munjal, m.l. iisc lecture notes series, volume 3
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I I S c L e c t u r e N o t e s S e r i e s V o l u m e 3
Noise and
Vibrat ion Control
M L M u n ja l
Indian Institute of Scien ce India
IISc
ress
World cientific
N E W J E R S E Y
.
L O N D O N
.
S I N G A P O R E
.
B E I J I N G
·
S H A N G H A I
.
H O N G K O N G
·
T A I P E I
.
C H E N N A I
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Published by
World Sc ien t i f ic Pub l i sh ing Co . P te . Ltd .
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IISc Lecture Notes Series — Vol. 3
NOISE AND VIBRATION CONTROL
Copyr igh t © 2013 by Wor ld Sc ien t i f ic Pub l i sh ing Co . P te . Ltd .
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I S B N 9 7 8 - 9 8 1 - 4 4 3 4 - 7 3 - 7
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ri s Preface
orl Scientific Publishing Co mp an y Indian Institute of Science Collaboration
IISc Press
and
WSPC
are
co-publishing books authored
by
world renowned
scientists and engineers. This collaboration, started in 2008 during IISc s centenary
year under a Memorandum of Understanding between IISc and WSPC, has
resulted in the establishment of three Series: IISc Centenary Lectures Series
(ICLS), IISc Research Monographs Series (IRMS), and IISc Lecture Notes Series
(ILNS).
This pioneering collaboration will contribute significantly in
disseminating current
Indian scientific advancement worldwide.
The IISc Centenary Lectures Series will comprise lectures by designated
Centenary Lecturers - eminent teachers and researchers from all over the world.
The IISc Research Monographs Series will comprise state-of-the-art
monographs written by experts in specific areas. They will include, but not
limited to, the authors own research work.
The IISc Lecture Notes Series will consist of books that are reasonably self-
contained and can be used either as textbooks or for self-study at the postgraduate
level in science and engineering. The books will be based on material that has been
class-tested for most part.
Editorial Board
for the
IISc Lecture Notes Series (ILNS):
Gadadhar Misra, Editor-in-Chief ( gm mat h . i i s c . e r n e t . i n )
Chandrashekar
S Jog
( jogc@mecheng
. i i s c .
e r n e t .
i n )
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e r n e t
. i n )
Κ
L
Sebastian ( k l s @ i p c
. i i s c . e r n e t . i n )
Diptiman Sen ( d i p t i m a n @ c t s . i i s c .
e r n e t
. i n )
Sandhya Visweswariah ( s a n d hy a @ m r dg . i i s c .
e r n e t
. i n )
Vll
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ontents
Dedication ν
Series Preface vii
Preface ί
χ
Chapter Noise and Its M easurement 1
1.1
Plane Wave Propagation 2
1.2 Spherical W ave Propagation 4
1.3 Decibel Level 8
1.4 Frequency Analysis 9
1.5 Weighted Sound Pressure Level 12
1.6 Logarithmic Addition, Subtraction and Averaging 13
1.7 Directivity 18
1.8 Measurement of Sound Pressure Level 20
1.9 Loudness 23
1.10 Noise Limits in India 25
1.10.1
The noise pollution regulation and control) rules, 2000 25
1.10.2
Permissible no ise exposure for industrial workers 27
1.10.3
Noise limit
for
diesel generator sets
29
1.10.4 Noise limit for portable gensets 29
1.10.5
Noise limit for fire crackers 30
1.10.6 Noise limit for vehicles 31
1.11 Masking 33
1.12 Sound Level Meter 33
1.13 Microphones 34
1.14 Microphone Sensitivity 35
1.15
Intensity M eter
36
References 36
Problems in Chapter 37
Chapter 2 Vibration and Its M easurement 40
xiii
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XIV
Noise and Vibration ontrol
2.1 Vibration of Single Degree of Freedom System 41
2.1.1 Free vibration 42
2.1.2 Forced response 45
2.2 Vibration of a Multiple Degrees of Freedom System 48
2.2.1 Free response 49
2.2.2 Forced response of multi-DOF system 50
2.2.3 Modal expansion 50
2.3 Transmissibility 52
2.4 Critical Speed 58
2.5 Dynam ical Analogies 60
2.6 Vibration of Beams and Plates 63
2.7 Vibration Measurem ent 69
2.8 Measurement of Damping Measurement of Sound Pressure Level 74
2.8.1 Logarithmic decrement method 74
2.8.2 Half-power bandwidth method 75
References 77
Problems in Chapter 2 78
Chapter 3 - Vibration Control 80
3.1 Vibration Control at the Source 81
3.2 Vibration Isolators 83
3.2.1 Bonded rubber springs 84
3.2.2 Effect of compliant foundation 89
3.2.3 Pneum atic suspension 92
3.3 Dynam ic Vibration Absorber DVA) 94
3.4 Impedance Mismatch to Block Transmission of Vibration 98
3.4.1 Viscoelastic interlayer 99
3.4.2 Effect of blocking mass on longitudinal waves 101
3.4.3 Effect of blocking mass on flexural waves 106
3.5 Damping Treatments for Plates 107
3.5.1 Free layer damping FLD) treatment 108
3.5.2 Constrained layer damping CLD) treatment 109
3.6 Active Vibration Control 112
References 115
Problems in Chapter 3 116
Chapter 4 - Acoustics of
Room s, Partitions, Enclosures and Barriers 118
4.1 Sound Field in a Room 118
4.2 Acoustics of a Partition Wall 125
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ontents xv
4.3 Design of Acoustic Enclosures 132
4.4 Noise Reduction of a Partition Wall and Enclosure 138
4.5 Acoustics of Barriers 142
References 148
Problems in Chapter 4 148
Chapter 5 - Mufflers and Silencers 151
5.1 Electro-Acoustic Modeling 152
5.2 Transfer Matrix Modeling 154
5.3 Simple Expansion Chamber SEC) 168
5.4 Extended Tube Expansion Chamber ETEC) 171
5.5 Extended Concentric Tube Resonator ECTR) 175
5.6 Plug Muffler 178
5.7 Multiply Connected Muffler 180
5.8 Absorptive Ducts and Mufflers 182
5.9 Com bination Mufflers 189
5.10 Acoustic Source Characteristics of I.C. Engines 190
5.11 Designing for Adequate Insertion Loss 196
5.12 Mufflers for High Pressure Vents and Safety Valves 201
5.13 Design of Muffler Shell and End Plates 203
5.14 Helmholtz Resonators 205
5.15 Active Noise Control in a Duct 209
5.16 P ressure Drop C onsiderations 212
References 215
Problems in Chapter 5 218
Chapter 6 - Noise Control Strategies 221
6.1 Control of No ise at the Source 221
6.1.1 Select a quieter machine 221
6.1.2 Select lossy materials 222
6.1.3 Use quieter processes or tools 222
6.1.4 Reduce radiation efficiency 223
6.1.5 Maintain for quietness 224
6.1.6 Design of flow machinery for quietness 224
6.2 Control of No ise in the Path 226
6.3 Noise Control at the Receiver End 227
6.4 Noise Control of an Existing Facility 227
6.5 Estimation and Control of Compressor Noise 229
6.6 Estimation and Control of Noise of Fans and Blowers 233
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XVI
Noise and Vibration ontrol
6.7 Estimation and Control of Noise of Packaged Chillers 237
6.8 Estimation and Control of Noise of Cooling Towers 237
6.9 Estimation and Control of Pump Noise 239
6.10 Estimation and Con trol of Noise of Prime M overs 241
6.10.1 Turbines 241
6.10.2 Diesel engines 246
6.10.3
Electric motors 248
6.11 Jet Noise Estimation and Control 251
6.12 Estimation and Control of Gear Noise 256
6.13 Earthmoving Equipment Noise Estimation and Control 258
6.14 Impact Noise Control 259
6.15 Environmental Impact Assessment EIA) 261
References 264
Problems in Chapter 6 265
Nomenclature 267
Index 271
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Chapter
Noise and Its Measurement
Sound is a longitudinal wave in air, and wave is a traveling disturbance.
Mass and elasticity of the air medium are primary characteristics for a
wave to travel from the source to the receiver. A wave is characterized
by two state variables, namely, pressure and particle velocity. These
represent perturbations on the static ambient pressure and the mean flow
velocity of wind, respectively. The perturbations depend on time as well
as space or distance.
