t, with a frequency band spectrum as in (f).displacing the next layer of air and compressing the next elemental volume. A pressure pulse is
formed which travels down the tube with the speed of sound, c. Let the piston stop and
subsequently move backward; a rarefaction is formed next to the surface of the piston whichfollows the previously formed compression down the tube. If the piston again moves forward,the process is repeated with the net result being a "wave" of positive and negative pressuretransmitted along the tube.
If the piston moves with simple harmonic motion, a sine wave is produced; that is, at any
instant the pressure distribution along the tube will have the form of a sine wave, or at any fixedpoint in the tube the pressure disturbance, displayed as a function of time, will have a sine waveappearance. Such a disturbance is characterised by a single frequency. The motion andcorresponding spectrum are illustrated in Figure 1.4a and b.
If the piston moves irregularly but cyclically, for example, so that it produces the waveform
shown in Figure 1.4c, the resulting sound field will consist of a combination of sinusoids ofseveral frequencies. The spectral (or frequency) distribution of the energy in this particular soundwave is represented by the frequency spectrum of Figure 1.4d. As the motion is cyclic, thespectrum consists of a set of discrete frequencies.
Although some sound sources have single-frequency components, most sound sources
produce a very disordered and random waveform of pressure versus time, as illustrated in Figure

Fundamentals of acoustics 27
1.4e. Such a wave has no periodic component, but by Fourier analysis it may be shown that the
resulting waveform may be represented as a collection of waves of all frequencies. For a randomtype of wave the sound pressure squared in a band of frequencies is plotted as shown; forexample, in the frequency spectrum of Figure 1.4f.
It is customary to refer to spectral density level when the measurement band is one Hz wide,
to one third octave or octave band level when the measurement band is one third octave or oneoctave wide and to spectrum level for measurement bands of other widths.
Two special kinds of spectra are commonly referred to as white random noise and pink
random noise. White random noise contains equal energy per hertz and thus has a constantspectral density level. Pink random noise contains equal energy per measurement band and thushas an octave or one-third octave band level which is constant with frequency.
1.1.2. Sound Field Definitions (see ISO 12001)
1.1.2.1. Free field
The free field is a region in space where sound may propagate free from any form of obstruction.
1.1.2.2. Near field
The near field of a source is the region close to a source where the sound pressure and acoustic
particle velocity are not in phase. In this region the sound field does not decrease by 6 dB eachtime the distance from the source is increased (as it does in the far field). The near field is limitedto a distance from the source equal to about a wavelength of sound or equal to three times thelargest dimension of the sound source (whichever is the larger).
1.1.2.3. Far field
The far field of a source begins where the near field ends and extends to infinity. Note that the
transition from near to far field is gradual in the transition region. In the far field, the direct fieldradiated by most machinery sources will decay at the rate of 6 dB each time the distance from thesource is doubled. For line sources such as traffic noise, the decay rate varies between 3 and 4dB.
1.1.2.4. Direct field
The direct field of a sound source is defined as that part of the sound field which has not suffered
any reflection from any room surfaces or obstacles.
1.1.2.5. Reverberant field
The reverberant field of a source is defined as that part of the sound field radiated by a source
which has experienced at least one reflection from a boundary of the room or enclosurecontaining the source.
1.1.3. Frequency Analysis
Frequency analysis may be thought of as a process by which a time varying signal in the time
domain is transformed to its frequency components in the frequency domain. It can be used forquantification of a noise problem, as both criteria and proposed controls are frequency dependent.In particular, tonal components which are identified by the analysis may be treated somewhatdifferently than broadband noise. Sometimes frequency analysis is used for noise sourceidentification and in all cases frequency analysis will allow determination of the effectiveness of

Fundamentals of acoustics 28
controls.
There are a number of instruments available for carrying out a frequency analysis of
arbitrarily time-varying signals as described in Chapter 6 . To facilitate comparison of
measurements between instruments, frequency analysis bands have been standardised. Thus theInternational Standards Organisation has agreed upon "preferred" frequency bands for soundmeasurement and analysis.
The widest band used for frequency analysis is the octave band; that is, the upper frequency
limit of the band is approximately twice the lower limit. Each octave band is described by its"centre frequency", which is the geometric mean of the upper and lower frequency limits. Thepreferred octave bands are shown in Table 1.1, in terms of their centre frequencies.
Occasionally, a little more information about the detailed structure of the noise may be
required than the octave band will provide. This can be obtained by selecting narrower bands;for example, one-third octave bands. As the name suggests, these are bands of frequencyapproximately one-third of the width of an octave band. Preferred one-third octave bands offrequency have been agreed upon and are also shown in Table 1.1.
Instruments are available for other forms of band analysis (see Chapter 6). However, they
do not enjoy the advantage of standardisation so that the inter-comparison of readings taken onsuch instruments may be difficult. One way to ameliorate the problem is to present such readingsas mean levels per unit frequency. Data presented in this way are referred to as spectral densitylevels as opposed to band levels. In this case the measured level is reduced by ten times thelogarithm to the base ten of the bandwidth. For example, referring to Table 1.1, if the 500 Hzoctave band which has a bandwidth of 354 Hz were presented in this way, the measured octaveband level would be reduced by 10 log
10 (354) = 25.5 dB to give an estimate of the spectral
density level at 500 Hz.
The problem is not entirely alleviated, as the effective bandwidth will depend upon the
sharpness of the filter cut-off, which is also not standardised. Generally, the bandwidth is takenas lying between the frequencies, on either side of the pass band, at which the signal is down 3dB from the signal at the centre of the band.
There are two ways of transforming a signal from the time domain to the frequency domain.
The first involves the use of band limited digital or analog filters. The second involves the useof Fourier analysis where the time domain signal is transformed using a Fourier series. This isimplemented in practice digitally (referred to as the DFT – digital Fourier Transform) using a veryefficient algorithm known as the FFT (fast Fourier Transform). This is discussed further in theliterature referenced at the end of the chapter.
1.1.3.1. A convenient property of the one-third octave band centre frequencies
The one-third octave band centre frequency numbers have been chosen so that their logarithms
are one-tenth decade numbers. The corresponding frequency pass bands are a compromise; ratherthan follow a strictly octave sequence which would not repeat, they are adjusted slightly so thatthey repeat on a logarithmic scale. For example, the sequence 31.5, 40, 50 and 63 has thelogarithms 1.5, 1.6, 1.7 and 1.8. The corresponding frequency bands are sometimes referred toas the 15th, 16th, etc., frequency bands.

