chapter 4 noise measurement and instrumentation

1

Noise Measurement and Instrumentation

Topics:• Introduction• Sound Measurement• Sound Intensity Mapping & source

identification• Instrumentation• Sound Power• Sound Power Measurement

2

IntroductionSound 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.

3

Introduction

4


Topics:• Introduction• Sound Measurement• Sound Intensity• Instrumentation• Intensity Spectrum Level• Sound Power• Sound Power Measurement

5

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.

6

Sound MeasurementQuantifying 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

12

2

0

1 [ ( )]T

p p t dtT⎡ ⎤

= ⎢ ⎥⎣ ⎦∫

0.707p a=

Acoustic Variables: Pressure and Particle Velocity

(for harmonic sound waves)

7

Sound Measurement

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 5000 times smaller than atmospheric pressure

The large range of associated pressure is one of the reasons we need alternate scale

Range of Pressure

8



9

Sound Intensity

Sound Intensity

10

Sound IntensityA 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

PIcρ

=

1010ref

IIL LogI

=

21 01

10 10 20

/( )20 102 5 (2 5) /( )

p cpSPL Log dB Log dBe e c

ρρ

= =− −

12 12

10 10 1012 2 20 0

10 1010 10 1010 (2 5) /( ) (2 5) /( )ref

I ISPL Log dB Log Loge c I e cρ ρ

− −

−= = +− −

For air, ρ0c ≈ 415Ns/m3 so that 0.16 dBSPL IL= +

Holds true also for spherical waves far away from source

11

Sound Intensity Measurement

12

Sound Intensity Measurement

13



14

Instrumentation

Instruments for analysing Noise

Constant Bandwidth Devices

Proportional Bandwidth Devices

2U

L

ff

= 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

ff

=

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

1/102U

L

ff

=For 1/10th Octave filters, 5.1% relative bandwidth

2nU

L

ff

=

n=1 for octave,

n=1/3 for 1/3rd octave

15

Octave Band Filters

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

16

Instrumentation- Microphones

Measurement transducer to measure noise

• Condenser Microphone• Dynamic Microphone• Ceramic Microphone

Condenser Microphone

17

Instrumentation- Condenser Microphone

• Can be used in extreme condition

• Insensitive to vibrations

• Very expensive • Sensitive to humidity &

moisture

•Measurements range can be from 0.01 Hz to 140 KHz•Dynamic range up to 140 dB

18

Instrumentation- Dynamic Microphone

• Generation of the electrical signal in a moving coil in a magnetic field. The moving coil is connected to the diaphragm that deflects under pressure fluctuations of the sound.

• Excellent sensitivity characteristics.• Relatively insensitive to extreme variation in the humidity.• Cheaper than condenser microphone.

But:-Can not be used in places where strong magnetic fields are present.Lower frequency response than condenser microphone.

19

Instrumentation- Ceramic Microphone

• Sensing element is the piezoelectric crystal.• High frequency response.• High dynamic range.• Very cheap & can often be custom built.• Common for research application as size is also small.

But:-• These are sensitive to the vibration and pressure fluctuation.

Ceramic Microphone is also called as “Piezoelectric” microphone

20



21

Intensity Spectrum Level

DeciBel measure of ℑ is the Intensity Spectrum Level (ISL)

.110logref

HzISLI

⎛ ⎞ℑ= ⎜ ⎟⎜ ⎟

⎝ ⎠If the intensity is constant over the frequency bandwidth w (= f2- f1),

then total intensity is just I= ℑ w and

and Intensity Level for the band is

1 .1

wI HzHz

= ℑ×

10logIL ISL 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

22

Intensity Spectrum Level

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

10logi

itotal

ref

IIL

I

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥=⎢ ⎥⎢ ⎥⎣ ⎦

∑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

IIL

I

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥=⎢ ⎥⎢ ⎥⎣ ⎦

∑ Can be written as

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

23



24

Sound Power

Intensity : Average Rate of energy transfer per unit area

22 W/m

4WI

rπ=

22 2

0

4 4 Watt pW r I rc

π πρ

= =

Sound Power Level: 1010 logref

WSWLW

=

Reference Power Wref =10-12 Watt

dB

Peak 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

25



26

From pressure measurement for varioussound fields

1.Free field technique

2.Reverberant field technique

3.Semi reverberant technique

Estimation of sound power

27

Free Field Condition Diffuse Field

I=0

Uniform sound energy density

2828

• Used for measuring the sound power of any m/cproducing soundo that contains prominent discreet frequency component or narrow

band spectra.

