This document provides an overview of fundamentals of noise. It defines sound as acoustic waves that propagate through a medium, with noise being unwanted or disturbing sound. Key concepts covered include: - Sound is measured by properties like frequency, sound pressure level, intensity level, and power level. - The decibel scale is used to quantify sound levels in a way that reflects human perception. - Sound can be analyzed by its intensity or pressure levels across frequency bands like octave or one-third octave bands. - The relationship between sound intensity, pressure, and power is explained. Combining sound from multiple sources is also addressed.

1. FUNDAMENTALS OF NOISE
Dr. ASHISH K DARPE
ASSISTANT PROFESSOR
DEPARTMENT OF MECHANICAL ENGINEERING
IIT DELHI

2. 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

3. • 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

4. 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 )

6. Speed of Sound
The rate at which the disturbance (sound wave) travels
Property of the medium
0
0
P
c



RT
c
M


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
273
1 






 c
T
c
c
s
m
c /
5
.
343
25 
s
m
c /
355
40 

7. 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.

8. 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
2
2
0
1
[ ( )]
T
p p t dt
T
 
  
 

0.707
p a

Acoustic Variables: Pressure and Particle Velocity

9. 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

10. 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

11. 10Log10W1= 10Log10W2 + 10Log10n to avoid fractions
Now we have above quantities in deciBel, 10dB=1Bel
deciBels are thus another way of expressing ratios
2
V
W
R

2
P
W
r

Electrical
Power
Sound
Power
20Log10V1= 20Log10V2 + 20Log10n(1/2)
20Log10P1= 20Log10P2 + 20Log10n(1/2)
r - acoustic impedance
Decibel

12. 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 20Pa (RMS)
SPL=20Log10(P1/2e-5) P1 is RMS pressure
n: Ratio of sound powers

13. 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 20Pa
Sound Pressure Level

15. Sound Intensity

16. 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 dt
T
 
2
0
P
I
c


10
10
ref
I
IL Log
I

2
1 0
1
10 10 2
0
/( )
20 10
2 5 (2 5) /( )
p c
p
SPL Log dB Log dB
e e c


 
 
12 12
10 10 10
12 2 2
0 0
10 10
10 10 10
10 (2 5) /( ) (2 5) /( )
ref
I I
SPL Log dB Log Log
e c I e c
 
 

  
 
For air, 0c  415Ns/m3 so that 0.16 dB
SPL IL
 
Hold true also for spherical
waves far away from source

17. COMBINATION OF SEVERAL SOURCES
Total Intensity produced by several sources
IT=I1+ I2+ I3+…
Usually, intensity levels are known (L1, L2,…)
3
1 2
10
10 10
10 10 10 10 ...
L
L L
T
L Log
 
   
 
   
     
 
   
 
 
 
12
10
10
T
T
I
L Log 
 
  
 
1
1 12
10
10
I
L Log 
 
  
 

18. If intensity levels of each of the N sources is same,
1
10
10 10
L
T
L Log N
 
 
 
 
  
 
 
1
10
T
L 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

19. 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

20. Musical
Instrument
For multiple frequency composition sound, frequency spectrum is
obtained through Fourier analysis
Pure tone
Frequency Composition of Sound

21. Amplitude
(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

22. 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 L
f f f

International Electrotechnical Commission

23. Octave Filters

24. Instruments for
analysing Noise
Constant Bandwidth Devices
Proportional Bandwidth Devices
2
U
L
f
f
 c U L
f 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.,
1/3
2
U
L
f
f

These bands are thus called 1/3rd octave bands with
% relative bandwidth of 23.1%
1/10
2
U
L
f
f

For 1/10th Octave filters, % relative bandwidth of 5.1%
2n
U
L
f
f

n=1 for octave,
n=3 for 1/3rd octave

25. 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

26. 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)
Intensity
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

27. DeciBel measure of  is the Intensity Spectrum Level (ISL)
.1
10log
ref
Hz
ISL
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
w
I Hz
Hz
 
10log
IL 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

28. IL is calculated and converted to Intensities Ii and then total
intensity level ILtotal is
10log
i
i
total
ref
I
IL
I
 