Fundamentals of acoustics 29
Table 1.1. Preferred octave and one-third octave frequency bands.
Band
numberOctave band
center frequencyOne-third octave band
center frequencyBand limits
Lower Upper
14
15 1631.525
31.5
4022
283528
3544
17
18 196350
638044
577157
7188
20
21 22125100
12516088
113141113
141176
23
24 25250200
250315176
225283225
283353
26
27 28500400
500630353
440565440
565707
29
30 311000800
10001250707
880
1130880
11301414
32
33 3420001600
200025001414
176022501760
22502825
35
36 3740003150
400050002825
353044003530
44005650
38
39 4080006300
8000
100005650
707088007070
8800
11300
41
42 431600012500
160002000011300
141401760014140
1760022500
NOTE: Requirements for filters see IEC 61260; there index numbers are used instead of band
numbers. The index numbers are not identical, starting with No.“0" at 1 kHz./G24
/G24/G24/G24/G24/G24/G24/G24/G24/G24

Fundamentals of acoustics 30
W/G0A/G50
AI/G23ndA(3)
W/G0A4/G25r2I (4)When logarithmic scales are used in plots, as will frequently be done in this book, it will be
well to remember the one-third octave band centre frequencies. For example, the centrefrequencies given above will lie respectively at 0.5, 0.6, 0.7 and 0.8 of the distance on the scalebetween 10 and 100. The latter two numbers in turn will lie at 1.0 and 2.0 on the samelogarithmic scale.
1.2. QUANTIFICATION OF SOUND
1.2.1. Sound Power ( W) and Intensity ( I) (see ISO 3744, ISO 9614 )
Sound intensity is a vector quantity determined as the product of sound pressure and the
component of particle velocity in the direction of the intensity vector. It is a measure of the rateat which work is done on a conducting medium by an advancing sound wave and thus the rateof power transmission through a surface normal to the intensity vector. It is expressed as wattsper square metre (W/m
2).
In a free-field environment, i.e., no reflected sound waves and well away from any sound
sources, the sound intensity is related to the root mean square acoustic pressure as follows
(2) Ip
crms=2
ρ
where /G27 is the density of air (kg/m3), and c is the speed of sound (m/sec). The quantity, /G27c is
called the "acoustic impedance" and is equal to 414 Ns/m³ at 20 /G28C and one atmosphere. At higher
altitudes it is considerably smaller.
The total sound energy emitted by a source per unit time is the sound power, W, which is
measured in watts. It is defined as the total sound energy radiated by the source in the specifiedfrequency band over a certain time interval divided by the interval. It is obtained by integratingthe sound intensity over an imaginary surface surrounding a source. Thus, in general the power,W, radiated by any acoustic source is,
where the dot multiplication of I with the unit vector, n, indicates that it is the intensity
component normal to the enclosing surface which is used. Most often, a convenient surface is an encompassing sphere or spherical section, but sometimes other surfaces are chosen, asdictated by the circumstances of the particular case considered. For a sound source producinguniformly spherical waves (or radiating equally in all directions), a spherical surface is mostconvenient, and in this case the above equation leads to the following expression:
where the magnitude of the acoustic intensity, I, is measured at a distance r from the source. In
this case the source has been treated as though it radiates uniformly in all directions.
1.2.2. Sound Pressure Level
The range of sound pressures that can be heard by the human ear is very large. The minimum
acoustic pressure audible to the young human ear judged to be in good health, and unsullied by

Fundamentals of acoustics 31
Lp/G0A10log10p2
rms
p2
ref/G0A20log10prms
pref/G0A20log10prms/G0920log10pref(dB) (5)
Lp/G0A20log10prms/G0894 (dB) (6)
LI/G0A10log10(sound intensity)
(ref. sound intensity)(dB) (7)
LI/G0A10log10I/G08120 (dB) (8)too much exposure to excessively loud music, is approximately 20 x 10-6 Pa, or 2 x 10-10
atmospheres (since 1 atmosphere equals 101.3 x 103 Pa). The minimum audible level occurs at
about 4,000 Hz and is a physical limit imposed by molecular motion. Lower sound pressurelevels would be swamped by thermal noise due to molecular motion in air.
For the normal human ear, pain is experienced at sound pressures of the order of 60 Pa or 6
x 10
-4 atmospheres. Evidently, acoustic pressures ordinarily are quite small fluctuations about
the mean.
A linear scale based on the square of the sound pressure would require 1013 unit divisions to
cover the range of human experience; however, the human brain is not organised to encompasssuch a range. The remarkable dynamic range of the ear suggests that some kind of compressedscale should be used. A scale suitable for expressing the square of the sound pressure in unitsbest matched to subjective response is logarithmic rather than linear. Thus the Bel wasintroduced which is the logarithm of the ratio of two quantities, one of which is a referencequantity.
To avoid a scale which is too compressed over the sensitivity range of the ear, a factor of 10
is introduced, giving rise to the decibel. The level of sound pressure p is then said to be L
p
decibels (dB) greater or less than a reference sound pressure pref according to the following
equation:
For the purpose of absolute level determination, the sound pressure is expressed in terms of a
datum pressure corresponding to the lowest sound pressure which the young normal ear candetect. The result is called the sound pressure level, L
p (or SPL), which has the units of decibels
(dB). This is the quantity which is measured with a sound level meter.
The sound pressure is a measured root mean square (r.m.s.) value and the internationally
agreed reference pressure pref = 2 x 10-5 N m-2 or 20 µPa . When this value for the reference
pressure is substituted into the previous equation, the following convenient alternative form isobtained:
where the pressure p is measured in pascals. Some feeling for the relation between subjective
loudness and sound pressure level may be gained by reference to Figure 1.5, which illustratessound pressure levels produced by some noise sources.
1.2.3. Sound Intensity Level
A sound intensity level, L
I, may be defined as follows:
An internationally agreed reference intensity is 10-12 W m-2, in which case the previous equation
takes the following form:
Use of the relationship between acoustic intensity and pressure in the far field of a source gives