• Can also be used when ‘directional nature’ of the soundradiation are required.

Free Field techniques

Anechoic Chamber

29

Sound Power Measurement• Free field technique

– Sound power of machines which is having discrete frequency spectrum

– Carried out in an anechoic chamber

• Test procedure

– Making no. of measurements on an imaginary surface of hemisphere/sphere with machine at centre.

– No. of microphone positions required depends upon degree of directionality of sound field

– Sound power once average sound pressure level is established then it is integrated over the surface area .

30

• Test procedure involves making number of SPLmeasurements on the surface of an imaginary averagesphere/hemisphere distance from the source is found.

Continues…

Free Field techniques

Finding sound power (ISO 3745)

The measurement can be made in

a large anechoic chamber or can

made in a free field above a

reflecting plane.

31

24I rπΠ = ×2

12 1210log 10log 10log 4 10log10 10I rπ− −

Π = +

11 20logIL L rΠ = + +

20log 11PL L r dBΠ = + + _ I Pwith L L≈

20log 8IL L r dBΠ = + +

For hemispherical surface

Sound power of the source is then computed using the following equations

Free Field techniques continues…

32

Sound Power Measurement

• Reverberant field technique

– Carried out in a reverberation room– Complete diffused sound field sound pressure is independent of

distance from the source

• Sound power can be calculated from

i) The acoustic characteristics of the roomii) The sound pressure level in the room

• Applicability

– Source which does not produce discrete frequencies – And narrow spectrum

33

Reverberant Field Techniques

Reverberant Chamber

• In a completely reverberant (diffused) field,o sound waves are continuously being

reflected from bounding surfaces.o sound pressure field is essentially

independent of distance from source.o the flow of the energy is uniform in all

directions and the sound energy densityis uniform.

• The sound power of a source is reverberant sound field can beobtained from

o The acoustic characteristics of the room ando Sound pressure level in the room.

34


• Principle– Consider directional sound source of total power

– Sound intensity because of direct field

where and

• Average sound absorption coefficient of the room is

∏

2 20/ / 4p c Q rθ θρ π= ∏

/ sQ I Iθ θ= 20; /I p cθ θ ρ= 2/ 4sI rπ= ∏

1 1 2 2

1 2

............

n navg

n

S S SS S S

α α αα + + +=

+ + +

α s are absorption coefficients of different materials

S are surface area of different absorbing materials in the chamber

35


• The energy which is reflected back is

• Upon making required substitutions

– Sound power level is given by

(1 )rev avgα∏ =∏ −

10 2

410log { }4pQL L

r Rθ

π∏ = − +

pL Is the sound pressure level in chamber

R is room the constant given by /(1 )avg avgR Sα α= −

3636

Consider a directional source (total sound power Π) placed inthe centre of the reverberation room. The contribution of thedirect (un reflected) field to the sound intensity in the room is

2

20 4p Q

C rθ θ

ρ πΠ

= ;s

IQIθ

θ =2

0

;p

ICθ

θ ρ= 2_

4sand IrπΠ

=Where

Considerationso the source does not produce any prominent discrete frequency

component or narrow band spectrao If such sound field exits, a rotating diffuser should be used ando The lowest discrete frequency which can be reliably is measured

about 200 Hz. The free field techniques is recommended fordiscrete noise source bellow 200 Hz .


3737

The sound field produced by the reflected sound has now got tobe determined. For the purpose we needed to introduce theconcept sound absorption

Sound Absorption Coeff

Sound Transmission CoeffT

i

II

ς =

a

i

II

α =

i R T DΠ = Π +Π +Π

Absorbed sound intensity

Incident sound intensity

Reflected sound energy

Transmitted sound energy

Dissipated within the surface.

Where

a

i

R

T

D

IIΠΠΠ


3838

Now all the energy which is not reflected is absorbed. (its either

transmitted through material or dissipated in the material as

heat via flow constriction and vibrational motion of the fibers in

the material. )

Hence the absorbed sound energy is given equation .

A D TΠ = Π +Π

Open Window has α = ?


