FUNDAMENTALS OF NOISE

Dr. ASHISH K DARPE

ASSISTANT PROFESSORDEPARTMENT 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.

Frequency: Number of pressure cycles / time

also called pitch of sound (in Hz)

Guess how much is particle displacement??

8e-3nm to 0.1mm

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

0

0

Pc

RT

cM

Alternatively,

c – Speed of sound P0, 0 - Pressure and Density

- Ratio of specific heats R – Universal Gas Constant

T – Temperature in 0KM – Molecular weight

Speed of Light: 299,792,458 m/s Speed of sound 344 m/s

2

1

0 2731

cT

ccsmc /5.34325

smc /35540

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

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

22

0

1[ ( )]

T

p p t dtT

0.707p a

Acoustic Variables: Pressure and Particle Velocity

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

RANGE OF PRESSURE

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

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

rElectrical

Power

Sound

Power

20Log10V1= 20Log10V2 + 20Log10n(1/2)

20Log10P1= 20Log10P2 + 20Log10n(1/2)

r - acoustic impedance

Decibel

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

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

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

0

1

T

I p u dtT

2

0

PI

c

1010ref

IIL Log

I

21 01

10 10 20

/( )20 10

2 5 (2 5) /( )

p cpSPL Log dB Log dB

e e c

12 12

10 10 1012 2 20 0

10 1010 10 10

10 (2 5) /( ) (2 5) /( )ref

I ISPL Log dB Log Log

e 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

COMBINATION OF SEVERAL SOURCES

Total Intensity produced by several sources

IT=I1+ I2+ I3+…

Usually, intensity levels are known (L1, L2,…)

31 2

1010 1010 10 10 10 ...LL L

TL Log

1210

10T

T

IL Log

1

1 1210

10

IL Log

If intensity levels of each of the N sources is same,

1

1010 10L

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=65.5dB 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

Musical Instrument

For multiple frequency composition sound, frequency spectrum is obtained through Fourier analysis

Pure tone

Frequency Composition of Sound

Am

plit

ude

(dB

) A1

f1 Frequency (Hz)

Complex Noise Pattern

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)

produced by exhaust of Jet Engine, water at base of Niagara Falls, hiss of air/steam jets, etc

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 1000Hz

Next lower center frequency = 1000/ 103/10 500Hz

Next higher center frequency = 1000*103/10 2000Hz

c U Lf f f

International Electrotechnical Commission

Octave Filters

Instruments for analysing Noise

Constant 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.,

1/32U

L

f

f

These bands are thus called 1/3rd octave bands with % relative bandwidth of 23.1%

1/102U

L

f

fFor 1/10th Octave filters, % relative bandwidth of 5.1%

2nU

L

f

f

n=1 for octave,

n=3 for 1/3rd octave

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

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)

Inte

nsit

y I

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 Δf=1Hz

DeciBel measure of is the Intensity Spectrum Level (ISL)

.110log

ref

HzISL

I

If the intensity is constant over the frequency bandwidth 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

IL is calculated and converted to Intensities Ii and then total intensity level ILtotal is

10logi

itotal

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 interval – so the SPL of a tone is same as its PSL

101010log 10

iIL

totali

IL

10log

ii

totalref

I

ILI

Can be written as

Thus, when intensity level in each band is known, total intensity level can be estimated

Combining Band Levels and Tones

SPL = PSL + 10 log w

For pure tones, PSL = SPLso, two SPL of the tones is 63 & 60 dB

For the broadband noise,SPL = PSL + 10 log w = PSL + 10 log 100SPL = 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

22

W/m 4

WI

r

22 2

0

4 4 Watt p

W r I rc

Sound Power Level: 1010logref

WSWL

W

Reference Power Wref =10-12 Watt

dB

Peak Power outputPeak Power output:

Female Voice – 0.002W, Male Voice – 0.004W, A 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

Recap

• Sound Measurement –Amplitude/Frequency

• Sound Pressure, Intensity, Power, ISL, PSL

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

22 2

0

4 4 Watt p

W r I rc

Point Source (Monopole)

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

WIL r

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

Ir

10 101210log 10log

10

WIL r

When distance doubles; 10log 2 + 10log r means 3dB difference in the Sound Intensity Level

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

VALIDITY OF POINT 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

DIRECTIVITY OF SOUND SOURCE

power W sound same theradiating source

ldirectiona-omni a fromr distanceat Intensity Sound

power W sound radiating source ldirectiona a

fromr distanceat and anglean at Intensity Sound

Q

Directivity Factor & Directivity Index

2

2

Ss p

p

I

IQ

pSp LLDI

thus

QDI

10log10

Q

Ir 24

Directivity Factor Directivity Index

Rigid boundaries force an omni-directional source to radiate sound in preferential direction

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

Free Field Condition Diffuse Field

I=0

Uniform sound energy density

Finding sound power (ISO 3745)

MWL Lab, KTH Sweden

Measurements made in semi-reverberant and free field conditions are in error of 2dB

Noise Mapping

Noise Contours

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

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

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!!!!

SOUND BITS

Equal Loudness Contours for pure tones, Free Field conditions

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

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)

8 Sones is twice as loud as 4 Sones

40

102P

S

Hearing Damage Potential to sound energy

depends on its level & duration of exposure

Equivalent Continuous Sound Level (Leq)

1010

1

10 10jLN

eq jj

L Log t dB

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

100 70

10 1010

1 710 10 10 91

8 8eqL Log dB

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

SOURCESThe 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.

Figure: Core overlap region

Noise level increases with increasing overlap length.

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):

Figure6: Configuration of the control simulation.

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

Thanks !!