Fundamentals of acoustics 32
LI/G0ALp/G0826/G0910log10(/G27c) (dB) (9)
LI/G0ALp/G090.2 (dB) (10)
Lw/G0A10log10(sound power)
(reference power)(dB) (11)
Lw/G0A10log10W/G08120 (dB) (12)
p2
trms/G0Ap2
1rms/G08p2
2rms/G082[p1p2]rmscos(/G071/G09/G072) (13)the following useful result:
LI = Lp + 10 log10 (8a)400
ρc

At sea level and 20 /G28C the characteristic impedance, /G27c, is 414 kg m-2 s-1, so that for both plane
and spherical waves,
1.2.4. Sound Power Level
The sound power level, Lw (or PWL), may be defined as follows:
The internationally agreed reference power is 10-12 W. Again, the following convenient form is
obtained when the reference sound power is introduced into the above equation:
where the power, W, is measured in watts.
For comparison of sound power levels measured at different altitudes a normalization according
to equation (8a) should be applied, see ISO 3745.
1.2.5. Combining Sound Pressures
1.2.5.1. Addition of coherent sound pressures
Often, combinations of sounds from many sources contribute to the observed total sound. In
general, the phases between sources of sound will be random and such sources are said to beincoherent. However, when sounds of the same frequency are to be combined, the phase betweenthe sounds must be included in the calculation.
For two sounds of the same frequency, characterised by mean square sound pressures p
2
1rms
and and phase difference , the total mean square sound pressure is given by thep2
2rms/G071/G09/G072
following expression (Bies and Hansen, Ch. 1, 1996).

Fundamentals of acoustics 33
Figure 1.5. Sound levels produced by typical noise sources

Fundamentals of acoustics 34
p2
trms/G0Ap2
1rms/G08p2
2rms(14)
p2
1rms/G0Ap2
ref×1090/10/G0Ap2
ref×10×108
p2
2rms/G0Ap2
ref×6.31×108When two sounds of slightly different frequencies are added an expression similar to that
given by the above equation is obtained but with the phase difference replaced with the frequencydifference, /G0C, multiplied by time, t. In this case the total mean square sound pressure rises and
falls cyclically with time and the phenomenon known as beating is observed, as illustrated inFigure 1.6.
Figure 1.6. Illustration of beating .
1.2.5.2. Addition of incoherent sound pressures (logarithmic addition)
When bands of noise are added and the phases are random, the limiting form of the previous
equation reduces to the case of addition of incoherent sounds; that is (Bies and Hansen, Ch. 1,1996),
Incoherent sounds add together on a linear energy (pressure squared) basis. A simple
procedure which may easily be performed on a standard calculator will be described. Theprocedure accounts for the addition of sounds on a linear energy basis and their representationon a logarithmic basis. Note that the division by 10 in the exponent is because the processinvolves the addition of squared pressures.
It should be noted that the add ition of two or more levels of sound pressure has a physical
significance only if the levels to be added were obtained in the same measuring point.
EXAMPLE
Assume that three sounds of different frequencies (or three incoherent noise sources) are to be
combined to obtain a total sound pressure level. Let the three sound pressure levels be (a) 90 dB,(b) 88 dB and (c) 85 dB. The solution is obtained by use of the previous equation.
Solution:
For source (a):
For source (b):

Fundamentals of acoustics 35
p2
3rms/G0Ap2
ref×3.16×108
p2
trms/G0Ap2
1rms/G08p2
2rms/G08p2
3rms/G0Ap2
ref×19.47×108
Lpt/G0A10log10[p2
trms/p2
ref]/G0A10log10[19.47×108]/G0A92.9dB
Lpt/G0A10log101090/10/G081088/10/G081085/10/G0A92.9dBFor source (c):
The total mean square sound pressure is,The total sound pressure level is, Alternatively, in short form,
Table 1.2 can be used as an alternative for adding combinations of decibel values. As an
example, if two independent noises with levels of 83 and 87 dB are produced at the same timeat a given point, the total noise level will be 87 + 1.5 = 88.5 dB, since the amount to be added tothe higher level, for a difference of 4 dB between the two levels, is 1.5 dB.
Table 1.2. Table for combining decibel levels.
Difference between the two db levels to be added dB
01234567891 0
3.0 2.5 2.1 1.8 1.5 1.2 1.0 0.8 0.6 0.5 0.4
Amount to be added to the higher level in order to get the total level dB
As can be seen in these examples, it is only when two noise sources have similar acoustic powers,
and are therefore generating similar levels, that their combination leads to an appreciable increasein noise levels above the level of the noisier source. The maximum increase over the levelradiated by the noisier source, by the combination of two random noise sources occurs when thesound pressures radiated by each of the two sources are identical, resulting in an increase of 3 dBover the sound pressure level generated by one source. If there is any difference in the originalindependent levels, the combined level will exceed the higher of the two levels by less than 3 dB.When the difference between the two original levels exceeds 10 dB, the contribution of the lessnoisy source to the combined noise level is negligible; the sound source with the lower level ispractically not heard.
1.2.5.3. Subtraction of sound pressure levels
Sometimes it is necessary to subtract one noise from another; for example, when background
noise must be subtracted from total noise to obtain the sound produced by a machine alone. Themethod used is similar to that described in the addition of levels and will be illustrated with anexample.
EXAMPLE
The noise level measured at a particular location in a factory with a noisy machine operating
nearby is 92 dB(A). When the machine is turned off, the noise level measured at the same

