Transcript Fundamental of Noise

FUNDAMENTALS OF NOISE
Dr. ASHISH K DARPE
ASSISTANT PROFESSOR
DEPARTMENT OF MECHANICAL ENGINEERING
IIT DELHI
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
• 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.
Guess how much is particle
displacement??
8e-3nm to 0.1mm
Frequency: Number of pressure
cycles / time
also called pitch of sound (in Hz)
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 )
Speed of Sound
The rate at which the disturbance (sound wave) travels
Property of the medium
 P0
c
0
c
Alternatively,
c – Speed of sound
 RT
M
P0, 0 - Pressure and Density
 - Ratio of specific heats
R – Universal Gas Constant
T – Temperature in 0KM – Molecular weight
T 

c  c0 1  c 
 273 
1
2
c25  343.5m / s
c40  355m / s
Speed of Light: 299,792,458 m/s
Speed of sound 344 m/s
Sound Measurement
• Provides definite quantities that describe and rate
sound
• Permit precise, scientific analysis of annoying
sound (objective means for comparison)
• Help estimate Damage to Hearing
• Powerful diagnostic tool for noise reduction
program: Airports, Factories, Homes, Recording
studios, Highways, etc.
Quantifying Sound
Acoustic Variables: Pressure and Particle Velocity
Root Mean Square Value (RMS) of Sound Pressure
Mean energy associated with sound waves is its
fundamental feature
energy is proportional to square of amplitude
1

2
p    [ p(t )] dt 
T 0

T
p  0.707 a
1
2
RANGE OF PRESSURE
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 sound
is 3500 times smaller than atm.pressure
The large range of associated pressure is one of the reasons we
need alternate scale
dB SCALE
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
Decibel
10Log10W1= 10Log10W2 + 10Log10n
to avoid fractions
Now we have above quantities in deciBel,
10dB=1Bel
deciBels are thus another way of expressing ratios
Electrical
Power
V2
W
R
Sound
Power
P2
W
r
r - acoustic impedance
20Log10V1= 20Log10V2 + 20Log10n(1/2)
20Log10P1= 20Log10P2 + 20Log10n(1/2)
Sound Pressure Level
20Log10P1= 20Log10P2 + 20Log10n(1/2)
20Log10(P1/P2) = 20Log10n(1/2)
n: Ratio of sound powers
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 20Pa (RMS)
SPL=20Log10(P1/2e-5)
P1 is RMS pressure
Sound Pressure Level
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 20Pa
Sound Intensity
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
1
I
T
T
 p u dt
0
P2
I
0 c
Hold true also for spherical
waves far away from source
p12 /( 0c)
p1
SPL  20 Log10
dB  10 Log10
dB
2
2e  5
(2e  5) /( 0c)
I
1012
I
1012
SPL  10 Log10 12
dB  10 Log10
 10 Log10
2
10 (2e  5) /( 0c)
I ref
(2e  5) 2 /( 0c)
IL  10Log10
I
I ref
For air, 0c  415Ns/m3 so that
SPL  IL  0.16 dB
COMBINATION OF SEVERAL SOURCES
Total Intensity produced by several sources
IT=I1+ I2+ I3+…
Usually, intensity levels are known (L1, L2,…)
 IT 
LT  10 Log  12 
10 
 I1 
L1  10 Log  12 
10 
L1 
 L3 
 L2 
  10

 10 

 10 
LT  10 Log 10   10   10   ...


COMBINATIONS OF SOURCES
If intensity levels of each of the N sources is same,
 L1 

