3 Basic Acoustics

7/29/2019 3 Basic Acoustics

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BASIC ACOUSTICS

A K Darpe

Department of Mechanical Engineering

A Short Course on

Machinery Noise Control and Muffler Design

December 10-13, 2008


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Basic Acoustics

Quantification of Sound

Sound Pressure, Pressure level (dB scale)

Sound Intensity, Sound Power

Combination of sound sources

Sound Frequency

Simple sound sources Directivity


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Sound Quantification

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.


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Power / Intensity / Pressure

Intensity & pressure measured using

instruments

Power is calculated

Power is basic measure of acoustic

energy it can produce

& is independent of surroundings


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Power / Intensity / Pressure ???

Sound Power:for noise rating of machines

unique descriptor of noisiness of

source

Sound Pressure:

evaluation of harmfulness and

annoyance of noise sources

Sound Intensity:

location & rating of noise sources

rate of energy flow perunit area


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Sound intensity measurement allows in-situ

estimation of noise source ranking


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Sound Intensity

Time averaged rate

of energy flow perunit area


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0

1

T

I p u dtT

Sound Intensity

Time averaged rate of

energy flow per unit

area


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Measuring sound

power fromintensity

measurements

2

2W/m

4

WI

r


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Steady background

noise is not a problem


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RANKING


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Sound Fields

ISO 3745

ISO 3741


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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 p

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 (Pascal)

(threshold of hearing)

to

20 N/m2 (Pascal)

(sensation of pain)

1,000,000 times larger

peak pressure of loudest

sound

is 3500 times smaller than

atm. pressure


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Very large range of

sound intensity which

the ear canaccommodate,

from the loudest

(1 watt/m2)

to the quietest(10-12 watts/m2),

energy received from a 50 watt bulb


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Levels

A unit of a logarithmic scale of power or intensitycalled thepower levelorintensity level.

The decibel is defined as one tenth of a bel

One bel represents a difference in level between twointensities (one of the two is ten times greater thanthe other)

Thus, the intensity level is the comparison of oneintensity to another and may be expressed:

Intensity level = 10 log10 (I1 /Iref) (dB)


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Why log ratio?

Logarithmic scale compresses the high amplitudes andexpands the low ones

The other reason: Equal relative modifications of the

strength of a physical stimulus lead to equal absolute

changes in the salience of the sensory events (Weber-

Fechner Law) and can be approximated by a logarithmic

characteristics

(Ear responds logarithmically to stimulus)


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Acoustic parameters are expressed as logarithmic ratio of the

measured value to a reference value

The Bel (B) is a unit of measurement invented by Bell Labs and

named after Alexander Graham Bell.

The Bel was too large, so the deciBel(dB), equal to 0.1 B,

became more commonly used as a unit for measuring soundintensity

Power Ratio of 2 = dB of 3

Power Ratio of 10 = dB of 10Power Ratio of 100 = dB of 20

dB SCALE


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Sound Pressure Level

In acoustics, the reference pressure

Pref=2e-5 N/m2 or 20Pa (RMS) loudest sound pressure that a

normal person can barely perceive at 1000Hz

In linear vibroacoustics, time averaged power values are

proportional to the squared rms-amplitudes of the field variables

(e.g., pressure, particle velocity)

Thus to calculate logarithmic levels from the field variables, it is

these squared rms-amplitudes that must be used.

2

110 2

10 rms

ref

pSPL Log dB

p

110

20 rms

ref

pSPL Log dB

p


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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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i l d ib l l l (d ) f d


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Threshold of hearing 0 dB Motorcycle (30 feet) 88 dBRustling leaves 20 dB Foodblender (3 feet) 90 dB

Quiet whisper (3 feet) 30 dB Subway (inside) 94 dB

Quiet home 40 dB Diesel truck (30 feet) 100 dB

Quiet street 50 dB Power mower (3 feet) 107 dB

Normal conversation 60 dB Pneumatic riveter (3 feet) 115 dB

Inside car 70 dB Chainsaw (3 feet) 117 dB

Loud singing (3 feet) 75 dB Amplified Rock and Roll (6 feet) 120 dB

Automobile (25 feet) 80 dB Jet plane (100 feet) 130 dB

Typical average decibel levels (dBA) of some common sounds.


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Sound Power

Intensity : Average Rate of energy transfer per unit area

22 W/m4

WIr

2

2 2

0

4 4 WattpW r I r c

Sound Power Level:10

10log

ref

WSWL

W

Reference PowerWref=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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Sound Intensity

0

1

T

I p u dt

T

2

0

PI

c

1010

ref

IIL Log

I

21 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 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

For plane progressive waves;

Hold true also for sphericalwaves far away from source

Reference IntensityIref=10-12 Watt/m2


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Effect of multiple sound sources

Lp1Lp22 2 2

1 2totp p p

12

1 102

10pL

ref

p

p

1 2

2 2 10 1010 10p pL L

tot ref p p

1 22

10 1010 102

10log 10log 10 10p pL L

tot

ref

pp

1010

1

10log 10nLpN

tot

n

Lp

2

110 2

10 rms

ref

pSPL Log dB

p


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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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Correlated and uncorrelated sources


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Which source to

first take care?


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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 Filters


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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


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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/pressureLevel

Inverse Square Law

22 2

04 4 Watt

p

W 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

110log2

10log 20log2 10

ref

WILr I

WIL r

20log 8PL L r dB Vs 20log 11PL L r dB

For source not on

ground

Pressure level gets

doubled at the same point


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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 + 10logr means 3dB difference in the Sound Intensity Level

10log 5PL L r dB

VALIDITY OF POINT SOURCE


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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

power from the sound pressure

VALIDITY OF POINT SOURCE


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Directivity of Sound 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

Directi it Factor & Directi it Inde


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Directivity Factor & Directivity Index

2

2

Ss p

p

I

IQ

pSp LLDI

thus

QDI

10log10

Q

Ir2

4

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 planesStrength 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) in free space

If source issufficiently above the ground this effect is reduced

EFFECT OF HARD REFLECTING GROUND


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Measurements made in semi-reverberant and free field conditions

are in error of 2dB

S d P E ti ti f


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24I r 2

12 1210log 10log 10log 4 10log10 10I r

11 20logIL L r

20log 11PL L r dB I Pwith L L

20log 8IL L r dB

If hemisphere surface is used then the above

equation changes to

Sound Power Estimation from

Pressure level measurements

M t f P i


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Measurement of Power in

Reverberant Room

10 2

410log

4p

QL L

r R

1avg

avg

SR

Which is called room

constant team used to

describe acoustic

characteristic of a room

Alternatively,

L = Lp + 10 log V 10 log T60 - 14


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Semi-reverberant field technique

When sound field isneither free norcompletely diffuse.

Use calibrated soundsource with known powerspectrum.

Then use

L = Lr - Lpr+Lp


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Semi-reverberant field technique

To take care of nearby

reflecting surfaces and

background noise,

Measure at number of locations

on measuring surface

Lpd = Lp 10log10(d/r)2

Then use

LLpd + 10log10 (2d

2)

Lpd is equivalent sound pressure level at

the reference radius d, and

Lp is mean sound pressure level

measured over surface of area S, and

radius r= (S/2)

Background noise < 10dB

r


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What we learnt

Sound Pressure, Intensity and Power

dB levels

Multiple Sound Sources Types of Sound Sources

Directivity


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Thanks !!

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3 Basic Acoustics