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FUNDAMENTALS OF NOISE
Dr. ASHISH K DARPE
ASSISTANT PROFESSOR
DEPARTMENT OF MECHANICAL ENGINEERING
IIT DELHI
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Sound is a sensation of acoustic waves (disturbance/pressure
fluctuations setup in a medium)
Unpleasant, unwanted, disturbing sound is generally treated
as Noise and is a highly subjective feeling
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Sound is a disturbance that propagates through a medium
having properties of inertia ( mass ) and elasticity. The
medium by which the audible waves are transmitted is air.
Basically sound propagation is simply the molecular
transfer of motional energy. Hence it cannot pass through
vacuum.
Frequency: Number of pressure
cycles / time
also called pitch of sound (in Hz)
Guess how much is particle
displacement??
8e-3nm to 0.1mm
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The disturbance gradually diminishes as it travels outwards
since the initial amount of energy is gradually spreading over
a wider area. If the disturbance is confined to one dimension( tube / thin rod), it does not diminish as it travels ( except
loses at the walls of the tube )
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Speed of Sound
The rate at which the disturbance (sound wave) travels
Property of the medium
0
0
Pc
RTc
M
Alternatively,
cSpeed of sound P0, 0 - Pressure and Density
- Ratio of specific heats RUniversal Gas Constant
TTemperature in 0K MMolecular weight
Speed of Light: 299,792,458 m/s Speed of sound 344 m/s
2
1
0273
1
c
Tcc
smc /5.34325
smc /35540
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Sound Measurement
Provides definite quantities that describe and rate
sound
Permit precise, scientific analysis of annoyingsound (objective means for comparison)
Help estimate Damage to Hearing
Powerful diagnostic tool for noise reductionprogram: Airports, Factories, Homes, Recording
studios, Highways, etc.
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Quantifying Sound
Root Mean Square Value (RMS) of Sound Pressure
Mean energy associated with sound waves is itsfundamental feature
energy is proportional to square of amplitude
1
22
0
1[ ( )]
T
p p t dtT
0.707p a
Acoustic Variables: Pressure and Particle Velocity
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Range of RMS pressure fluctuations that a human ear can
detect extends from
0.00002 N/m2 (threshold of hearing)
to
20 N/m2 (sensation of pain) 1000000 times larger
Atmospheric Pressure is 105N/m2
so the peak pressure associated with loudest soundis 3500 times smaller than atm.pressure
The large range of associated pressure is one of the reasons we
need alternate scale
RANGE OF PRESSURE
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Human ear responded logarithmically to power difference
Alexander Graham Bell
invented a unit Bel to measure the ability of people to hear
Power Ratio of 2 = dB of 3
Power Ratio of 10 = dB of 10
Power Ratio of 100 = dB of 20
In acoustics, multiplication by a given factor is encountered most
W1=W2*n
So, Log10W1= Log10W2 + Log10n
Thus, if the two powers differ by a factor of 10 (n=10), the
difference between the Log values of two power quantities is 1Bel
dB SCALE
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10Log10W1= 10Log10W2 + 10Log10n to avoid fractions
Now we have above quantities in deciBel, 10dB=1Bel
deciBels are thus another way of expressing ratios
2VW
R
2PW
r
Electrical
Power
Sound
Power
20Log10V1= 20Log10V2 + 20Log10n(1/2)
20Log10P1= 20Log10P2 + 20Log10n(1/2)
r- acoustic impedance
Decibel
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Sound Pressure Level
20Log10P1= 20Log10P2 + 20Log10n(1/2)
20Log10(P1/P2) = 20Log10n(1/2)
20Log10n(1/2) is still in deciBel, defined as Sound Pressure Level
Sound pressure level is always relative to a reference
In acoustics, the reference pressure P2=2e-5 N/m2 or 20Pa (RMS)
SPL=20Log10(P1/2e-5) P1 is RMS pressure
n: Ratio of sound powers
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Corresponding to audio range of Sound Pressure
2e-5 N/m2 - 0 dB
20 N/m2 - 120 dB
Normal SPL encountered are between 35 dB to 90 dB
For underwater acoustics different reference pressure is used
Pref= 0.1 N/m2
It is customary to specify SPL as 52dB re 20Pa
Sound Pressure Level
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Sound Intensity
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Sound Intensity
A plane progressive sound wave traveling in a medium (say
along a tube) contains energy and
rate of transfer of energy per unit cross-sectional area is
defined as Sound Intensity
0
1
T
I p u dtT
2
0
P
I c
1010
ref
IIL Log
I
2
1 01
10 10 2
0
/( )20 10
2 5 (2 5) /( )
p cpSPL Log dB Log dB
e e c
12 12
10 10 1012 2 2
0 0
10 1010 10 1010 (2 5) /( ) (2 5) /( )
ref
I ISPL Log dB Log Loge c I e c
For air, 0c 415Ns/m3 so that 0.16 dBSPL IL
Hold true also for spherical
waves far away from source
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COMBINATION OF SEVERAL SOURCES
Total Intensity produced by several sources
IT=I1+ I2+ I3+
Usually, intensity levels are known (L1, L2,)
31 2
1010 10
10 10 10 10 ...