3939

• When sound field is neither free nor complete diffuse.

• Use calibrated sound source with known power spectrum.

• No. of microphones position

Q N1 202 124 68 3

•When sound field is neither free nor complete diffuse.

Semi-Reverberant Field Techniques

4040

Let

Then

o For semi reverberant field, small αt of room, room size belarge so that measurement are made in free field.

o Make no. of measurements (Lpi) or spherical on hemispherical area at radius r1.


4141

o For reverberant field measurement b/g noise < 10dB of

the sound source level.

o No valid measurements if b/g noise difference < 4 dB

o When large room size can not exist. Near field

measurements may be necessary.

o Test surface should be within 1m from radiating surface.

o After averaging out SPL measurements

S : Surface area of measuringsurface


4242

Room type V/S (m)Room without highly

reflecting surface 20 - 50 50 - 90 90 - 3000 >3000

Room with highly reflecting surface 50-100 100 - 200 200-600 >600

∆ 3 2 1 0

A correction factor to account for absorption andreflection from nearby areas.


43

Noise Metrics

44

Sound level measurements

• IEC International Standard 651 ”Sound Level Meters”

• Tolerances per frequency band defined for 4 classes of accuracy– Type 0: precision laboratory use– Type 1: general purpose– Type 2: low price– Type 3: not used in practice (too wide

tolerances)

45

Calibration of Sound Level meters

46

The acoustic signal is a very small compared to

the atmospheric pressure

Sound Pressure Level dB scale

And the pressure amplitude varies over a very wide range Sound Pressure Level dB

scale.

47

Sound Pressure Level dB scale

48

The acoustic pressure is very small compared to the atmospheric pressure

SPL (dB scale)

What sound level meter will do, pick up N samples over a period T

2

0

1 ( )T

rmsp p t dtT

= ∫

2

1

1 N

rms ip pN

= ∑

49

How much this N should be ? Most of sound level meters offer two options

• Fast averaging • 125 m sec of averaging

time (slow)• Fast varying signals• Impulse Averaging (I)• 35 ms of averaging time,

for impacts

• Slow Averaging• Approx 1 second of time

averaging • Slow varying signals• When we are interested

in representative values

SPL (dB scale)

51

Equivalent Level Leq

52

Leq ValueEquivalent constant level that wouldgive the same sound exposure

Why Integrating sound level meters?

][)(1100

2

2

, dBdtp

tpT

LogLT

refTeq ⎟

⎟⎠

⎞⎜⎜⎝

⎛= ∫

][10110 10, dBt

TLogL

jL

jTeq ⎟⎟⎠

⎞⎜⎜⎝

⎛= ∑

53

Sound Intensity

54

Sound Intensity

Instantaneous sound intensity

I r t p r t u r t( , ) ( , ) ( , )=

I rT

p r t u r t dtT

( ) ( , ) ( , )= ∫1

0

We are normally interested in the time average of the intensity, which gives the “active” intensity, corresponding to a net transport of sound energy

_ on the variable represents it a vector quantity

55

Measurement of sound intensity

The pressure is approximated by the average of the two pressure measurements

2)()()( tptptp BA +

=

56

Measurement of Sound Intensity

tu

rp r

∂∂

ρ∂∂

0−=

The zero mean flow momentum equation in the r direction

gives

u t pr

dr

p p dr

t

B A

t

( ) ( ( ) ( ))≈ − = − −−∞ −∞∫ ∫

1 1

0 0ρτ

ρτ τ τ

ΔΔ Δ

approximated by

u t pr

dr

t

( ) = −−∞∫

1

0ρ∂∂

τ

57

The direct method

dtdpptptpTr

It

AB

T

BAr ∫∫∞−

−+Δ

−= τττρ

))()(())()((12

1

00

58

The indirect or FFT method

59

Approximate measure of Sound Intensity

Intensity measured in dB with reference as 10-12 W/ m2

For a localized source general, intensity is a directional quantity

In order to capture this directional effect, special intensity probes are used which measure the correlated signal from two microphones. Aligned in a directional line.