Fundamentals of acoustics 36
Lpm/G0A10 log101092/10/G091088/10/G0A89.8dB(A)
Lpi/G0ALpR/G09ILi (15)
Lp/G0ALpR/G0810log10/G4Dn
i /G0A110/G09(ILi/10)(16)
IL/G0A10log10/G4DnA
i /G0A110/G09(ILAi/10)/G0910log10/G4DnB
i /G0A110/G09(ILBi/10)(17)location is 88 dB(A). What is the level due to the machine alone?
Solution
For noise-testing purposes, this procedure should be used only when the total noise exceeds the
background noise by 3 dB or more. If the difference is less than 3 dB a valid sound test probablycannot be made. Note that here subtraction is between squared pressures.
1.2.5.4. Combining level reductions
Sometimes it is necessary to determine the effect of the placement or removal of constructions
such as barriers and reflectors on the sound pressure level at an observation point. The differencebetween levels before and after an alteration (placement or removal of a construction) is calledthe insertion loss, IL. If the level decreases after the alteration, the IL is positive; if the level
increases, the IL is negative. The problem of assessing the effect of an alteration is complex
because the number of possible paths along which sound may travel from the source to theobserver may increase or decrease.
In assessing the overall effect of any alteration, the combined effect of all possible
propagation paths must be considered. Initially, it is supposed that a reference level L
pR may be
defined at the point of observation as a level which would or does exist due to straight-linepropagation from source to receiver. Insertion loss due to propagation over any other path is thenassessed in terms of this reference level. Calculated insertion losses would include spreading dueto travel over a longer path, losses due to barriers, reflection losses at reflectors and losses dueto source directivity effects (see Section 1.3).
For octave band analysis, it will be assumed that the noise arriving at the point of observation
by different paths combines incoherently. Thus the total observed sound level may be determinedby adding together logarithmically the contributing levels due to each propagation path.
The problem which will now be addressed is how to combine insertion losses to obtain an
overall insertion loss due to an alteration. Either before alteration or after alteration, the soundpressure level at the point of observation due to the ith path may be written in terms of the ith
path insertion loss, IL
i, as (Bies and Hansen, Ch. 1, 1996)
In either case, the observed overall noise level due to contributions over n paths is
The effect of an alteration will now be considered, where note is taken that, after alteration,
the propagation paths, associated insertion losses and number of paths may differ from thosebefore alteration. Introducing subscripts to indicate cases A (before alteration) and B (after
alteration) the overall insertion loss (IL = L
pA – LpB) due to the alteration is (Bies and Hansen, Ch.
1, 1996),

Fundamentals of acoustics 37
IL/G0A10log1010/G090/10/G0810/G095/10/G0910log1010/G094/10/G0810/G096/10/G0810/G097/10/G0810/G0910/10EXAMPLE
Initially, the sound pressure level at an observation point is due to straight-line propagation and
reflection in the ground plane between the source and r eceiver. The arrangement is altered by
introducing a barrier which prevents both initial propagation paths but introduces four new paths.Compute the insertion loss due to the introduction of the barrier. In situation A, before alteration,
the sound pressure level at the observation point is L
pA and propagation loss over the path
reflected in the ground plane is 5 dB. In situation B, after alteration, the losses over the four new
paths are respectively 4, 6, 7 and 10 dB.
Solution:
Using the preceding equation gives the following result.
= 1.2 + 0.2 = 1.4 dB
1.3. PROPAGATION OF NOISE
1.3.1. Free field
A free field is a homogeneous medium, free from boundaries or reflecting surfaces. Considering
the simplest form of a sound source, which would radiate sound equally in all directions from aapparent point, the energy emitted at a given time will diffuse in all directions and, one secondlater, will be distributed over the surface of a sphere of 340 m radius. This type of propagationis said to be spherical and is illustrated in Figure 1.7.
Figure 1.7. A representation of the radiation of sound from a simple source in free field.

Fundamentals of acoustics 38
p2/G0A/G27cI/G0A/G27cW
4/G25r2 (18)
Lp/G0ALw/G0810log10/G27c
400/G0910log10(4/G25r2) (19)
Lp/G0ALw/G0910log10(4/G25r2) (20)
Lp/G0ALm/G0920log10r
rm(21)
Iav/G0AW
4/G25r2 (22)In a free field, the intensity and sound pressure at a given point, at a distance r (in meters) from
the source, is expressed by the following equation:
where /G27 and c are the air density and speed of sound respectively.
In terms of sound pressure the preceding equation can be written as:
which is often approximated as:
Measurements of source sound power, Lw, can be complicated in practice (see Bies and
Hansen, 1996, Ch. 6). However, if the sound pressure level, Lm, is measured at some reference
distance, rm, from the noise source (usually greater than 1 metre to avoid source near field effects
which complicate the sound field close to a source), then the sound pressure level at some otherdistance, r, may be estimated using:
From the preceding expression it can be seen that in free field conditions, the noise level
decreases by 6 dB each time the distance between the source and the observer doubles. However,true free-field conditions are rarely encountered in practice, so in general the equation relatingsound pressure level and sound power level must be modified to account for the presence ofreflecting surfaces. This is done by introducing a directivity factor, Q which may also be used
to characterise the directional sound radiation properties of a source.
1.3.2. Directivity
Provided that measurements are made at a sufficient distance from a source to avoid near field
effects (usually greater than 1 meter), the sound pressure will decrease with spreading at the rateof 6 dB per doubling of distance and a directivity factor, Q, may be defined which describes the
field in a unique way as a function solely of direction.
A simple point source radiates uniformly in all directions. In general, however, the radiation
of sound from a typical source is directional, being greater in some directions than in others. Thedirectional properties of a sound source may be quantified by the introduction of a directivityfactor describing the angular dependence of the sound intensity. For example, if the soundintensity I is dependent upon direction, then the mean intensity, I
av, averaged over an
encompassing spherical surface is introduced and,
The directivity factor, Q, is defined in terms of the intensity I/G15 in direction (/G15,/G35) and the mean
intensity (Bies and Hansen, Ch. 5, 1996):

