Fundamental of Noise (1)

7/29/2019 Fundamental of Noise (1)

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FUNDAMENTALS OF NOISE

Dr. ASHISH K DARPE

ASSISTANT PROFESSOR

DEPARTMENT OF MECHANICAL ENGINEERING

IIT DELHI


2/70

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


4/70

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


7/70

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


9/70

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



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


35/70

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


36/70

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


38/70

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


43/70

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


50/70

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


54/70

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


56/70

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


58/70

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


62/70

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


69/70

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 !!

Documents

Fundamental of Noise (1)