3 Basic Acoustics
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Transcript of 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 !!