Fundamentals of acoustics 39
Q/G15/G0AI/G15
Iav(23)
DI/G0A10log10Q/G15 (24)
W/G0AI4/G25r2
Q/G0Ap2
rms4/G25r2
/G27cQ(25a,b)
Lp/G0ALw/G0810log10Q
4/G25r2/G0ALw/G0810log101
4/G25r2/G08DI (26a,b)The directivity index is defined as (Bies and Hansen, Ch. 5, 1996),
1.3.2.1. Reflection effects
The presence of a reflecting surface near to a source will affect the sound radiated and the
apparent directional properties of the source. Similarly, the presence of a reflecting surface nearto a receiver will affect the sound received by the receiver. In general, a reflecting surface willaffect not only the directional properties of a source but also the total power radiated by thesource (Bies, 1961). As the problem can be quite complicated the simplifying assumption is oftenmade and will be made here, that the source is of constant power output which means that itsoutput sound power is not affected by reflecting surfaces (see Bies and Hansen, 1996 for a moredetailed discussion).
For a simple source near to a reflecting surface outdoors (Bies and Hansen, Ch. 5, 1996),
which may be written in terms of levels as
For a uniformly radiating source, the intensity I is independent of angle in the restricted region
of propagation, and the directivity factor Q takes the value listed in Table 1.3. For example, the
value of Q for the case of a simple source next to a reflecting wall is 2, showing that all of the
sound power is radiated into the half-space defined by the wall.
Table 1.3. Directivity factors for a simple source near reflecting surfaces.
Situation Directivity factor, QDirectivity Index,
DI (dB)
free space 1 0centred in a large flat surface 2 3centred at the edge formed by the junction of
two large flat surfaces46
at the corner formed by the junction of three
large flat surfaces89

Fundamentals of acoustics 40
Lp/G0ALw/G0810log10Q
4/G25r2/G084(1/G09¯/G05)
S¯/G05(27)1.3.3. Reverberant fields
Whenever sound waves encounter an obstacle, such as when a noise source is placed within
boundaries, part of the acoustic energy is reflected, part is absorbed and part is transmitted. Therelative amounts of acoustic energy reflected, absorbed and transmitted greatly depend on thenature of the obstacle. Different surfaces have different ways of reflecting, absorbing andtransmitting an incident sound wave. A hard, compact, smooth surface will reflect much more,and absorb much less, acoustic energy than a porous, soft surface.
If the boundary surfaces of a room consist of a material which reflects the incident sound, the
sound produced by a source inside the room – the direct sound – rebounds from one boundary toanother, giving origin to the reflected sound. The higher the proportion of the incident soundreflected, the higher the contribution of the reflected sound to the total sound in the closed space.This "built-up" noise will continue even after the noise source has been turned off. Thisphenomenon is called reverberation and the space where it happens is called a reverberant soundfield, where the noise level is dependent not only on the acoustic power radiated, but also on thesize of the room and the acoustic absorption properties of the boundaries.
As the surfaces become less reflective, and more absorbing of noise, the reflected noise
becomes less and the situation tends to a "free field" condition where the only significant soundis the direct sound. By covering the boundaries of a limited space with materials which have avery high absorption coefficient, it is possible to arrive at characteristics of sound propagationsimilar to free field conditions. Such a space is called an anechoic chamber, and such chambersare used for acoustical research and sound power measurements.
In practice, there is always some absorption at each reflection and therefore most work spaces
may be considered as semi-reverberant.
The phenomenon of reverberation has little effect in the area very close to the source, where
the direct sound dominates. However, far from the source, and unless the walls are veryabsorbing, the noise level will be greatly influenced by the reflected, or indirect, sound. Thesound pressure level in a room may be considered as a combination of the direct field (soundradiated directly from the source before undergoing a reflection) and the reverberant field (soundwhich has been reflected from a surface at least once) and for a room for which one dimensionis not more than about five times the other two, the sound pressure level generated at distance r
from a source producing a sound power level of L
w may be calculated using (Bies and Hansen,
Ch. 7, 1996),
where is the average absorption coefficient of all surfaces in the room.¯/G05
These principles are of great importance for noise control and will be further discussed in
more detail in Chapter 5 and 10.
1.4. PSYCHO-ACOUSTICS
For the study of occupational exposure to noise and for the establishment of noise criteria, not
only the physical characteristics of noise should be considered, but also the way the human earresponds to it.
The response of the human ear to sound or noise depends both on the sound frequency and
the sound pressure level. Given sufficient sound pressure level, a healthy, young, normal human

Fundamentals of acoustics 41
ear is able to detect sounds with frequencies from 20 Hz to 20,000 Hz. Sound characterised by
frequencies between 1 and 20 Hz is called infrasound and is not considered damaging at levelsbelow 120 dB. Sound characterised by frequencies in excess of 20,000 Hz is called ultrasoundand is not considered damaging at levels below 105 dB. Sound which is most damaging to therange of hearing necessary to understand speech is between 500 Hz and 2000 Hz.
1.4.1. Threshold of hearing
The threshold of hearing is defined as the level of a sound at which, under specified conditions,
a person gives 50% correct detection responses on repeated trials, and is indicated by the bottomline in Figure 1.8.
1.4.2. Loudness
At the threshold of hearing, a noise is just "loud" enough to be detected by the human ear. Above
that threshold, the degree of loudness is a subjective interpretation of sound pressure level orintensity of the sound.
The concept of loudness is very important for the evaluation of exposure to noise. The human
ear has different sensitivities to different frequencies, being least sensitive to extremely high andextremely low frequencies. For example, a pure-tone of 1000 Hz with intensity level of 40 dBwould impress the human ear as being louder than a pure-tone of 80 Hz with 50 dB, and a 1000Hz tone at 70 dB would give the same subjective impression of loudness as a 50 Hz tone at 85dB.
In the mid-frequency range at sound pressures greater than about 2 10
-3 Pa (40 dB re 20 µPa×
SPL), Table 1.4 summarises the subjective perception of noise level changes and shows that a
reduction in sound energy (pressure squared) of 50% results in a reduction of 3 dB and is justperceptible to the normal ear.
Table 1.4. Subjective effect of changes in sound pressure level.
Change in sound level
(dB)Change in power
Decrease IncreaseChange in apparent
loudness
3 1/2 2 just perceptible5 1/3 3 clearly noticeable
10 1/10 10 half or twice as loud20 1/100 100 much quieter or louder
The loudness level of a sound is determined by adjusting the sound pressure level of a
comparison pure tone of specified frequency until it is judged by normal hearing observers to be
equal in loudness. Loudness level is expressed in phons, which have the same numerical value
as the sound pressure level at 1000 Hz. Attempts have been made to introduce the sone as the
unit of loudness designed to give scale numbers approximately proportional to the loudness, butit has not been used in the practice of noise evaluation and control.
To rate the loudness of sounds, "equal-loudness contours" have been determined. Since these