Noise is unwanted sound. It may be unwanted or undesirable because
of its loudness or frequency characteristics. Excessive or prolonged
exposure to noise may lead to several physiological effects like
annoyance, headache, increase in blood pressure, loss of concentration,
speech interference, loss of working efficiency, or even accidents in the
workplace. Persistent exposure of a worker to loud noise in the
workplace may raise his/her threshold of hearing.
The study of generation, propagation and reception of audible sound
constitutes the science of Acoustics. There are several branches of
acoustics, namely, architectural acoustics, electroacoustics, musical
acoustics, underwater acoustics, ultrasonics, physical acoustics, etc. The
field of industrial noise, automotive noise and environmental noise
constitutes engineering acoustics or technical acoustics. This in turn
comprises sub-areas like duct acoustics, vibro-acoustics, computational
acoustics,
etc.
The speed at which the longitudinal disturbances travel in air is called
sound speed, c. It depends on the ambient temperature, pressure and
density as follows.
c
=
(
r
RT)
m
=(
r
p
0
/p
0
f 1.1)
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2 Noise and Vibration Control
(1.6)
Here γ is the ratio of specific heats C
p
and C
v
, R is gas constant,
p
is s tat ic ambient pressure, p
0
is m ass densi ty, and Τ is the absolute
temperature of the medium. For air at s tandard pressure
(γ =1Α ,
R = 287.05 Jftkg.K), p
0
=
1.013xl0
5
Pa ), i t can ea sily b e
seen that
(1.2)
where Τ is the absolute temperature in Kelvin.
S y m b o l Τ is used for the t ime period of harmonic disturbances as
w ell. It is relate d to freque ncy f as follow s:
(1.3)
Fre que ncy / is m easu red in Hertz (Hz) or cycles per second.
Wave l eng t h λ of m oving disturbanc es, of fre qu en cy / , is given by
(1.4)
where c denotes speed of sound.
1 .1 P lane W ave Prop agat ion
Plane waves moving inside a wave guide (a duct with rigid walls) are
cal led one- dim ensio nal wav es. Th ese are charac terized by the fol low ing
one-dimensional wave equat ion [1] :
(1.5)
where ρ , ζ and t are acoust ic pressure, coordinate along direct ion of wave
propagation and t ime, respectively.
For harmonic waves , the t ime dependence is g iven by
e
]COt
o r cos(cot) or s in ( ùt),
wh r
ω =2π / is the circu lar freque ncy
in rad/s.
General solution of Eq. (1.5) may be written as
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Noise and Its Measurement 3
or as
p{z,t)= Ae
Mt
~
z/c)
+Be-
X
t+z/c
)
(1.7)
where k =
0/
c = 2n/X is cal led the wa ve num ber.
It can easily be seen that A is ampli tude of the forward progressive
wa ve and Β i s am pl i tude of the reflected or rearward progress ive wa ve.
Algebraic sum of the two progress ive waves moving in opposi te
direct ions is cal led a standing wav e. Th us, Eq . (1.6) represe nts acoust ic
pressure of a one-dim ensional s tanding wa ve. Th e corresponding
equation for particle velocity is given by
One-dimensional wave occurs primari ly in the exhaust and tai l pipe
of automot ive engines and reciprocat ing compressors . These waves are
characterized by a plane wave front normal to the axis of the pipe or
tube, and therefore they are cal led plane waves.
The forward wave is generated by the source and the rearward wave
is the result of reflection from the passiv e term ination dow nstre am . In
part icular, B/A = R is called the Reflection Coefficient, and may be
determined from the termination impedance [1]. In part icular, R = 0 for
anec hoic term ination, 1 for rigid (closed) term ination, and -1 for
expansion in to vacuu m . In general , R is a function of frequency.
In view of the plane wave character of the one-dimensional waves,
the acoust ic power flux W of a plane progressive wave may be wri t ten as
(1.8)
(1.9)
p
0
c,
prod uct of the m ean densi ty and sound speed, represen ts the
character is t ic impedance of the medium
For an ambient temperature of 25° C and the standard atmospheric
pressure (corresponding to the mean sea level) , we have
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4 Noise and Vibration Control
1 .2 Spherica l W ave Prop agat ion
Wave propagation in free space is characterized by the fol lowing Three-
Dimensional (3D) Wave Equat ion [1]
(1.13)
where V
2
is the La placian . In term s of spherical pola r coordina tes,
neglect ing angular dependence for spherical waves, Eq. (1.13) can be
written as
(1.14)
where Y = p
0
c
0
/ S is the Ch aracterist ic Im ped anc e of plan e w ave s,
defined as rat io of acoust ic pressure and volume velocity of a plane
progressive wave along a tube of area of cross-sect ion S.
(1.12)
Note that the factor of 2 in the denominator is due to the mean square
values required in the pow er calculat ion s. Th us, the net pow er
associated with a standing wave is given by
(1.10, 1.11)
where I is Sound Intensi ty defined as power per unit area in a
direction normal to the wave front (in the axial direction for plane
waves ) , S is area of cross-sect ion of the pipe, and V is cal led the Volume
Velocity.
Thus, the acoust ic power flux associated with the incident progressive
wave and the reflected progressive wave are given by
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Noise and Its Measurement 5
Comparison of Eqs. (1.5) and (1.14) suggests the fol lowing solut ion
for spherical waves:
(1.15)
(1.16)
(1.17)
Substi tut ing i t into the momentum equation
yields
Here r is the radial distance between the receiver and a point source.
It may again be noted that the first component of Eqs. (1.15) and (1.17)
represents the spherical ly outgoing or diverging wave and the second one
repres ents the incom ing or con verg ing spherical wa ve. In prac t ice, the
second component is hypothetical ; in al l pract ical problems dealing with
noise radiat ion from vibrat ing bodies one deals with the diverging wave
only. Th e rat io of pressu re and part icle velocity for the diverging
progress ive wave may be seen to be
(1.18a)
It may be observed that unlike for plane progressive waves, this rat io
is a function of dista nce r. Th is indic ates that for a sph erica l div ergin g
w ave , press ure and velocity are not in pha se. Ho we ver w hen the
Helmhol tz number kr tends to infinity (or is much larger than unity), then
this ratio tends to p
0
c. Ph ysic ally, i t im plies that in the far field a
spherical d iverging wave becomes or behaves as a p lane progress ive
wave. This also indicates that the microphone of the sound level meter
should not be near the vibrating surface; it should be in the far field.
In the far f ield, Helmholtz number is much larger than unity
[kr
» l)
and then Eqs. (1.15), (1.17) and (1.18a) reduce to
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6 Noise and Vibration Control
(1.18 b, c)
and therefore, sound intensi ty and total power are given by
(1.18 d-h)
where
4nr
2
is the surface area of a hy po thetic al sphe re of rad ius r ove r
which the to tal pow er Wis divid ed equally to yield intensity l(r).
Example 1 .1 A bubble-l ike sphere of 5 mm radius is pulsat ing
harmonical ly at a frequency of 1000 Hz with ampli tude of radial
displac em ent 1 m m in air at m ean sea level and 25° C. E valu ate
(a) am plitu de of the rad ial velo city of the sphere surface ;
(b) ampli tude of the acoust ic pressure and part icle velocity at a
radial distance of 1 m.
(a) For harm onic radial mo t ion, radial velocity u equals ω t imes
th e radial d isp lacem ent ξ , w here ω = 2 π / . T hu s ω = 2 π χ 1 0 0 0
= 6 2 8 3. 2 r a d / s
Solution
Helmhol tz number , kr = 18.16 at r = lm, and 0.091 at r = 0.005 m
(i.e., on the surface). As per Eq. (1.17), for a diverging spherical
wave in free field, Β = 0, and
(b) Wave number,
Dis tance ,
r=lm
(given)
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Noise and Its Measurement
7
It is worth noting that
or
Substi tut ing this value of A in Eq. (1.17) for r = lm yields
Now, use of Eq. (1.15) yields
Incidental ly, sou nd pressure am pli tude at 1 m ma y also be obtained
by means of Eq. (1.18a):
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8 Noise and Vibration Control
where log denotes log to the base 10, and p
th
= 2 x l 0
- 5
Pa represents
the threshhold of hearing. This standard quanti ty represents the root-
mean-square pressure of the faintest sound of 1000 Hz frequency that a
normal human ear can jus t p ick up. The corresponding value of the
reference intensi ty represents
(1.22)
Human ear is a fantast ic t ransducer. I t can pick up pressure fluctuations
of the order of 1CT
5
Pa to 1 0
3
Pa; that is, i t has a dynamic range of
1 0
8
The refore, a l inear unit of m easu rem ent is ruled out . Instead,
universal ly a logari thmic unit of decibels has been adopted for
measurements of Sound Pressure Level , In tens i ty Level and Power
Level . These are defined as fol lows [1-3]:
1.3 De cibe l Le vel
Thus, at the surface (or in the nearfield), sound pressure leads radial
veloci ty by 90° (because j = e
J7rl2
}
,
w he rea s in the farfield sound
pressure is in phase with part icle velocity.
ikr at the surface, where kr 1,
(1.19)
(1.20)
(1.21)
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1.4 Fre qu enc y An alys is
The human ear responds to sounds in the frequency range of 20 Hz to
20,000 Hz (20 kHz), al though the human speech range is 125 Hz to 8000
(1.26)
Here , n
s
is the nu m ber of surfaces touch ing at the source. Th us,
n
s
-
0 for a source in mid air (or free space),
1 for a source lying on the floor,
2 for a source located on the edge of two surfaces, and
3 for a source located in a corner (where three surfaces meet).