 
 
 
 
 

 
 
 

10log
i i i
IL ISL w
 
as SPL and IL are numerically same, 10log
SPL PSL w
 
PSL (Pressure Spectrum Level) is defined over a 1Hz interval – so the SPL of a tone is same as its PSL
10
10
10log 10
i
IL
total
i
IL
 
  
 

10log
i
i
total
ref
I
IL
I
 
 
 
 
 
 

 
 
 
 Can be
written as
Thus, when intensity level in each band is known, total intensity level can be estimated

29. Combining Band Levels and Tones
SPL = PSL + 10 log w
For pure tones, PSL = SPL
so, two SPL of the tones is 63 & 60 dB
For the broadband noise,
SPL = PSL + 10 log w
= PSL + 10 log 100
SPL = 60 dB
Thus the overall band level
= Band level of broadband noise + Level of tones
= 60 + 63 + 60 = 64.7 + 60
≈ 66 dB

30. Sound Power
Intensity : Average Rate of energy transfer per unit area
2
2
W/m
4
W
I
r


2
2 2
0
4 4 Watt
p
W r I r
c
 

 
Sound Power Level: 10
10log
ref
W
SWL
W

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

31. Recap
• Sound Measurement –Amplitude/Frequency
• Sound Pressure, Intensity, Power, ISL, PSL

33. 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 10
2 12 2
10 10
12
1 1
10log 10log
4 4 10
10log 20log
4 10
ref
W W
IL
r I r
W
IL 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
2
2 2
0
4 4 Watt
p
W r I r
c
 

 
Point Source (Monopole)

34. If the point source is placed on ground,
it radiates over a hemisphere,
the intensity is then doubled and
10 2
10 10
12
1
10log
2
10log 20log
2 10
ref
W
IL
r I
W
IL r

 
 
  
 
 

35. 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
I
r


10 10
12
10log 10log
10
W
IL r
 
 
When distance doubles; 10log 2 + 10log r means 3dB difference in the Sound Intensity Level

36. 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

37. 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
the
radiating
source
l
directiona
-
omni
a
from
r
distance
at
Intensity
Sound
power W
sound
radiating
source
l
directiona
a
from
r
distance
at
and
angle
an
at
Intensity
Sound 
 
Q

38. Directivity Factor & Directivity Index
2
2
S
s p
p
I
I
Q


 

pS
p L
L
DI
thus
Q
DI






 10
log
10



Q
I
r2
4


Directivity Factor Directivity Index
Rigid boundaries force an omni-directional source to radiate sound in preferential direction

39. 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

41. Free Field Condition Diffuse Field
I=0
Uniform
sound
energy
density

42. Finding sound power (ISO 3745)
MWL Lab, KTH Sweden

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

44. Noise Mapping
Noise Contours

45. 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

46. Environmental Effects…

47. HUMAN PERCEPTION

48. 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

49. 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

50. 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

51. Weighting Characteristics
A-weighting: 40Phon equal loudness level contour
C-weighting: 90Phon equal loudness level contour
D-weighting for Aircraft Noise

52. BASIC SOUND LEVEL METER

53. LOUDNESS INDEX
Direct relationship between
Loudness Level ‘P’ (Phons) and
Loudness Index ‘S’ (Sones)
8 Sones is twice as loud as
4 Sones
40
10
2
P
S



54. Hearing Damage Potential to sound energy
depends on its level & duration of exposure
Equivalent Continuous Sound Level (Leq)
10
10
1
10 10
j
L
N
eq j
j
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 10
10
1 7
10 10 10 91
8 8
eq
L Log dB
 
  
 
 

55. 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…

56. 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

57. Noise Rating Curves (ISO R 1996)
Level of
Noise
Annoyance
NR78

58. Errors of the order of 6dB around 400Hz due to reflections

59. 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

60. TRANSFORMER NOISE CASE STUDY

61. SOURCES
The 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

62. • 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.

65. 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.

66. 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.

67. This may change an efficiently radiating
vibration shape into an ineffectively radiating
shape resulting in a lower sound radiation ratio.

68. Active noise control (ANC):

69. 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

70. Thanks !!