Fundamentals of acoustics 42
contours involve subjective reactions, the curves have been determined through psycho-acoustical
experiments. One example of such curves is presented in Figure 1.8. It shows that the curvestend to become more flattened with an increase in the loudness level.
The units used to label the equal-loudness contours in the figure are called phons. The lines
in figure 1.8 are constructed so that all tones of the same number of phons sound equally loud.The phon scale is chosen so that, at 1 kHz, the number of phons equals the sound pressure level.For example, according to the figure a 31.5 Hz tone of 50 phons sounds equally as loud as a 1000Hz tone of 50 phons, even though the sound pressure level of the lower-frequency sound is 30dB higher. Humans are quite "deaf" at low frequencies. The bottom line in Figure 1.8 representsthe average threshold of hearing, or minimum audible field ( MAF).
1.4.3. Pitch
Pitch is the subjective response to frequency. Low frequencies are identified as "low-pitched",
while high frequencies are identified as "high-pitched". As few sounds of ordinary experienceare of a single frequency (for example, the quality of the sound of a musical instrument isdetermined by the presence of many frequencies other than the fundamental frequency), it is ofinterest to consider what determines the pitch of a complex note. If a sound is characterised bya series of integrally related frequencies (for example, the second lowest is twice the frequencyof the lowest, the third lowest is three times the lowest, etc.), then the lowest frequencydetermines the pitch.
Figure 1.8. Loudness level (equal-loudness) contours, internationally standardised for pure
tones heard under standard conditions (ISO 226) . Equal loudness contours are determinedrelative to the reference level at 1000 Hz. All levels are determined in the absence of thesubject, after subject level adjustment. MAF means minimum audible field.
Furthermore, even if the lowest frequency is removed, say by filtering, the pitch remains the

Fundamentals of acoustics 43
same; the ear supplies the missing fundamental frequency. However, if not only the fundamental
is removed, but also the odd multiples of the fundamental as well, say by filtering, then the senseof pitch will jump an octave. The pitch will now be determined by the lowest frequency, whichwas formerly the second lowest. Clearly, the presence or absence of the higher frequencies isimportant in determining the subjective sense of pitch.
Sense of pitch is also related to level. For example, if the apparent pitch of sounds at 60 dB
re 20 µPa is taken as a reference, then sounds of a level well above 60 dB and frequency below500 Hz tend to be judged flat, while sounds above 500 Hz tend to be judged sharp.
1.4.4. Masking
Masking is the phenomenon of one sound interfering with the perception of another sound. For
example, the interference of traffic noise with the use of a public telephone on a busy street corneris probably well known to everyone.
Masking is a very important phenomenon and it has two important implications:
/G04speech interference, by which communications can be impaired because of high levels of
ambient noise;
/G04utilisation of masking as a control of annoying low level noise, which can be "covered" by
music for example.
In general, it has been shown that low frequency sounds can effectively "mask" high frequency
sounds even if they are of a slightly lower level. This has implications for warning sounds whichshould be pitched at lower frequencies than the dominant background noise, but not at such a lowfrequency that the frequency response of the ear causes audibility problems. Generallyfrequencies between about 200 and 500 Hz are heard most easily in the presence of typicalindustrial background noise, but in some situations even lower frequencies are needed. If thewarning sounds are modulated in both frequency and level, they are even easier to detect.
Other definitions of masking are used in audiometry and these are discussed in Chapter 8 of
this document.
1.4.5. Frequency Weighting
As mentioned in the previous section, the human ear is not equally sensitive to sound at different
frequencies. To adequately evaluate human exposure to noise, the sound measuring system mustaccount for this difference in sensitivities over the audible range. For this purpose, frequencyweighting networks, which are really "frequency weighting filters" have been developed.
These networks "weight" the contributions of the different frequencies to the over-all sound
level, so that sound pressure levels are reduced or increased as a function of frequency before
being combined together to give an overall level. Thus, whenever the weighting networks areused in a sound measuring system, the various frequencies which constitute the sound contributedifferently to the evaluated over-all sound level, in accordance with the given frequency'scontribution to the subjective loudness of sound, or noise.
The two internationally standardised weighting networks in common use are the "A" and "C",
which have been built to correlate to the frequency response of the human ear for different soundlevels. Their characteristics are specified in IEC 60651.

Fundamentals of acoustics 44
Figure 1.9. Frequency weighting characteristics for A and C networks .Figure 1.9 and Table 1.5 describe the attenuation provided by the A, and C networks (IEC
60651).
The "A" network modifies the frequency response to follow approximately the equal loudness
curve of 40 phons, while the "C" network approximately follows the equal loudness curve of 100phons, respectively. A "B" network is also mentioned in some texts but it is no longer used innoise evaluations.
The popularity of the A network has grown in the course of time. It is a useful simple means
of describing interior noise environments from the point of view of habitability, community
disturbance, and also hearing damage , even though the C network better describes the loudness
of industrial noise which contributes significantly to hearing damage. Its great attraction lies in
its direct use in measures of total noise exposure (Burns and Robinson, 1970).
When frequency weighting networks are used, the measured noise levels are designated
specifically, for example, by dB(A) or dB(C). Alternatively, the terminology A-weighted soundlevel in dB or C-weighted sound level in dB are often preferred. If the noise level is measuredwithout a "frequency-weighting" network, then the sound levels corresponding to all frequenciescontribute to the total as they actually occur. This physical measurement without modificationis not particularly useful for exposure evaluation and is referred to as the linear (or unweighted)sound pressure level.
1.5. NOISE EVALUATION INDICES AND BASIS FOR CRITERIA
To properly evaluate noise exposure, both the type and level of the noise must be characterised.
The type of noise is characterised by its frequency spectrum and its variation as a function oftime. The level is characterised by a particular type of measurement which is dependent on thepurpose