Specifically, for a source located on the floor in the open, Eq. (1.24)
yields
(1.25)
where Q is the locational directivity factor, given by [2, 3]
(1.24)
This indicates that in the far field, the sound pressure level or sound
intensi ty level would decrease by 6 decibels when the measurement
distance from the source is doubled.
For spherical ly diverging waves the sound pressure level at a distance
r
from a point source is related to the total sound power level as follows
[2]:
(1.23)
Similarly,
ref
=10~
12
W.
Making use of Eqs. (1.15) and (1.17) in Eq. (1.20) indicates that in
the far field the acoustical intensity is inversely proportional to the radial
distance r . Th is inverse square law wh en interpreted in logari thm ic units
becomes
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10 Noise and Vibration Control
2
1 / 3
= 1 . 2 6 a nd 1 0
1
= 1.259
(1.32)
It may also be noted that
(1.31)
In Eqs. (1.27) to (1.30), subscripts / , u and m denote lower, upper and
m ean , respec tively. I t m ay be noted that three contigu ous 1/3-octave
bands would have the combined frequency range of the octave band
centered at the centre frequency of the midd le 1/3-octave ban d.
1000 Hz has been recognized internationally as the standard reference
freque ncy, and the m id frequ encie s of all octa ve ba nd s and 1/3-octave
bands have been fixed around this frequency. Table 1.1 gives a
comparison of different octave and 1/3-octave bands.
Incidental ly, the standard frequency of 1000 Hz happens to be the
geometric mean of the human speech frequency range; that is ,
so that
(1.30)
(1.29)
(1.28)
(1.27)
Similarly, for a one-third octave band,
and
and
and
so that
Hz . Prec isely, m ale speech l ies betw een 125 Hz to 40 00 Hz, and fem ale
speech is one octave higher, that is , 250 Hz to 8000 Hz.
T he audible frequency ra nge is divided into octave and 1/3-octave
bands. For an octave band,
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Table 1.1 Bandwidth and geometric mean frequency of standard octave and
Vs-octave bands [12].
1
OCTAVE
OCTAVE
Lower
Center
Lower
Center
cutoff
frequency
(Hz)
Center
Upper
cutoff
frequency
(Hz)
Center
Upper
cutoff
frequency
(Hz)
frequency
(Hz)
cutoff
frequency
cutoff
frequency
(Hz)
frequency
(Hz)
cutoff
frequency
22.4
25
28.2
22
31.5
44 28.2
35.5
44.7
31.5
40
50
35.5
44.7
56.2
44
63 88
56.2
70.8
89.
1
63
80
100
70.8
89.1
112
88 125 177
112
141
178
125
160
20
0
141
178
224
177 250 355 224
282
355
250
315
400
282
355
447
355 500 710 447
562
708
500
630
800
562
708
891
710 1000 1420 891
1122
1413
1000
1250
1600
1122
1413
1778
1420
2000 2840
1778
2239
2818
2000
2500
3150
2239
2818
3548
2840 4000 5680 3548
4467
5623
4000
5000
6300
4467
5623
7079
5680 8000 11360 7079
8913
11220
8000
10000
12500
8913
11220
14130
11360
16000 22720
14130
17780
16000
20000
17780
22390
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Thus, for pract ical purposes, 2
1 / 3
= 1 0
1 / 1 0
. Tha t is why w orkin g ei ther
way around 1000 Hz, 100 Hz, 200 Hz, 500 Hz, 2000 Hz, 5000 Hz,
10,000 Hz represent the mean frequencies of the respective
1/3-octave
bands .
It m ay also be noted that the cen ter frequ encie s in dica ted in the
2
n d
and 5
t h
columns of Table 1.1 are internationally recognized nominal
frequencies and may not be precise.
It may also be noted that the octave band and
1/3-octave
band filters
are constant percentage band-width f i l ters . The percentage bandwidth of
an η -octave fil ter ma y be wri t ten as
Th us, for an octave filter (n = 1), ba nd w idth is 70.7 % and for a on e-
third octave filter (n = 1/3), the bandwidth is 23.16% of the mean or
centre frequency of the particular fil ter.
Power spectral densi ty represents acoust ic power per unit frequency
as a function of freque ncy. Po w er in a ba nd of frequ encies rep rese nts
area under the curve within this band. For example, for a flat (constant
power) spectrum, the power in a frequency band would be proport ional
to the ban dw idth in He rtz. As the ban dw idth of an octave band doub les
from one band to the next , the sound pressure level or power level would
increase by 10 log 2 = 3 dB . Similarly, the SPL or SWL of a 1/3-octave
band would increase by 10 log2
1 / 3
=
1
dB, as w e m ov e from one ban d to
the next . As a corollary of the phenomenon, SPL in an octave band
would be equal to the logari thmic sum of the SPLs of the three
cont iguous 1/3-octave bands const i tut ing the octave band.
1 .5 W eighted Soun d Pressure Level
Th e hum an ear resp ond s differently to sounds of different frequenc ies.
Extensive audiological surveys have resulted in weighting factors for
different purposes. Originally, A-weighting was for sound levels below
55 dB, B-weighting was for levels between 55 and 85 dB, and C-
weighting was for levels above 85 dB. These are shown in Fig. 1.1.
(1.33)
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Noise and Its Measurement 13
Significantly , howe ver the Α -weight ing netwo rk is now used exclus ively
in most measurement standards and the mandatory noise l imits .
Fig. 1.1 Approxim ate electrical frequency response of the A-, B- , and C-weighted
networks of sound level meters [12].
Table 1.2 contains a listing of the corrections in decibels to be added
algebraically to all f requency ba nds . Th e Α -weighted sound pressure
level is denoted as
The former notat ion is more logical . However, the lat ter continues to
be in wide use. Incidental ly, symbol dBA is often wri t ten as dB(A).
The second column in Table 1.2 indicates octave numbers in popular
use among profess ionals .
(1.34)
1 .6 Loga ri thmic Add i t ion , Subtract ion and Ave rag ing
The total sound power level of two or more incoherent sources of noise
may be calculated as fol lows:
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Table 1.2 Sound level conversion chart from flat response to A, B, and C weightings.
Frequency
(Hz)
Octave band
number
A weighting
(dB)
Β weighting
(dB)
C weighting
(dB)
20 -50.5
-24.2 -6.2
25 -44.7
-20.4 -4.4
31.5
-39.4
-17.1 -3.0
40 -34.6
-14.2
-2.0
50
-30.2
-11.6 -1.3
63 1
-26.2
-9.3 -0.8
80 -22.5 -7.4 -0.5
100 -19.1 -5.6 -0.3
125
2
-16.1
-4.2 -0.2
160
-13.4
-3.0 -0.1
200 -10.9 -2.0 0
250 3 -8.6 -1.3 0
315 -6.6 -0.8 0
400 -4.8 -0.5 0
500 4 -3.2 -0.3 0
630 -1.9 -0.1 0
800 -0.8 0 0
1000 5 0 0 0
1250 +0.6 0 0
1600 +1.0 0 -0.1
2000 6
+1.2
-0.1
-0.2
2500 +1.3
-0.2
-0.3
3150 +1.2 -0.4 -0.5
4000 7 +1.0 -0.7 -0.8
5000 +0.5
-1.2
-1.3
6300 -0.1 -1.9 -2.0
8000 8 -1.1 -2.9 -3.0
10000 -2.5 -4.3
-4.4
12500 -4.3 -6.1
-6.2
16000 -6.6
-8.4
-8.5
20000 -9.3 -11.1
-11.2
(1.35)
or
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(1.36)
He re η denotes the to tal num ber of incoherent sources l ike m achines
in a workshop or different sources of noise in an engine, etc. Similarly,
the corresponding total SPL at a point is given by
(1.37)
Incidental ly, Eqs. (1.35) - (1.37) would also apply to logari thmic
addit ion of SPL or SWL of different frequency bands in order to
calculate the total level . The logari thmic addit ion of power levels or
sound pressure levels have some interest ing implicat ions for noise
con trol. It m ay easily be verified from E qs . (1.36) and (1.37) that
10 0® 100 = 103
dB
10 0® 90 = 100.4 dB
χ ® x = x + 3 dB
Similarly, 10 identical sources of
χ
dB w ould add up to x + 10 d B .