LL L
TL Log
1210
10
TT
IL Log
11 12
1010
IL Log
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If intensity levels of each of the N sources is same,
1
1010 10
L
TL Log N
110TL LogN L
Thus for 2 identical sources, total Intensity Level is 10Log2
i.e., 3dB greater than the level of the single source
For 2 sources of different intensities: L1 and L2
COMBINATIONS OF SOURCES
L1=60dB, L2=65.5dBLT=66.5dB
L1=80dB, L2=82dB
LT=84dB
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FREQUENCY & FREQUENCY BANDS
Frequency of sound ---- as important as its level
Sensitivity of ear
Sound insulation of a wall
Attenuation of silencer all vary with freq.
20000Hz
Infrasonic Audio Range Ultrasonic
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Musical
Instrument
For multiple frequency composition sound, frequency spectrum is
obtained through Fourier analysis
Pure tone
Frequency Composition of Sound
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Amplitude(dB)
A1
f1 Frequency (Hz)
Complex Noise Pattern
No discrete tones, infinite frequencies
Better to group them in frequency bandstotal strength in
each band gives measure of sound
Octave Bands commonly used (Octave: Halving / doubling)
produced by exhaust of Jet Engine, water at base of
Niagara Falls, hiss of air/steam jets, etc
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OCTAVE BANDS
1= 1
1x2=2
2x2=4
4x2=8
8x2=16
16x2=32
32x2=64
64x2=128
128x2=256
256x2=512
512x2=1024
10 bands(Octaves)
For convenience Internationally accepted ratio is
1:1000 (IEC Recommendation 225)
Center frequency of one octave band is 1000Hz
Other center frequencies are obtained by continuously
dividing/multiplying by 103/10
starting at 1000HzNext lower center frequency = 1000/ 103/10 500Hz
Next higher center frequency = 1000*103/10 2000Hz
c U Lf f f
International Electrotechnical Commission
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Octave Filters
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Instruments for
analysing NoiseConstant Bandwidth Devices
Proportional Bandwidth Devices
2U
L
f
f
c U Lf f f
Absolute Bandwidth =fU-fL=fL
% Relative Bandwidth = (fU-fL/ fc) = 70.7%
If we divide each octave into three
geometrically equal subsections, i.e.,1/ 3
2U
L
f
f
These bands are thus called 1/3rd octave bands with
% relative bandwidth of 23.1%
1/102U
L
f
f
For 1/10th
Octave filters, % relative bandwidth of 5.1%
2nU
L
f
f
n=1 for octave,
n=3 for 1/3rd octave
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Octave and 1/3rd Octave
band filters
mostly to analyse relatively
smooth varying spectra
If tones are present,
1/10th Octave or Narrow-band
filter be used
INTENSITY SPECTRAL DENSITY
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For most noise, the instantaneous spectral density
(t) is a time varying quantity, so that in thisexpression is average value taken over a suitable
period so that =< (t)>
So, many acoustic filters & meters have both fast (1/8s) and slow (1s)
integration times (For impulsive sounds some sound meters haveIcharacteristics with 35ms time constant)
IntensityI
f1 Frequency (Hz)f2
INTENSITY SPECTRAL DENSITY
Acoustic Intensity for most sound
is non-uniformly distributed over time and frequency
Convenient to describe the distribution through spectral density
2
1
f
f
I
f
I df
is the intensity within the frequency band f=1Hz
I t it S t L l (ISL)
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DeciBel measure ofis the Intensity Spectrum Level (ISL)
.110log
ref
HzISL
I
If the intensity is constant over the frequencybandwidth w (=f2- f1),
then total intensity is just I= w and
and Intensity Level for the band is
1 .1
wI Hz
Hz
10logIL ISL w
Intensity Spectrum Level (ISL)
If the ISL has variation within the frequency band (w),
each band is subdivided into smaller bands so that in each band ISL
changes by no more than 1-2dB
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IL is calculated and converted to IntensitiesIi and then total
intensity level ILtotal is
10log