Fundamentals of acoustics 45
of the measurement (either to evaluate exposure or to determine the optimum approach for noise
control).
Table 1.5. Frequency weighting characteristics for A and C networks (*) .
Frequency
HzWeighting, dB
AC
31.5 – 39 – 3
63 – 26 – 1
125 – 16 0250 – 9 0500 – 3 0
1,000 0 02,000 1 04,000 1 – 18,000 – 1 – 3
*This is a simplified table, for illustration purposes. The full characteristics for the A, B and
C weighting networks of the sound level meter have been specified by the IEC (IEC 60651).
1.5.1. Types of Noise ( see ISO 12001 )
Noise may be classified as steady, non-steady or impulsive, depending upon the temporal
variations in sound pressure level. The various types of noise and instrumentation required fortheir measurement are illustrated in Table 1.6.
Steady noise is a noise with negligibly small fluctuations of sound pressure level within the
period of observation. If a slightly more precise single-number description is needed, assessmentby NR (Noise Rating) curves may be used.
A noise is called non-steady when its sound pressure levels shift significantly during the
period of observation. This type of noise can be divided into intermittent noise and fluctuating
noise.
Fluctuating noise is a noise for which the level changes continuously and to a great extent
during the period of observation.
Tonal noise may be either continuous or fluctuating and is characterised by one or two single
frequencies. This type of noise is much more annoying than broadband noise characterised byenergy at many different frequencies and of the same sound pressure level as the tonal noise.

Fundamentals of acoustics 46
Table 1.6. Noise types and their measurement.
Characteristics Type of Source
Constant continuous sound Pumps, electric motors,
gearboxes, conveyers
Constant but intermittent
soundAir compressor, automatic
machineryduring a work
cycle
Periodically fluctuating
soundMass production, surface
grinding
Fluctuating non-periodic
soundManual work, grinding,
welding, component
assembly
Repeated impulses Automatic press, pneumatic
drill, riveting
Single impulse Hammer blow, material
handling, punch press,
gunshot, artillery fire
Noise characteristics classified according to the way they vary with time. Constant noise remains
within 5 dB for a long time. Constant noise which starts and stops is called intermittent.
Fluctuating noise varies significantly but has a constant long term average ( LAeq,T). Impulse noise
lasts for less than one second.

Fundamentals of acoustics 47
Type of Measurement Type of Instrument Remarks
Direct reading of A-weighted
valueSound level meter Octave or 1/3 octave analysis
if noise is excessive
dB value and exposure time
or LAeqSound level meter,
Integrating sound level meterOctave or 1/3 octave analysis
if noise is excessive
dB value, LAeq or noise
exposureSound level meter
Integrating sound level meter Octave or 1/3 octave analysis
if noise is excessive
LAeq or noise exposure
Statistical analysisNoise exposure meter,
Integrating sound level meterLong term measurement
usually required
LAeq or noise exposure &
Check "Peak" valueIntegrating sound level meter
with "Peak" hold and "C-
weighting"Difficult to assess. More
harmful to hearing than it
sounds
LAeq and "Peak" value Integrating sound level meter
with "Peak" hold and "C-
weighting"Difficult to assess. Very
harmful to hearing especially
close

Fundamentals of acoustics 48
Intermittent noise is noise for which the level drops to the level of the background noise
several times during the period of observati on. The time during which the level remains at a
constant value different from that of the ambient background noise must be one second or more.This type of noise can be described by
/G04the ambient noise level
/G04the level of the intermittent noise
/G04the average duration of the on and off period.
In general, however, both levels are varying more or less with time and the intermittence rate
is changing, so that this type of noise is usually assimilated to a fluctuating noise as describedbelow, and the same indices are used.
Impulsive noise consists of one or more bursts of sound energy, each of a duration less than
about 1s . Impulses are usually classified as type A and type B as described in Figure 1.10,according to the time history of instantaneous s ound pressure (ISO 10843) . Type A
characterises typically gun shot types of impulses, while type B is the one most often found inindustry (e.g., punch press impulses). The characteristics of these impulses are the peak pressurevalue, the rise time and the duration (as defined in Figure 1.10) of the peak.
Figure 1.10. Idealised waveforms of impulse noises. Peak level = pressure difference AB;
rise time = time difference AB; A duration = time difference AC; B duration = timedifference AD ( + EF when a reflection is present).
(a) explosive generated noise.(b) impact generated noise.
1.5.2. A-weighted Level
The noise level in dB, measured using the filter specified as the A network (see figure 1.9) is
referred to as the "A-weighted level" and expressed as dB(A). This measure has been widelyused to evaluate occupational exposure because of its good correlation with hearing damage eventhough the "C" weighting better describes the loudness of industrial noise.