Percept ion wise,
3 dB increase in SP L is hardly no ticeab le;
5 dB increase in SP L is clearly notice able; an d
10 dB increase in SPL appears to be twice as loud.
Similarly, 10 dB decrease in SPL would appear to be half as loud,
indicat ing 50% reduction in SPL. Therefore, i t fol lows that :
(i) In a co m ple x noisy situation, on e m ust first identify all significant
sources, rank them in descending order and plan out a s trategy for
reducing the noise of the largest source of noise first , and then only
tackle other sources in a descending order.
(ii ) W hile designing an industrial layout or the arran gem ent of m ach ines
and processes in a workshop, one must identify and locate the
noisiest machines and processes together in one corner, and isolate
this area acoustically from the rest of the workshop or factory.
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(iii) It is m ost cost effective to redu ce all significant sourc es of noise
down to the same desired level .
Addit ion of the sound pressure levels of the incoherent sources of
noise may be done easi ly by making use of Fig. 1.2 which is based on the
following formula:
(1.38)
It may be noted that the addit ion AL to the higher of the two levels is
only 0.4 dB when the difference of the levels ( L
pl
-L
p2
J
equa ls 10 dB .
Therefore for all practical purposes, in any addition, if the difference
between the two levels is more than 10 decibels , the lower one may be
ignored as relatively insignificant.
If one is adding more than two sources, one can still use Fig. 1.2,
adding two at a time starting from the lowest, as shown Fig. 1.2
The concept of addit ion can also be extended to averaging of sound
pressure level in a community locat ion. Thus, the equivalent sound
pressure level during a t ime period of 8 hours may be calculated as an
avera ge of the hourly read ings; that is ,
(1.39)
This averaging is done automatical ly in an integrat ing sound level
meter or dosimeter used in the factories in order to ensure that a worker
is not subjected to more than 90 dBA of equivalent sound pressure level
during an 8 hou r shift. Sim ilarly, one can m eas ure L
d
, the day t ime
average (6 AM to 9 PM) and
L
n
, the night t ime average (9 PM to 6
A M ) .
Making use of the fact that one needs quieter environment at night ,
the day-night average (24-hour average) is calculated as fol lows:
(1.40)
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It may be noted that the L
n
has be en increased by 10 dB A in order to
account for our increased sensitivity to noise at night.
Fig. 1.2 Logarithmic add ition of two SPLs, L
p l
® L
p 2
.
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Example 1 .2 For a reasonably flat frequency spectrum with no sharp
peaks or t roughs, the band is nearly equal to the sum of the sound powers
in the three contiguous one-third octave bands. Make use of this fact to
evaluate sound pressure level of the 500 Hz band if the measured values
of the 400-Hz, 500-Hz and 630-Hz 1/3-octave bands are 80, 90 and 85
d B ,
respectively.
Solut ion
It m ay be noted from Ta ble 1.1 that the freque ncy ran ge of
400 -H z 1/3-octave ba nd is 355 - 4 47 Hz,
500 -Hz 1/3-octave ba nd is 447 - 562 Hz,
630 -Hz 1/3-octave ba nd is 562 - 708 Hz , and
5 0 0 - H z l / l - o c t a v e b a n d i s 3 5 5 - 7 1 0 H z
Th us, the 500 -Hz oc tave ban d spans all three contiguous 1/3-octave
bands. Therefore making use of Eq. (1.37),
L
p
(500 Hz octave band) = 10 log ( l 0
8 0 / 1 0
+ 1 0
9 0 / 1 0
+ 1 0
8 5 / 1 0
)
= 91.5 dB
1.7 Directivity
Most pract ical sources of noise do not radiate noise equally in al l
directions. This directionality at distance r in the far field is measured in
terms of a directivity index DI, or directivity factor DF, as follows:
(1.41)
The average sound pressure level L
pav
is calc ulate d from the total
sound power level by
(1.42)
The average sound pressure level can be evaluated by averaging the
measured sound pressure levels at different angles at the same distance
(r) around the source, making use of the formula
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Noise and Its Measurement 19
(1.43)
If all the levels around the machine are within 5 dB of each other,
then instead of Eq. (1.43) one can take the ari thmetic average of SPLs
and ad d 1 dB to i t in order to get a reason ably app roxim ate v alue of the
average sound pressure level .
Example 1 .3 Sou nd pressure levels at four points around a m ach ine are
85, 88 , 92 and 86 dB wh en the m ach ine is on. Th e ambien t SPL at the
four points (when the machine is off) is 83 dB. Calculate the average
SPL of the machine alone (by i tself) .
Solution
Making use of Eq. (1.43),
Incidental ly, the ari thmetic average of the SPLs at the four points
works out to be
So, the logari thmic average is quite close ' to the ari thmetic average
p lus 1 d B ' .
Now, logari thmically subtract ing the ambient SPL we get
m chine lone
L
av
machine ambient
)
= 10 log
= 88.6
dB
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1 .8 M easur em ent o f Soun d Pow er Level
A more precise method of measuring the average sound pressure level
and the total power level of a source consists in making use of an
anechoic room. This is a special ly constructed room to simulate free field
en viro nm en t. Its w alls as w ell as the floor and the ceiling are lined w ith
long thin wedges of acoust ical ly absorbent material with power
absorption coefficient of 0.99 (99%) or more in the frequency range of
interest . Low frequency noise is not absorbed easi ly. The lowest
frequency upto which the absorption coefficient is at least 0.99 is called
the cut-off frequency of the anechoic room. Such rooms are used for
precise measurements as per international s tandards.
However, i t is logistically very difficult to mount large and heavy test
ma chines on suspended net f looring. Therefore the Enginee ring M ethod
of measurement of sound pressure level of a machine to a reasonable
accuracy is to make use of a hemi-anechoic room where one s imulates a
hem i-sphe rical free field. This is l ike test ing a m ach ine on the grou nd in
an open ground . In such a roo m the floor is acoust ical ly hard (highly
reflective) while all the four walls and the ceiling are lined with highly
absorbent acoust ical wedges as indicated above for an anechoic room.
Table 1.3 Co-ord inates of the 12 microphone locations.
Location
X
y_
No.
r r
ζ
1 1
0
1.5 m
2
0.7 0.7
1.5 m
3 0 1
1.5 m
4
-0.7 0.7
1.5 m
5 -1 0
1.5 m
6 -0.7 -0.7
1.5 m
7 0 -1 1.5 m
8 0.7 -0.7
1.5 m
9 0.65 0.27 0.71 r
10 -0.27 0.65 0.71 r
11
-0.65 -0.27 0.71 r
12
0.27 0.65 0.71 r
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Fig. 1.3 Microphone locations on a hypo thetical hem i-spherical surface.
21
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Noise
and
Vibration Control
Alternatively, one can use the so-called Survey Method where
measurements are made at discrete microphone locations on the
parallelepiped shown in Fig. 1.4.
If
S
m
is the area of the hypothetical measurement surface in m
2
, then
^ = ^ v + 1 0 1 o g ( 5 J 1.44)
For a hemi spherical hypothetical surface shown in Fig. 1.3, the
measurement surface area S
m
= 2nr
2
, and for the parallelepiped surface
of Fig. 1.4,
S
m
=2ax2b + 2 2a+2b)c = 4 ab + bc + ca\ m
2
1.45)
Fig. 1.4
Microphone locations
on a
hypothetical parallelepiped (Survey Method)
[8].