6060

Source Intensity ( I )Decibel intensity

level

Multiple of TOH

intensityThreshold of Hearing (TOH) ITOH = 10−12 W/m2 0 dB 100

Rustling leaves 10−11 W/m2 10 dB 101

Whisper 10−10 W/m2 20 dB 102

Normal conversation 10−6 W/m2 60 dB 106

Busy street traffic 10−5 W/m2 70 dB 107

Vacuum cleaner 10−4 W/m2 80 dB 108

Large orchestra 6.3*10−3 W/m2 98 dB 109.8

iPod at maximum volume level 10−2 W/m2 100 dB 1010

Front rows of a rock concert 10−1 W/m2 110 dB 1011

Threshold of pain 101 W/m2 130 dB 1013

Military jet takeoff 102 W/m2 140 dB 1014

Instant perforation of eardrum 104 W/m2 160 dB 1016

Common sounds with estimates of intensity and decibel level22

TOH10 m

Wmeterwattsin measured is

areaunit powerintensity wherelog10levelintensity Decibel ==⎟

⎟⎠

⎞⎜⎜⎝

⎛= I

II

<http://www.glenbrook.k12.il.us/gbssci/Phys/Class/sound/u11l2b.html>

http://www.glenbrook.k12.il.us/gbssci/Phys/Class/sound/u11l2b.html

61

Filtering and Weighting Filters

6262

Frequency components present in a general noise source

Sum of 3 harmonics (based on http://zone.ni.com/cms/images/devzone/tut/a/8c34be30580.gif)

Nice demo to listen to Fourier series harmonics: http://www.jhu.edu/~signals/listen-new/listen-newindex.htm

http://zone.ni.com/cms/images/devzone/tut/a/8c34be30580.gif

http://www.jhu.edu/~signals/listen-new/listen-newindex.htm

63

Filtering

64

Weighting Filters

Source: Sound and Vibration Book, MWL, KTH, Sweden

65

Weighting Filters

66

Human hearing frequency response

For subjective responses in special cases there are B-, C- and D-weighting curves•very high or low level•special noise, e.g., of aircraft

A-weighting curve

67

Octave Analysis

68

Octave Analysis

220 Hz 440 Hz 880 Hz

A AA

• Analysis performed through a parallel bank of bandpass filters

• One octave corresponds to the doubling of the frequency

• Reference frequency is 1 kHz (audio domain)

69

Octave AnalysisOctave analysis gives log-spaced frequency information.

Similar to human perception of sound1/1, 1/3, 1/12, and 1/24 octave analysisFFT gives linearly-spaced frequency information.

Applications

•noise emissions testing

•acoustic intensity measurement

•sound power measurement

•audio equalization

72

Source Localizationn

73

Localization: Beamforming

),(1 θωY

),(2 θωY)(1 ωF

)(2 ωF

)(ωmF ),( θωmY

)(ωMF),( θωMY

)(ωS

Σ ),( θωZ

θcosmd

md

θ

74

64 Microphone Array

75

Beamforming Data model:• Microphone signals are delayed versions of S(ω)

Stack all microphone signals in a vector

d is `steering vector’

• Output signal Z(ω,θ) is

)]([][ θτ mm ksky −=s

mm f

cd θθτ cos)( =

[ ]Tjj Mee )()(21),( θωτθωτθω −−= Kd

∑=

⋅==M

m

Hmm YFZ

1

* ),()(),()(),( θωωθωωθω YF

)(.),( )( ωθω θωτ SeY mjm

−=

)().,(),( ωθωθω SdY =

76

Beamforming

• Spatial directivity pattern: `transfer function’ for source at angle θ

• Fixed Beamforming– Delay-and-sum beamforming– Weighted-sum beamforming– Near-field beamforming

∑=

− ⋅===M

m

Hjm

meFS

ZH1

)(* ),()()()(),(),( θωωω

ωθωθω θωτ dF

77

Delay-and-sum beamforming• M=5 microphones

• d=3 cm inter-microphone distance

• ψ=60° steering angle

• fs=5 kHz sampling frequency

-20

-10

0

90

270

180 0

Spatial directivity pattern for f=5000 Hz

78

Weighted-Sum beamforming• Sensor-dependent complex weight + delay• Weights added to allow for better beam shaping

ψcos)1( dm−

Σ d

d2Δ

mΔ

1Δ

ψ

1w

2w

mw

∑=

Δ+=M

mmmm kywkz

1

][.][

79

Noise Source Location in an Engine

Fillip et al (2007)

chapter 4 noise measurement and instrumentation

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