i
i
total
ref
I
ILI
10logi i iIL ISL w
as SPL and IL are numerically same, 10logSPL PSL w
PSL (Pressure Spectrum Level) is defined over a 1Hz intervalso the SPL of a tone is same as its PSL
101010log 10
iIL
total
i
IL
10logi
i
total
ref
I
IL
I
Can be
written as
Thus, when intensity level in each band is known, total intensity level can be estimated
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Combining Band Levels and Tones
SPL = PSL + 10 log w
For pure tones, PSL = SPL
so, two SPL of the tones is 63 & 60 dB
For the broadband noise,
SPL = PSL + 10 log w
= PSL + 10 log 100
SPL = 60 dB
Thus the overall band level
= Band level of broadband noise + Level of tones
= 60 + 63 + 60 = 64.7 + 60
66 dB
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Sound Power
Intensity : Average Rate of energy transfer per unit area
2
2W/m
4
WI
r
22 2
0
4 4 Wattp
W r I r c
Sound Power Level: 1010logref
WSWLW
Reference Power Wref=10-12 Watt
dB
Peak Power output:
Female Voice0.002W, Male Voice0.004W, A
Soft whisper10-9W, An average shout0.001W Large
Orchestra10-70W, Large Jet at Takeoff100,000W
15,000,000 speakers speaking simultaneously generate 1HP
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Recap
Sound MeasurementAmplitude/Frequency
Sound Pressure, Intensity, Power, ISL, PSL
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Radiation from Source
Radiates sound waves equally in all directions (spherical radiation)
W: is acoustic power output of the source;
power must be distributed equally over spherical surface area
10 102 12 2
10 1012
1 110log 10log
4 4 10
10log 20log4 10
ref
W WIL
r I r
WIL r
Constant term Depends on distance
from source
When distance doubles (r=2r0) ; 20log 2 + 20log r0 means 6dB difference in the Sound Intensity Level
Inverse Square Law
2
2 2
0
4 4 WattpW r I r c
Point Source (Monopole)
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If the point source is placed on ground,
it radiates over a hemisphere,
the intensity is then doubled and
10 2
10 1012
110log
2
10log 20log2 10
ref
WIL
r I
W
IL r
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Line Source
(Long trains, steady stream of traffic, long straight run of pipeline)
If the source is located on ground,
and has acoustic power output of
Wper unit length
radiating over half the cylinder
Intensity at radius r,W
Ir
10 101210log 10log
10
WIL r
When distance doubles; 10log 2 + 10log r means 3dB difference in the Sound Intensity Level
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In free field condition,
Any source with its characteristic dimension small compared tothe wavelength of the sound generated is considered a point
source
Alternatively a source is considered point source if the receiver is
at large distance away from the source
Some small sources do not radiate sound equally in all directions
Directivity of the source must be taken into account to calculate
level from the source power
VALIDITY OF POINT SOURCE
DIRECTIVITY OF SOUND SOURCE
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Sound sources whose dimensions are small compared to the wavelength of
the sound they are radiating are generally omni-directional;
otherwise when dimensions are large in comparison, they are directional
DIRECTIVITY OF SOUND SOURCE
power Wsoundsametheradiatingsource
ldirectiona-omniafromrdistanceatIntensitySound
power Wsoundradiatingsourceldirectionaa
fromrdistanceatandangleanatIntensitySound
Q
Di i i F & Di i i I d
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Directivity Factor & Directivity Index
2
2
Ss p
p
I
IQ
pSp LLDI
thus
QDI
10log10
Q
Ir24
Directivity Factor Directivity Index
Rigid boundaries force an omni-directional source to radiate sound in preferential direction
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Radiated Sound Power of the source can be affected by a
rigid, reflecting planes
Strength and vibrational velocity of the source does not
change but the hard reflecting plane produces double the