Example 1 4 The overall dimensions of a diesel generator DG) set
are 3m χ 1.5m χ 1.2m height). The A-weighted sound pressure levels at
1 m from the five 4+1) radiating surfaces are 100, 95, 93, 102 and 98
dBA, respectively. Assuming that the contribution from the four walls
and ceiling for the DG room is negligible, and making use of the Survey
method, evaluate the sound power level of the DG set.
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Noise and Its Measurement
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Average value of the SPL may be calculated by means of Eq. (1.43):
Solut ion W ith refere nce to Fig . 1.4,
Thus ,
Using Eq. (1.45), surface area of the hypothetical measurement surface is
given by
Finally, the power level of the DG set is given by Eq. (1.44). Thus,
(1.46)
Lou dness index S is m easured in terms of sones and the loudness level Ρ
in phons. They are related to each other as fol lows:
1.9 Loudness
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Solut ion The exercise is bes t don e in a tabular form show n be low .
E x a m p l e 1 5 If the measured values of the S P L s for the octave bands
with mid-frequencies
of
6 3 ,
125, 250, 500, 1000,
2000 , 4000
and
8000
H z are 100, 95 , 90, 85, 80, 75 , 70 and 65 dB, respectively, calculate the
total loudness level
in
sones
as
wel l
as
phon s .
where 5, is the loudness of the
i
th
band and
S
max
is the m a x im u m of
these values . Constant Β = 0.3 for octave band analysis and 0.15 for 1/3-
octave band analys is .
The
summ at ion does
not
include S
max
.
(1.47)
The band loudness index
for
each
of the
octave bands
is
read from
Fig . 1.5, and then the com posi te loudn ess level , L (sones) is determined
bv Γ 41
Fig.
1.5
Equal loudness index contours,
(adopted with permission from Bies
and
Hansen [3]).
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The measured values of SPL are entered in the first row of the table.
Th e band loud ness ind ex Si for each octave ban d is read from
Fig . 1.5 an d ente red in the seco nd row of the Ta ble . It m ay be note d
that the maximum value of the loudness index, S
max
, is 28 son es.
Con stant Β = 0 .3 for octave ban ds , Th us , ma king use of Eq. (1 .47) ,
the composite loudness index, L, is calculated as fol lows:
L = 28 + 0.3 (2 5 + 2 2 + 19 + 17 + 14 + 13 + 11)
= 28 + 0 .3x 121 = 6 4 .3 sones
Now use of Eq. (1.46) yields the loudness level in phons:
Ρ = 4 0 + 33 .2 log 64 .3
= 100.0 phons
1.10 N oise Lim its in Ind ia
The Minis t ry of Environment and Fores ts (MOEF) of the Government of
India, on the advice of the National Committee for Noise Pollut ion
Control (NCNPC) has been issuing Gazette Notificat ions prescribing
noise limits as well as rules for regulation and control of noise pollution
in the urban environme nt . Th ese are sum ma rized below .
1 10 1
The noise pollution regulation and control) rules, 2000 [5]
These rules make use of Table 1.4 for the ambient air quali ty standards.
These are more or less the same as in Europe and USA.
Example 1.5 Table
Octave-band center
frequency Hz)
63 125 250 500 1000 2000 4000 8000
Octave-band level
dB)
100 95 90 85 80 75 70 65
Band loudness
index sones) 28 25
22
19 17
14
13
11
from Fig. 1.5)
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26 Noise and Vibration Control
Table 1.4 Ambient air quality standards in respect of noise [7].
Limits in Leq (dB A)
Category of Area/Zone
Day Time Night Time
Industrial area 75 70
Commercial area 65 55
Residential area 55 45
Silence zone 50 40
Note:
1. Day time shall mean from 6:00 a.m. to 10:00 p.m.
2.
Night time shall mean from 10:00 p.m . to 6:00 a.m.
(i). A loud spea ker or a public addre ss system shall not be us ed
except after obtaining writ ten permission from the authori ty.
(ii). A loud speaker or a public address system or any sound
producing instrument or a musical instrument or a sound
amplifier shall not be used at night time except in closed
premises for communication within, l ike auditoria, conference
rooms, community hal ls , banquet hal ls or during a public
emergency .
(iii).
The noise level at the boundary of the public place, where
loudspeaker or public address system or any other noise source
is being used, shal l not exceed 10 dB(A) above the ambient
noise standards for the area (see Table 1.4) or 75 dB(A)
whichever is lower.
(iv).
Th e periph eral noise level of a privately own ed sound system
or a sound producing instrument shall not , at the boundary of
the private place, exceed by more than 5 dB(A) the ambient
noise standards specified for the area in which it is used,
(v). N o horn shall be used in si lence zones or during night t im e in
residential areas except during a public emergency.
(vi).
So und em itt ing fire crack ers shall not be burst in si lence zo ne
or during night t ime.
(vii).
So und em itt ing construct ion equipm ents shall not be used or
operated during night t ime in residential areas and si lence
zones .
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1 10 2 Perm issible noise exposure for industrial workers
In keeping with the pract ice in most countries, India has adopted the
international l imit of 90 dBA during an 8-hour shift for industrial
workers .
Table 1.5 Permissible noise exposure.
Duration/day (h)
Sound Level (dBA)
Slow response
16 87
8 90
4
93
2
96
1
99
0.5
102
0.25 or less 105
As shown in Table 1.5, for every 3 dB increase in the A-weighted
sound level , the permiss ible maximum exposure has been reduced to
half. Dosimeters have been provided to the factory inspectors and also to
the traffic police. Th e technician s wo rking on noisy mach ines or in
noisy areas are provided with ear muffs or ear plugs, and are required to
use them compulsori ly .
The total daily dose, D, is given by
Alternatively, i f we want to evaluate the maximum time that a
technician may be asked to work in a noisy environment without risking
him to over exposure, we may make use of an integrat ing sound level
meter to evaluate the 8-hour average o f the Α -weigh ted SPL as fo l lows :
(1.48)
Ci = Total actual time of exposure at a specified noise level, and
Ti - Total t ime of exposure permit ted by the table above at that
level.
where
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(1.49)
where t i s in hours . The n, the m axim um al lowed exposu re time to an
equivalent SPL, L
A e q
8 A
, would be given by
(1.50)
where D, the dai ly noise dosage with reference to the base level cri terion
of 90 dBA is given by
2)
—
2^
LAeqM
~
9 0
)/
3
( 1 5 1 )
Here, constant 3 represents the decibel t rading level which
corresponds to a change in exposure by a factor of two for a constant
exp osur e time (10 log 2 = 3). Fo r use in U SA , this consta nt wou ld be
replaced with 5.
Example 1 .6 T he ope rator of a nois y grind er in an India n factory is to
be protected against over-exposure to the work stat ion noise by rotat ion
of duties. The operator 's ear level noise is 93 dBA near the grinder and
87 dBA in an al ternat ive work place. What i s the maximum durat ion
during an 8-hour shift that the worker may work on the grinder?
Solution
Referring to Table 1.5,
Ti for 93 d B A is 4 ho urs , and T
2
for 87 d B A is 16 hour s.
Let the wo rker ope rate the grinder for χ hou rs, and w ork in the
quieter locat ion for the remaining durat ion of 8-x hours.
Use of Eq. (1.48) yields
whence
Therefore, the technician should not be made to operate the
grinder for more than 2.67 hours during an 8-hour shift .
2 67 hours
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1 10 3
Noise limit for diesel generator sets
India has the problem of power scarci ty al though the government has set
up a number of thermal power plants , hydropower plants and atomic
po w er plan ts . The refore, m ost of the m anufacture rs have their ow n
captive power plants based on diesel engines. The relevant gazette
notificat ion of the MOEF prescribes as fol lows [6].
• Th e m ax im um perm issible sound pressu re level for new diesel
generator (DG) sets with rated capacity upto 1000 KVA shall be 75
dB (A ) at 1 m etre from the enclosu re surface, in free field con dit ions.
• Th e diesel genera tor sets should be prov ided with integral acoust ic
enclosure at the manufacturing stage
itself.
Noise limits for diesel generator sets of higher capacity shall be as
follows [7].
• N oise from DG set shal l be control led by prov iding an acoust ic
enclosure or by treat ing the room acoustical ly, at the user 's end.