 10  
LT  10 Log  N 10  


LT  10LogN  L1
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
L1=60dB, L2=65.5dB
LT=66.5dB
L1=80dB, L2=82dB
LT=84dB
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.
<20Hz
20Hz to 20000Hz
> 20000Hz
Infrasonic
Audio Range
Ultrasonic
Frequency Composition of Sound
Pure tone
Musical
Instrument
For multiple frequency composition sound, frequency spectrum is
obtained through Fourier analysis
Complex Noise Pattern
Amplitude (dB)
produced by exhaust of Jet Engine, water at base of
Niagara Falls, hiss of air/steam jets, etc
A1
f1
Frequency (Hz)
No discrete tones, infinite frequencies
Better to group them in frequency bands – total strength in
each band gives measure of sound
Octave Bands commonly used (Octave: Halving / doubling)
OCTAVE BANDS
1=
1
1x2=2
2x2=4
4x2=8
For convenience Internationally accepted ratio is
1:1000
(IEC Recommendation 225)
Center frequency of one octave band is 1000Hz
16x2=32
Other center frequencies are obtained by continuously
dividing/multiplying by 103/10 starting at 1000Hz
32x2=64
Next lower center frequency = 1000/ 103/10  500Hz
64x2=128
Next higher center frequency = 1000*103/10  2000Hz
8x2=16
128x2=256
256x2=512
512x2=1024
fc 
fU f L
10 bands(Octaves)
International Electrotechnical Commission
Octave Filters
Instruments for
analysing Noise
Constant Bandwidth Devices
Proportional Bandwidth Devices
fU
2
fL
fU
 2n
fL
n=1 for octave,
n=3 for 1/3rd octave
fc 
fU f L
Absolute Bandwidth = fU - fL = fL
% Relative Bandwidth = (fU-fL / fc) = 70.7%
fU
If we divide each octave into three
 21/ 3
geometrically equal subsections, i.e., f L
These bands are thus called 1/3rd octave bands with
% relative bandwidth of 23.1%
For
1/10th
fU
 21/10 % relative bandwidth of 5.1%
Octave filters,
fL
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
Acoustic Intensity for most sound
is non-uniformly distributed over time and frequency
Intensity
Convenient to describe the distribution through spectral density
I
f1

I
f
f2
I    df
f1
f2
Frequency (Hz)
 is the intensity within the frequency band Δf=1Hz
For most noise, the instantaneous spectral density
(t) is a time varying quantity, so that  in this
expression is average value taken over a suitable
period τ so that =< (t)>τ
So, many acoustic filters & meters have both fast (1/8s) and slow (1s)
integration times (For impulsive sounds some sound meters have I
characteristics with 35ms time constant)
Intensity Spectrum Level (ISL)
DeciBel measure of  is the Intensity Spectrum Level (ISL)
 .1Hz 
ISL  10 log 

 I
 ref 
If the intensity is constant over the frequency
bandwidth w (= f2- f1),
then total intensity is just
I=  w and
I   1Hz.
and Intensity Level for the band is
IL  ISL  10 log w
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
w
1Hz
IL is calculated and converted to Intensities Ii and then total
intensity level ILtotal is
ILi  ISLi  10log wi
ILtotal


I
  i  
 10 log   i  
 I ref 




as SPL and IL are numerically same, SPL  PSL  10 log w
ILtotal


I
  i  
 10 log   i  
 I ref 




Can be
written as
ILtotal
ILi


10
 10log10 10 
 i

Thus, when intensity level in each band is known, total intensity level can be estimated
PSL (Pressure Spectrum Level) is defined over a 1Hz interval – so the SPL of a tone is same as its PSL
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
Sound Power
Intensity : Average Rate of energy transfer per unit area
W
I
4 r 2
W/m
2
Sound Power Level:
p2
W  4 r I  4 r
Watt
0c
2
2
W
SWL  10log10
dB
Wref
Reference Power Wref =10-12 Watt
Peak Power output:
Female Voice – 0.002W,
Male Voice – 0.004W,
Soft whisper – 10-9W, An average shout – 0.001W Large
Orchestra – 10-70W, Large Jet at Takeoff – 100,000W
15,000,000 speakers speaking simultaneously generate 1HP
A
Recap
• Sound Measurement –Amplitude/Frequency
• Sound Pressure, Intensity, Power, ISL, PSL
Radiation from Source
Point Source (Monopole)
2
p
W  4 r 2 I  4 r 2
Watt
0c
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
W
1
 W  1
IL  10 log10 

