Sound Power
Intensity : Average Rate of energy transfer per unit area
W p2
I W/m 2
W 4 r I 4 r
2 2
Watt
4 r 2 0 c
W
Sound Power Level: SWL 10log10 dB
Wref
Reference Power Wref =10-12 Watt
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
Recap
Sound Measurement Amplitude/Frequency
Sound Pressure, Intensity, Power, ISL, PSL
Radiation from Source
Point Source (Monopole) p 2
W 4 r 2 I 4 r 2 Watt
0 c
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
W 1 W 1
IL 10 log10 2
10 log
4 r I ref 4 1012 r 2
10
W
IL 10 log10 20 log10 r
4 10 12
Constant term Depends on distance
Inverse Square Law
from source
When distance doubles (r=2r0) ; 20log 2 + 20log r0 means 6dB difference in the Sound Intensity Level
If the point source is placed on ground,
it radiates over a hemisphere,
the intensity is then doubled and
W 1
IL 10 log10 2
2 r I ref
W
IL 10 log10 20 log10 r
2 10 12
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
W
Intensity at radius r, I
r
W
IL 10log10 10log10 r
10 12
When distance doubles; 10log 2 + 10log r means 3dB difference in the Sound Intensity Level
VALIDITY OF POINT SOURCE
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
DIRECTIVITY OF SOUND 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
Sound Intensityat an angle and at distance r from
a directional source radiating sound p ower W
Q
Sound Intensityat distance r from a omni - directional
source radiating the same sound p ower W
Directivity Factor & Directivity Index
Directivity Factor Directivity Index
I p2 DI 10 log10 Q 4r 2 I
Q 2 thus
Is pS Q
DI L p L pS
Rigid boundaries force an omni-directional source to radiate sound in preferential direction
EFFECT OF HARD REFLECTING GROUND
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
I=0
Uniform
sound
energy
density
Free Field Condition Diffuse Field
MWL Lab, KTH Sweden
Finding sound power (ISO 3745)
Measurements made in semi-reverberant and free field conditions
are in error of 2dB
Noise Mapping
Noise Contours
Environmental
Effects
Wind Gradient
Hot Sunny
Day
Velocity
Gradient (-)
Temperature Gradient
Cool Night
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
SOUND BITS
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!!!!
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
Equal Loudness Contours for pure tones, Free of 10Phon
Field conditions
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)
P 40
S 2 10
8 Sones is twice as loud as
4 Sones
Hearing Damage Potential to sound energy
depends on its level & duration of exposure
Equivalent Continuous Sound Level (Leq)
tj : Fraction of total time
duration for which SPL of
Lj
10
N
Lj was measured
Leq 10 Log10 t j 10 dB
j 1
Total time interval
considered is divided in N
parts
with each part has constant
SPL of Lj
1 100 7 70
Leq 10 Log10 10 10 91dB
10 10
8 8
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
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:
core laminations strike against each
vibration of the core other due to residual gaps between
laminations