pressure and four-fold increase in sound intensity compared to
monopole (point spherical source)
If source is sufficiently above the ground this effect is reduced
EFFECT OF HARD REFLECTING GROUND
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Free Field Condition Diffuse Field
I=0Uniform
sound
energy
density
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Finding sound power (ISO 3745)
MWL Lab, KTH Sweden
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Measurements made in semi-reverberant and free field conditions
are in error of 2dB
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Noise Mapping
Noise Contours
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Environmental
Effects
Wind Gradient
Temperature Gradient
Hot Sunny
Day
Cool Night
Velocity
Gradient (-)
Wind & Temp effects tend to
cancel out
Increase or decrease of 5-6dB
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Environmental Effects
HUMAN PERCEPTION
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HUMAN PERCEPTION
Th H E
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The Human Ear
Outer Ear: Pinna and auditory canal
concentrate pressure on to drum
Middle Ear: Eardrum, Small Bones
connecting eardrum to inner ear
Inner Ear: Filled with liquid, cochlea
with basilar membrane respond to
stimulus of eardrum with the help of
thousands of tiny, highly sensitive hair
cells, different portions responding
different frequencies of sound.
The movement of hair cells is
conveyed as sensation of sound to the
brain through nerve impulses
Masking takes place at the membrane;
Higher frequencies are masked by
lower ones, degree depends on
freq.difference and relative
magnitudes of the two sounds
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Unless there is a 3 dB difference in SPL, human beings can
not distinguish the difference in the sound
Sound is perceived as doubled in its loudness when there is
10dB difference in the SPL.
(Remember 6dB change represents doubling of sound pressure!!)
Ear is not equally sensitive at all frequencies:
highly sensitive at frequencies between 2kHz to 5kHzless at other freq.
This sensitivity dependence on frequency is also dependent
on SPL!!!!
SOUND BITS
RESPONSE OF HUMAN EAR
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Equal Loudness Contours for pure tones,
Free Field conditions
RESPONSE OF HUMAN EAR
Loudness Level
(Phon)
Equal to numericalvalue of SPL at
1000Hz
0Phon: threshold of
hearing
Loudness Level
(Phon) useful for
comparing two
different frequencies
for equal loudness
But, 60Phon is stillnot twice as loud as
30Phon
Doubling of loudness
corresponds to increase
of 10Phon
Weighting Characteristics
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g g
A-weighting: 40Phon equal loudness level contour
C-weighting: 90Phon equal loudness level contour
D-weighting for Aircraft Noise
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BASIC SOUND LEVEL METER
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LOUDNESS INDEX
Direct relationship between
Loudness Level P (Phons) and
Loudness Index S (Sones)
8 Sones is twice as loud as
4 Sones
40
102
P
S
Hearing Damage Potential to sound energy
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Hearing Damage Potential to sound energy
depends on its level & duration of exposure
Equivalent Continuous Sound Level (Leq)
1010
1
10 10jLN
eq j
j
L Log t dB
tj :Fraction of total time
duration for which SPL of
Lj wasmeasured
Total time interval
considered is divided in N
parts
with each part has constant
SPL ofLj
100 70
10 1010
1 710 10 10 91
8 8eqL Log dB
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Integrating Sound Level Meter for randomly varying sound
e.g., 60secLeq
Sound Exposure Level (SEL)
Constant level acting for 1sec
that has the same acoustic
energy as the original sound
Vehicle passing by;
Aircraft flying over
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Noise Dose Meters display
Noise Exposure Measurements
Regulations:
Basis of 90dB(A) for 8hr a day.