• T he acoustic enclo sure or acoust ic t reatm ent of the roo m shall be
designed for minimum 25 dB(A) insert ion loss or for meeting the
am bient noise standards, wh iche ver is on the highe r side. Th e
measurement for Insert ion Loss may be done at different points at
0.5 m from the acoust ic enclosure/room, and then averaged.
• T he D G set shal l be prov ided with a prop er exha ust muffler with
inser t ion loss of minimum 25 dB(A).
• T he m anufac turer sho uld offer to the user a standard acou st ic
enclosure of 25 dB(A) insert ion loss, and also a sui table exhaust
muffler with IL of at least 25 dB (A) .
1 10 4
Noise limit for portable gensets
Most shops and commercial es tabl ishments have thei r kerosene-s tar t ,
petrol-run portable gensets with power range of 0.5 to 2.5 KVA. The
relevant gazette notificat ion for such small portable gensets prescribes as
follows [7].
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where
^ i s the environm ental correct ion, 10 log (1+4S/A )
S
is the area of the hypothetical measurement surface, m
2
S
0
= 1 m
2
A is the room absorption, m
2
(see Eq. (4.13) in Chapter 4).
• Th e prescribe d l imit of sound pow er level of portab le gensets is 86
dBA.
• Th is noise l imit m ay nec essi tate use of acoust ic hoo ds in m ost case s.
1.10 5 Noise limit for fire crackers
The Indian Society is a mix of different racial and rel igious communit ies.
Each community has i ts fest ivals that are usually celebrated by means of
sound em itt ing fire crackers . M ost of the t im e, these crackers are fired in
hand, and therefore the chance of body damage, part icularly to the
hearing for the players as well as on-lookers standing nearby, is high.
Therefore, the government has mandated as fol lows [9].
• T he m anufa cture, sale or use of fi re-crackers generat ing noise level
exceeding 125 dB(A) or 145 dB(C) peak at 4 meters distance from
the point of bursting shall be prohibited.
• Fo r ind ividu al fire-crac ker con stituting a series (joined fire-cra cke rs),
the above ment ioned l imi t be reduced by 5 log (N), wh ere Ν =
num ber of crackers jo ine d together .
• T he m easu rem ents shall be m ade on a hard con crete surface of
minimum 5 meter d iameter or equivalent .
• T he m easu rem ents shall be m ade in free field cond it ions, i .e. , there
shall not be any reflecting surface upto 15 meter distance from the
point of burst ing.
Sound power level may be determined by means of the Survey
method [8] (see Fig. 1.4).
Th e Α -weighted sound power level of the source in the case of the
Direct Method is calculated from the equation
(1.52)
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1 10 6 No ise limit for vehicles
Table 1.6 Noise limits for vehicles at manufacturing stage applicab le since 1
s t
April 2005
[10].
SI.
No.
Type of Vehicle
Noise
Limits
dB (A)
Two-wheelers
1 Displacement upto 80 cc
2 Displacement more than 80 cc but upto 175 cc
3 Displacement more than 175 cc
75
77
80
Three-wheelers
4 Displacement upto 175 cc
5 Displacement more than 175 cc
77
80
Four-wheelers
Vehicles used for the carriage of passengers and capable of having
not more than nine seats, including the d river's seat
Vehicles used for carriage of passengers having more than nine
seats, including the driver's seat, and a maximum Gross Vehicle
Weight (GVW) of more than 3.5 tonnes
With an engine power less than 150 kW
With an engine power of 150 kW or above
74
78
80
10
Vehicles used for carriage of passengers having more than nine
seats,
including the driver's seat \ vehicles used for the carriage of
goods
With a maximum GVW not exceeding 2 tonnes
With a maximum GVW greater than 2 tonnes but not exceeding
3.5 tonnes
76
77
Vehicles used for the transport of goods with a maximum GVW
exceeding 3.5 tonnes
11 With an engine power less than 75 kW 77
12 With an engine power of
75
kW or above but less than 150 kW 78
13 With an engine power of 150 kW or above 80
6
7
8
9
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Environmental noise of vehicles is measured in a pass-by noise test [10]
as show n in Fig. 1.6. T he vehic le appr oach es line Α -A at a s teady speed
corresponding to 3/4 times the m axim um p ow er speed of the engine. As
the vehicle front end reaches point Q , the accelerator is push ed to ful l
open thrott le posi t ion and kept so unti l the rear of the vehicle touches
line B-B at point C
2
. Th e m axim um S PL reading is recorded at the two
m icrop hon e locations show n in Fig. 1.6. Th e test is repea ted with the
vehic le m oving in the oppo site direct ion. Th is is repea ted three t imes .
The average of the peak SPL readings represents the pass-by noise of the
veh icle. Detai led operat ing instruct ions as we ll as test cond it ions are
given in Ref. [10].
Table 1.6 gives the pass-by noise limits for vehicles at the
m anufac turing stage [11] applicab le since Ap ri l 20 05 . Th ese l imits are
similar to those prescribed in Europe since 1996. The l imits are enforced
by the Automot ive Research Associat ion of India (ARAI, Pune) during
Fig. 1.6 Measurement of passby noise of an automobile [10].
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the type test ing of the new vehicles for establishing their road
worthiness .
1.11 Masking
Often env ironm ental noise m asks a wa rning signal . M ask ing is the
phenomenon of one sound interfering with the perception of another
sound. Th is is w hy hon king has to be consid erably loude r than the
gen era l traffic n oise around . It has be en obser ve d that m ask ing effect of
a sound of a particular frequency is more at higher frequencies than at
the low er frequenc ies. Th us if w e wa nt to m ask amb ient sound of 500
Hz to 2000 Hz then we should introduce sound in the 500 Hz one-third
octav e ban d. In fact, the m askin g effect of a narro w ban d noise is mo re
than that of a pure tone at the centre frequency of the ban d. Th e am oun t
of masking is such that a tone which is a few decibels above the masking
noise appears to be as loud as i t would sound if the masking noise were
not present . Masking can be put to effect ive use in giving acoustic
privacy to intellectuals located in open cubicles in large call centers or
similar large offices under the same roof. Pla yin g of soft instru m enta l
music in the background is enough to mask the conversat ion in the
neighboring cubicles .
1.12 Sou nd Leve l M eter
The basic components of a portable sound level meter are microphone,
pre-amplifier, weighting network, amplifier, rect ifier, the output quanti ty
calculator, and display unit .
The microphone is a t ransducer for conversion of acoust ic signal into
a voltage signal . Pre-amplifier is an impedance matching unit with high
input impedance and low output impedance. The wai t ing network relates
to Α -weight ing or C-w eight ing; B-weight ing is rarely used these days .
The display unit is essential ly a sensi t ive digi tal voltmeter, pre-cal ibrated
in term s of sound pressure levels in dec ibels . Fo r con ven ienc e, the
at tenuators are usua lly arrang ed in 10 dB steps. Th e dyn am ic rang e is
genera l ly 60 or 80 dec ibels . Th ere is invariably a m eter respo nse
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function labeled as slow, fast and impulse with averaging t ime constants
of 1 sec, 100 ms and 35 ms, respectively.
The Sound level meter is classified as Class I or Class II (also termed
as Ty pe I and Ty pe II), dep end ing on accu racy. Class I sound leve l
meter is a precision sound level meter intended for accurate
measurements whereas Class II sound level meter is a general purpose
sound level meter intended for field use.
1 .13 Microphones
The re are several types of m icropho nes . Th ree major types in com m on
use are described here. The most precise microphone consists of a
diaphragm which serves as one electrode of condenser and a polarized
backing plate separated from i t by a very narrow air gap which serves as
the other electro de. Th e con den ser is polarized by m ean s of a bou nd
charge so that small variat ions in the air gap due to pressure induced
displacement of the diaphragm result in corresponding variat ions in the
voltage across the con dens er. C ond ens er m icro pho ne has relat ively flat
frequency response, which makes i t very desirable for precise
measurements .
In a p iezo-elect r ic microphone sound incident upon the diaphragm
tends to stress or unstress the piezo-electric element which in return
induce s a bou nd cha nge across i ts cap acitanc e. Piezo-e lectric
microphones are also cal led ceramic microphones .
Table 1.7 Basic microphone types and characte ristics.
SI.
No.