10
log
10
2 
4 1012 r 2
 4 r  I ref
IL  10 log10
W
 20 log10 r
12
4 10
Constant term
Depends on distance
from source
Inverse Square Law
When distance doubles (r=2r0) ; 20log 2 + 20log r0 means 6dB difference in the Sound Intensity Level
If the point source is placed on ground,
it radiates over a hemisphere,
the intensity is then doubled and
 W  1
IL  10 log10 
2 
 2 r  I ref
IL  10 log10
W
 20 log10 r
12
2 10
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
W per unit length
radiating over half the cylinder
Intensity at radius r,
W
I
r
W
IL  10 log10
 10 log10 r
12
 10
When distance doubles;
10log 2 + 10log r means 3dB difference in the Sound Intensity Level
VALIDITY OF POINT SOURCE
In free field condition,
Any source with its characteristic dimension small compared to
the 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
DIRECTIVITY OF SOUND SOURCE
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
Sound Intensity at an angle  and at distance r from
a directiona l source radiating sound power W
Q 
Sound Intensity at distance r from a omni - directiona l
source radiating the same sound power W
Directivity Factor & Directivity Index
Directivity Factor
p2
I
Q   2
Is
pS
Directivity Index
DI   10 log 10 Q
thus
DI   L p  L pS
4r 2 I

Q
Rigid boundaries force an omni-directional source to radiate sound in preferential direction
EFFECT OF HARD REFLECTING GROUND
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
I=0
Uniform
sound
energy
density
Free Field Condition
Diffuse Field
MWL Lab, KTH Sweden
Finding sound power (ISO 3745)
Measurements made in semi-reverberant and free field conditions
are in error of 2dB
Noise Mapping
Noise Contours
Environmental
Effects
Wind Gradient
Hot Sunny
Day
Velocity
Gradient (-)
Temperature Gradient
Cool Night
Wind & Temp effects tend to
cancel out
Increase or decrease of 5-6dB
Environmental Effects…
HUMAN PERCEPTION
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
SOUND BITS
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 5kHz
less at other freq.
This sensitivity dependence on frequency is also dependent
on SPL!!!!
RESPONSE OF HUMAN EAR
Loudness Level
(Phon)
Equal to numerical
value of SPL at
1000Hz
0Phon: threshold of
hearing
Loudness Level
(Phon) useful for
comparing two
different frequencies
for equal loudness
But, 60Phon is still
not twice as loud as
30Phon
Equal Loudness Contours for pure tones,
Free Field conditions
Doubling of loudness
corresponds to increase
of 10Phon
Weighting Characteristics
A-weighting: 40Phon equal loudness level contour
C-weighting: 90Phon equal loudness level contour
D-weighting for Aircraft Noise
BASIC SOUND LEVEL METER
LOUDNESS INDEX
Direct relationship between
Loudness Level ‘P’ (Phons) and
Loudness Index ‘S’ (Sones)
S 2
P  40
10
8 Sones is twice as loud as
4 Sones
Hearing Damage Potential to sound energy
depends on its
level & duration of exposure
Equivalent Continuous Sound Level (Leq)
Lj
 N

10 
Leq  10 Log10  t j 10  dB
 j 1

tj : Fraction of total time
duration for which SPL of
Lj was measured
Total time interval
considered is divided in N
parts
with each part has constant
SPL of Lj
70
 1 100

7
10
10
Leq  10 Log10  10  10   91dB
8
8

Integrating Sound Level Meter for randomly varying sound
e.g., 60sec Leq
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…
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
Noise Rating Curves (ISO R 1996)
Level of
Noise
Annoyance
NR78
Errors of the order of 6dB around 400Hz due to reflections
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
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
• 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-carrying
coil windings can induce vibrations.
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.
Noise level increases with
increasing overlap length.
Figure: Core overlap region
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 absorbing
bricks.
•
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 outer
one does not vibrate.
This may change an efficiently radiating
vibration shape into an ineffectively radiating
shape resulting in a lower sound radiation ratio.
Active noise control (ANC):
Decentralized ANC can be implemented. In this transformer tank surface is divided
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
Figure6: Configuration of the control simulation.
Thanks !!