ISO(1999): Increase in SPL
from 90 to 93dB(A) must
reduce time of exposure from 8
to 4 hours
OSHA: with every 5dB(A)
increase, reduce exposure by
half
Occupational Safety and Health Administration
N i R i C (ISO R 1996)
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Noise Rating Curves (ISO R 1996)
Level of
Noise
Annoyance
NR78
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Errors of the order of 6dB around 400Hz due to reflections
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Sources:
Vibration and Noise for Engineers, K Pujara
Fundamentals of Acoustics, Kinsler and Frey
Fundamentals of Noise and Vibration Analysis for
Engineers, M Norton and D Karczub
Introduction to Acoustics, R D Ford
Measuring Sound, B&K Application Notes
Sound Intensity, B&K Application Notes
Basic Concepts of Sound, B&K Application Notes
TRANSFORMER NOISE CASE STUDY
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TRANSFORMER NOISE CASE STUDY
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SOURCES
The primary source of acoustic noise generation in a transformer is the
periodic mechanical deformation of the transformer core under the
influence of fluctuating electromagnetic flux associated with these parts.
The physical phenomena associated with this tonal noise generation can be
classified as follows:
vibration of the core
core laminations strike against each
other due to residual gaps between
laminations
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The material of a transformer core exhibits magnetostrictive
properties. The vibration of the core is due to its
magnetostrictive strain varying at twice the frequency of the
alternating magnetic flux. The frequencies of the magnetic flux
are equal to the power system supply frequency and its
harmonics.
When there are residual gaps between laminations of the core,
the periodic magneto-motive force may cause the core
laminations to strike against each other and produce noise.
Also, the periodic mutual forces between the current-carryingcoil windings can induce vibrations.
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A core structure is a complicated stack of Si-Fe alloy laminations clamped
together at suitable points. Clamping is essential to hold together the laminations.
The clamping arrangement also influences the dynamic behaviour of a core.
As laminations do not have good matching flat surfaces and as they are not
clamped together over an entire surface area, hence residual gaps between the
laminations are unavoidable. Magneto-motive forces acting across these air gaps
could set relative transverse motions between the laminations also with clamped
constraint points in place.
Higher the core loss (eddy current loss, hysterisis, copper loss) greater the noise
level.
Figure: Core overlap region
Noise level increases withincreasing overlap length.
METHODS
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METHODS
By changing the conventional grain-oriented (grade M4) material of core
with any of high-permeability (Grade MOH) and laser-scribed (grade ZDKH)
material can reduce noise 2-4db because higher-grade materials have
lower magnetostriction.
A method of controlling noise is to construct a wall with high sound absorbingbricks.
The most effective way to reduce noise is varnishing or using adhesive
material inside transformer tank (Viscoelastic materials) Enclosing transformer inside an enclosure which uses two thin plates separated by
viscous material.
The noise hits inner plate and energy is damped out by viscous material so that outerone does not vibrate.
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This may change an efficiently radiating
vibration shape into an ineffectively radiatingshape resulting in a lower sound radiation ratio.
Active noise control (ANC):
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Active noise control (ANC):
Decentralized ANC can be implemented. In this transformer tank surface is divided
into n mber of elements For each element nit consist of micro phone located in
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Figure6: Configuration of the control simulation.
into number of elements. For each element unit consist of micro phone located in
front of loud speaker delivers error signal, this signal is fed to controller which drives
loud speaker is attached. An experimentation of decentralized active noise control
on power transformer is shown in figure 5 and Configuration of the control simulation
is shown in figure 6.
Figure 5: experimentation of decentralized active noise
control on power transformer
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Thanks !!