Microphone
type
Sensing element
Typical
frequency range
(Hz)
Temperature and
humidity
stability
1 Condenser Capacitor
2-20000
Fair
2 Ceramic Piezoelectric 20-10000 Good
3 dynamic Magnetic coil 25-15000 Good
Dynamic microphones produce an elect r ical s ignal by moving a coi l
wh ich is con necte d to a diap hrag m through a m agne tic field. Ob viously,
a dynamic microphone must not be used in the vicini ty of devices that
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create magnetic fields; e.g. , t ransformers, motors and al ternators. The
relat ive performance of these microphones is given in Table 1.7.
1.14 Microphone Sensi t iv i ty
Microphone sensi t ivi ty is essential ly the rat io of electrical output to
aco ustic al inpu t. In loga rithm ic un its it is defined as
E
ref
, the refere nce voltag e is gen erally 1 volt and p
ref
the reference
pressure which can be 1 Pa or 0.7 Pa (l microb ar) . Eq. (1 .53) m ay be
rearranged as
S = 20 l o g £ - L
p
+ 9 4 , dB (1.54)
where
Ε
is in volts and
L
p
is the soun d pre ssu re level (re 20
micropascal ) on the microphone. Typical values of microphone
sensi tiv it ies range be tween - 2 5 and - 6 0 d B re lV/P a .
General ly there is a t rade-off between frequency response and
sensi t ivi ty. For example, 6-mm diameter microphones have flat
frequency response over a wide range of frequencies but they have less
sensi t iv i ty , as compared to the corresponding 25-mm diameter
microphones . Therefore 12-mm diameter microphones are used
commonly on most portable sound level meters .
Example 1 .7 A condenser microphone with sensi t ivi ty of - 30 dB rel.O
V
Pa
1
is used as the transd uce r on a portab le sound level me ter. W ha t
would be the SPL reading on the meter i f the internal electronic noise is
10
μ Υ Ί
Solution
(1.53)
Use of (1.54) yields
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36 Noise and Vibration Control
A s the internal electronic n oise level is 24 d B , and 24 ® 30 = 31,
this sound level meter cannot be used to measure SPL of less than 30
dB with an accuracy of ±1 dB.
1.15 Intensity Meter
Intensity is defined as the time average of the product of acoustic
pressure and normal par t ic le veloci ty . As per the momentum equat ion,
part icle velocity is prop ort ional to pressu re gradient . The refore, an
intensi ty probe consists of two microphones with an acoust ical ly
transpa rent spacer in betw een . Th e acoustic pressu re is then the avera ge
of the pressure s picked up by the tw o m icrop hon es individually. Part icle
velocity is proport ional to the difference of the two pressures divided by
the distance d between the two (equal to spacer length). Thus,
For this equation to represent the real intensity flux normal to a surface,
the intensi ty probe must be held near the surface in such a way that the
axis of the two m icrop hon es is perpe ndicu lar to the surface. Th e outpu t
of both the microphones is fed to the intensi ty meter which is cal ibrated
to m eas ure intensi ty direct ly in term s of decib els as per Eq. (1.20). Often
a good intensi ty meter has provision for measurement of sound pressure
levels and velocity level too. The sound intensi ty meter is also
programmed for the octave and 1/3-octave frequency analysis .
References
1. Munjal, M. L., Acoustics of Ducts and Mufflers, W iley, New York, (1987).
2.
Irwin, J. D. and Graf, E. R., Industrial Noise and Vibration Control, Prentice Hall,
Englewood Cliffs, (1979).
(1.55)
whence
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Noise and Its Measurement
37
3. Bies,
D. A. and
Hansen,
C. H.,
Engineering Noise Control, Fourth Ed ition, Spon
Press, London, (2009).
4.
Procedure
for
the Com putation
of
Loudness
of
Noise, Am erican National Standard
USA S3.4-1968, American National Standards Institute, New York, (1968).
5.
The
Noise Po llution (Regulation
and
Control) (Am endment) Rules, 2010, M OEF
Notification S.O. 50(E), The Gazette of India Extraordinary, (11 January 2010).
6. MO EF Notification G .S.R. 371(E): Environment (Protection) Second Amendment
Rules, (2002).
7.
MO EF Notification G.S.R. 742(E): Environment (Protection) Amendment Rules,
(2000).
8. Acoustics
-
Determination
of
sound power levels
of
noise sources using sound
pressure - Survey method using an enveloping measurement surface over a
reflecting plane, ISO 3746: 1995(E), International Standards Organization, (1995).
9. MO EF Notification G .S.R. 682(E): Environment (Protection) Second Amendment
Rules,
(1999).
10. Measurement
of
noise emitted
by
moving road vehicles, Bureau
of
Indian
Standards, IS: 3028-1998, New Delhi, (1998).
11. MO EF Notification G.S.R. 849(E): Environment (Protection) Second Amendment
Rules, (2002).
12.
Joint Departments
of
the Army,
Air
Force
and
Navy,
TM
5-805-4/AFJMAN
32-
1090,
Noise and Vibration Control, (1995).
Problems in Chapter 1
Problem 1 1 Often, an approximate value of characteristic impedance
Z
0
=p
0
c) of air is taken as a round figure of 400 kg / m
2
s). What
temperature does this value correspond to? Adopt the mean sea level
pressure.
[Ans : 40° C]
Problem 1 2 What are the amplitudes of the particle velocity and sound
intensity associated with a plane progressive wave of 100 dB sound
pressure level? Assum e that the medium is air at mean sea level and
25° C.
[Ans : 6 9 mm/s and 9 76 mW m
2
]
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Problem 1.3
A bub ble-l ike pulsat ing sphere is radiat ing sound po w er of
0.1 W att at 50 0 Hz. Calc ula te the follow ing at a farfield po int located 1.0
m away from the centre of the sphere:
a) intensi ty level and sound pressu re level
b) rm s value of acoust ic pressu re
c) rm s va lue of the radia l partic le veloc ity
d) ph ase difference betw een press ure and velocity
[An s.: a) bo th 99.0 dB, b) 1.78 P a, c) 4.37 m m /s , d) 6.3°]
Problem 1.4 So und pressu re levels at a point near a noisy blow er are
115, 110, 105, 100, 95, 90, 85 and 80 dB in the 63, 125, 250, 500, 1000,
2000 ,
400 0 and 8000 Hz octave ban ds, respec tively. Ev alua te the total
L
p
and L
pA
.
[Ans. :
L
p
=
116.6 dB ,
L
pA
=
102 .4 dB A]
Problem 1.5
So und pressu re levels m easu red in free space at 12
equisp aced loc ations on a hyp othetica l hem i-sphe rical surface of radius
2m around a small portable genset lying on an acoust ical ly hard floor
are:
7 0, 72, 74, 76, 78 , 80, 8 1 , 79 , 77 , 75 , 73 and 71 dB , respectively,
(a). Ev alua te the sound pow er level of the portab le genset .
(b). W ha t is the direct ivi ty factor for the locat ions w here S PL is
maximum and where SPL i s min imum?
[Ans. :
a) 90.5 d B , b) 5.62 and 0 .562]
Problem 1.6 At a point in a part icular env ironm ent, the octave-ban d
sound pressure levels are 80, 85, 90, 85, 80, 75, 70 and 65 dB in the
octave bands centered at 63, 125, 250, 500, 1000, 2000, 4000 and 8000
Hz , respec tively. Ev aluate the loudn ess index in sones for each of these
eight octave bands, and thence calculate the total loudness level in sones
and phons .
[Ans. :
49.6 sones and 96.5 phons]
Problem 1.7 If the hourly Α -weigh ted am bient SP L in an Indian
workshop during an 8-hour shift are recorded as 85, 86, 87, 88, 90, 93,
93 , 91 dBA, evaluate (a) the dai ly noise dose of the technicians
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employed in the workshop, and (b) the maximum permiss ible exposure
t ime a ccord ing to the industrial safety standard s.
[An s.: a) 0.93 and b) 8.6 ho ur s]
Problem 1.8 Th e techn ical specificat ion sheet of a cond ense r
microphone has been misplaced. In order to measure sensi t ivi ty of the
microphone, i t is subjected to SPL of 90 dBA in the 1000-Hz octave
ban d. Th e output voltage is m easu red to be 1.0 mil l ivolt . Find the
sensi t ivi ty of the microphone.
[A ns . : -5 6
dB re
l V / P a ]
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Chapter 2
Vibration and Its Measurement
Vibration is an oscillatory motion of a particle or an object about its
me an posi t ion. This m ot ion ma y or may not be per iodic . W hen
vibrat ion is caused by the unbalanced forces or moments of a
reciprocating or rotary machine rotat ing at a constant speed, then i t is
perio dic. In this chapter, and indeed in this textbook , vibrat ion and the
resultant acoust ic pressure are assumed to be periodic.
