Post on 16-Dec-2015
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 !!