Fundamentals of acoustics 49
LAeq,T/G0A10log101
T/G50T
0pA(t)
p02
dt (28)
LAeq,T/G0A10log101
T/G4DM
i /G0A1Ti×10(LAeq,Ti)/10dB (29)
EA,T/G0A/G50t2
t1p2
A(t)dt (30)
EA,T/G0A4T×10(LAeq,T/G09100)/10(31)
LAeq,8h/G0A10log10EA,8h
3.2×10/G099(32)1.5.3. Equivalent Continuous Sound Level ( see ISO 1999 )
Very often industrial noise fluctuates. This can be easily observed as the oscillations in the visual
display of a sound level meter in a noisy environment. The equivalent continuous sound level(L
eq) is the steady sound pressure level which, over a given period of time, has the same total
energy as the actual fluctuating noise. The A-weighted equivalent continuous sound level isdenoted L
Aeq. If the level is normalised to an 8-hour workday, it is denoted LAeq,8h. If it is over
a time period of T hours, then it is denoted LAeq,T, and is defined as follows:
where pA(t) is the time varying A-weighted sound pressure and p0 is the reference pressure
(20µPa). A similar expression can be used to define LCeq,T, the equivalent continuous C-weighted
level.
The preferred method of measurement is to use an integrating sound level meter averaging
over the entire time interval, but sometimes it is convenient to split the time interval into anumber (M) of sub-intervals, T
i, for which values of LAeq,Ti are measured. In this case, LAeq,T is
determined using,
1.5.4. A-weighted Sound Exposure
Sound exposure may be quantified using the A-weighted sound exposure, EA,T, defined as the
time integral of the squared, instantaneous A-weighted sound pressure, (pa2) over a p2
A(t)
particular time period, T = t2 – t1 (hours). The units are pascal-squared-hours (Pa2.h) and the
defining equation is,
The relationship between the A-weighted sound exposure and the A-weighted equivalent
continuous sound level, LAeq,T, is
A noise exposure level normalised to a nominal 8-hour working day may be calculated from
EA,8h using

1.5.5. Noise Rating Systems
These are curves which were often used in the past to assess steady industrial or community
noise. They are currently used in some cases by machinery manufacturers to specify machinery

Fundamentals of acoustics 50
Figure 1.11. Noise rating (NR) curvesnoise levels.
The Noise Rating ( NR) of any noise characterised in octave band levels may also be
calculated algebraically. More often the family of curves is used rather than the direct algebraiccalculation. In this case, the octave band spectrum of the noise is plotted on the family of curvesgiven in Figure 1.11. The NR index is the value of that curve which lies just above the spectrumof the measured noise. For normal levels of background noise, the NR index is equal to the valueof the A-weighted sound pressure level in decibels minus 5. This relationship should be usedas a guide only and not as a general rule.
The NR approach actually tries to take into account the difference in frequency weighting
made by the ear, at different intensity levels. NR values are especially useful when specifyingnoise in a given environment for control purposes.
NR curves are similar to the NC (Noise criterion) curves proposed by Beranek (Beranek,
1957). However, these latter curves are intended primarily for rating air conditioning noise and
have been largely superseded by Balanced Noise Criterion (NCB) curves, Fig. 1.12 .
Balanced Noise Criterion Curves are used to specify acceptable noise levels in occupied
spaces. More detailed information on NCB curves may be found in the standard ANSI S12.2-
1995 and in the proposals for its revision by Schomer (1999). The designation number of an NCBcurve is equal to the Speech Interference Level (SIL) of a noise with the same octave band levelsas the NCB curve. The SIL of a noise is the arithmetic average of the 500 Hz, 1 kHz, 2 kHz and4 kHz octave band levels.

Fundamentals of acoustics 51
/G13/G14/G13/G15/G13/G16/G13/G17/G13/G18/G13/G19/G13/G1A/G13/G1C/G13
/G1B/G13/G14/G13 /G13
/G19/G18
/G18/G18
/G17/G18
/G16/G18
/G14/G18
/G14/G13
/G13
/G19/G16 /G14/G19 /G14/G15 /G18 /G16/G14 /G11 /G18 /G15/G18 /G13 /G18/G13 /G13 /G14/G4E /G15/G4E /G17/G4E /G1B/G4E
/G32 /G46/G57 /G44/G59 /G48 /G45/G44 /G51 /G47 /G46/G48/G51 /G57 /G48/G55 /G49/G55 /G48/G54/G58 /G48/G51 /G46/G5C /G0B/G2B /G5D/G0C/G32 /G46 /G57/G44 /G59/G48 /G45/G44 /G51/G47 /G56/G52/G58 /G51/G47 /G53 /G55 /G48 /G56 /G56 /G58/G55 /G48 /G4F/G48 /G59 /G48 /G4F /G0B /G47/G25 /G55 /G48 /G15/G13 /G33 /G44/G0C µ /G0B/G31 /G26 /G25/G0C
/G15/G18/G24
/G25
Figure 1.12. Balanced Noise Criterion (NCB)
curves. Region A represents exceedance of
criteria for readily noticeable vibrations andRegion B represents exceedance of criteria formoderately (but not readily) noticeablevibrations.
REFERENCES
ANSI S12.2-1995, American National Standard . Criteria for Evaluating Room Noise.
Beranek, L.L. (1957) Revised Criteria for Noise in Buildings, Noise Control , Vol. 3, No. 1, pp
19-27.
Bies, D.A. (1961). Effect of a reflecting plane on an arbitrarily oriented multipole. Journal of
the Acoustical Society of America, 33, 286-88.
Bies, D.A. and Hansen, C.H. (1996). Engineering noise control: theory and practice , 2nd edn.,
London: E. & F.N. Spon.

Fundamentals of acoustics 52
Burns, W. and Robinson, D.W. (1970). Hearing and noise in industry . London: Her Majesty's
Stationery Office.
Schomer, P.D. (1999) Proposed revisions to room noise criteria, Noise Control Eng. J. 48 (4),
85-96
INTERNATIONAL STANDARDS
Titles of the following standards related to or referred to in this chapter one will find
together with information on availability in chapter 12:
ISO 226, ISO 1999, ISO 2533, ISO 3744, ISO 9614, ISO 12001, ISO 10843,
IEC 60651, IEC 60804, IEC 60942, IEC 61043, IEC 61260.
FURTHER READING
Filippi, P. (Ed.) (1998). Acoustics: Basic physics, theory and methods. Academic Press (1994
in French)
Lefebvre, M. avec J.Jacques (1997). Réduire le bruit dans l ‘entreprise . Edition INRS ED 808
Paris
Smith, B.J. et al. (1996). Acoustics and noise control . 2nd Ed. Longman
Suter, A.H. (Chapter Editor) (1998). Noise. In: ILO Encyclopaedia of Occupational Health and
Safety,4th edition, wholly rearranged and revised in print, on CD-ROM and online, ILOInternational Labour Organization, Geneva.
Zwicker, E. (1999). Psychoacoustics: Facts and models (Springer series in information sciences,
22)