Vibrat ion is caused by the interact ion of two primary elements: mass
and spring (stiffness), or in other words, inertia and elasticity. Damping
represents a third element, which is invariably there in the system but is
not an essential or prim ary elem ent for vibrat ion to take place. M ass and
spring are characterized by kinetic energy and potential energy,
respec tively. Du ring a steady state osci l lat ion, there is a continuo us
exchange between the two types of energy, with their total remaining
constan t . Th e external excitat ion, then, supplies jus t eno ugh energ y to
compensate for the energy dissipated into heat by the damping in the
system, or radiated out as acou st ic energ y. In the absenc e of external
excitat ion, the system would execute free vibrat ions (if ini t ial ly disturbed
and left alone) with successively decreasing ampli tude depending on the
amount of damping in the system and radiat ion resistance on the
vibrat ing surfaces.
In this book, vibrat ion and i ts control have been dealt with primari ly
insofar as vibrat ing structures radiate noise. However, excessive
vibrat ion can degrade the performance and decrease the fat igue l i fe of
m ach ine bea rings and structures, result ing in eco nom ic loss. In extre m e
cases, they may cause fatal accidents.
Study of vibrat ions involves Newton's laws of motion and hence the
science of Dynamics. Vibratory systems are therefore cal led dynamical
40
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Vibration and Its Mea surement 41
systems. These may be classified as l inear or nonlinear, lumped or
dis t r ibuted, conservat ive or nonconservat ive, depending upon the
governing differential equations, and the absence or presence of
damping, respect ively .
The number of independent coordinates required to descr ibe mot ion
com pletely is term ed the degre es of freedom (D OF ) of the system . All
basic features of vibrat ion of a mult i degree of freedom (MDOF)
dynamical system may be easi ly understood by means of a single degree
of freedom (SDOF) system as fol lows.
2.1 Vib ration of a Single De gree of Fre edo m S ystem
For a l inear lumped-parameter SDOF system shown in Fig . 2 .1 , making
use of the free body diagram and the Newton 's Second Law of Mot ion,
the ins tantaneous displacement x(t) of the lum ped m ass m is given by
the equation
mx(t) = f(t)- kx(t)- cx(t)
or
mx(t)
cx(t)
kx(t)= f(t)
(2.1)
where m is the mass, c is the damping coefficient, k is the stiffness of the
spring, f(t) is the excitation or exte rnal force acting on the m ass ,
x(t)= dx/dt is the instantan eous velocity, and x(t)=d
2
x/dt
2
is the
instantaneous acceleration of the mass in the positive (left to right)
direct ion.
Fig. 2.1 A SDOF system with viscous damping along with the free-body diagram of the
mass, m.
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42 Noise and Vibration Control
Equation (2.1) is a l inear, second-order, ordinary differential equation
with constant coefficients . I ts solut ion consists of a complementary
function and part icular integral , representing the free vibrat ion and
forced vibrat ion responses of the system, respectively.
2.1.1
Free vibration
The free vibrat ion response of an underdamped system may be seen to be
[1]
(2.2a)
where
is the natural frequency (in rad/s) of the undamped
system (when c = 0),
is the natural frequency of the damped system,
is the damping rat io of the system, and
is the critical damping of the system,
beyond which there would be no osci l lat ion; the mass
wou ld approach the mean posi t ion asymp tot ical ly .
A and Β are arbi trary constants that can easily be determ ined from the
ini t ial displacement x
0
and velocity u
0
of the m ass, m. Thus, i t can
readily be seen that
For most mechanical vibro-acoustic systems, the damping rat io is
much less than unity, or in other words, the damping coefficient is much
less than the cri t ical damping. Thus,
(2.2b)
(2.3)
Figure 2.2 shows the typical free vibrat ion response of such a system,
where mass
m
is given an ini t ial displacement
x
0
,
and released with zero
initial velocity.
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Vibration and Its Mea surement 43
Example 2 .1 Th e rat io of two successive am pli tudes of the dam ped
spring-m ass sy stem of the type sho wn in Fig. 2. 1 , w hen d isturbed and
left to vibrate freely, is 0.9. If the mass is 10 kg and the spring stiffness is
10 N/mm, evaluate the damping rat io , cr i t ical damping and the damped
natural frequency of the system.
Solution
Fig. 2.2 Free vibration of a typical lightly damped system.
The undamped natural frequency in Hertz, or cycles per second, and
the corresponding t ime period in seconds are given by
(2.4)
M a s s , m = 10 kg
Stiffness, it = 10
Undamped natural frequency of the system,
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As per Eq. (2.2a) and Fig. 2.2, the ratio of successive amplitudes
is given by
Thus,
or
or
Thus, damping ratio of the system is given by
Critical damping of the system,
c
c
= 2mu)
n
Finally, damped natural frequency of the system,
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Vibration and Its Mea surement 45
This natural frequency and the associated free vibrat ion parameters
play a seminal role in our understanding of the forced response of the
system, which is of primary concern in the field of noise and vibration
control as shown below.
(2.7)
(2.8)
(2.6)
(2.5)
A periodic forcing funct ion wi th time per iod Τ ma y be expressed as a
Fourier series
2.1.2
Forced response
or as an exponential series
where
In this book, the exponential form (Eq. 2.6) wil l be used, with
For a l inear system, the principle of superposi t ion holds; i .e. , response
of a periodic forcing function may be expressed as sum of the system
responses to individual harmonics. Thus, Eq. (2.1) for the part icular
integral may be wri t ten as
(2.9)
Ob viously , the steady state resp ons e to the harm onic forcing function
is given by
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46 Noise and Vibration Control
or
(2.12)
This may be rewrit ten in the non-dimensional form [2, 3]
Fig. 2.3 Normalized displacement of mass of the single DOF system of Fig. 2.1 with
damping ratio as parameter.
(2.11)
where the complex ampli tude of the steady state displacement is given
by
(2.10)
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Vibration and Its Measurement 47
where
γ -ω Ι ω
η
is the freque ncy ratio, and
x
st
= FI k is the stat ic displacem ent w hich serves as a
normalizat ion factor
The non-dimensional forced response or s teady-state response given
by Eq. (2.12) is plot ted in Fig. 2.3, whence the fol lowing observations
may be made:
(a) At very low f requencies , ( r « l ) the dynamic response ampl i tude
\x\
tends to the static displace m ent
x
st
.
(b) In the abse nce of dam ping , the system res pon se wou ld tend to
infinity when the forcing frequency
ω
approaches the undamped
natural frequency 0
n
. This ph eno m enon is termed Reso nance . In
fact, the spring of Fig. 2.1 would break in no time if the system were
excited at i ts natural frequency.
(c) At higher frequencies ύ ) » ύ )
η
), the dynam ic response am pl i tude
decreases monotonical ly as
(2.13a)
Thus ,
it is imperative to design the system with as low a natural
frequency as feasible.
(d) Th e restraining effect of dam ping is l imited to the re son anc e
frequency and i ts immediate neighborhood. Nevertheless, i ts role is
crucial .
(e) In a damped single DOF system, resonance peak does not occur
precisely at
r-1
or
ω -ω
η
.
As can be seen from Eq. (2.13) and
Fig ure 2. 3, i t occurs at a s l ightly lower frequency. H ow eve r for
l ightly damped system
c«c
c
ο τ ζ «ΐ),
this shift ca n be
neglected.
(2.13)
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48 Noise and Vibration Control
2.2 Vib ration of a M ult iple De grees of Fr eed om S ystem
A dynamical sys tem with more than one lumped masses in terconnected
with spring (and damper) elements would require more than one
coordinates for descript ion of the instantaneous displacements (and
velocit ies). Such a system is said to have, or be characterized by,
mul t ip le degrees of f reedom (MDOF). An example of an undamped three
DOF system is shown in Fig. 2.4, where, for convenience, the forcing
function is assumed to be harmonic.
Fig. 2.4 Example of a 3-DOF dynam ical system.
Equations of dynamical equil ibrium for the system of Fig. 2.4 are
given by the matrix equation [1]
Natural frequency,
stiffness,
whence ,
Stat ic displacement,
Solution
Example 2 .2 A machine of 500 kg mass when lowered onto
top related