The document provides an overview of basic acoustics concepts including quantification of sound through measurements of sound pressure, intensity, and power. It discusses acoustic variables such as sound pressure level and intensity level which are expressed on a logarithmic decibel scale. Key concepts covered include the inverse square law describing how sound pressure/intensity decreases with distance from a point source, effects of multiple sound sources, relationships between frequency and sound perception, and directionality of sound sources. Measurement techniques and standards are also summarized.

1. 1
BASIC ACOUSTICS
A K Darpe
Department of Mechanical Engineering
A Short Course on
Machinery Noise Control and Muffler Design
December 10-13, 2008

2. 2
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

3. 3
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.

4. 4

5. 5

6. 6
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

7. 7
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 per unit area

8. 8
Sound intensity measurement allows in-situ
estimation of noise source ranking

9. 9
Sound Intensity
Time averaged rate
of energy flow per
unit area

10. 10
0
1
T
I p u dt
T
 
Sound Intensity
Time averaged rate of
energy flow per unit
area

11. 11
Measuring sound
power from
intensity
measurements
2
2
W/m
4
W
I
r



12. 12
Steady background
noise is not a problem

13. 13
RANKING

14. 14
Sound Fields
ISO 3745
ISO 3741

15. 15
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
 
  
 

ˆ
0.707
p p

Acoustic Variables: Pressure and Particle Velocity

16. 16
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

17. 17
Very large range of
sound intensity which
the ear can
accommodate,
from the loudest
(1 watt/m2)
to the quietest
(10-12 watts/m2),
energy received from a 50 watt bulb

18. 18
Levels
• A unit of a logarithmic scale of power or intensity
called the power level or intensity level.
• The decibel is defined as one tenth of a bel
• One bel represents a difference in level between two
intensities (one of the two is ten times greater than
the other)
• Thus, the intensity level is the comparison of one
intensity to another and may be expressed:
Intensity level = 10 log10 (I1 /Iref) (dB)

19. 19
Why log ratio?
• Logarithmic scale compresses the high amplitudes and
expands 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)

20. 20
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 sound
intensity
Power Ratio of 2 = dB of 3
Power Ratio of 10 = dB of 10
Power Ratio of 100 = dB of 20
dB SCALE

21. 21
Sound Pressure Level
In acoustics, the reference pressure
Pref=2e-5 N/m2 or 20Pa (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
1
10 2
10 rms
ref
p
SPL Log dB
p

1
10
20 rms
ref
p
SPL Log dB
p


22. 22
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

23. 23

24. 24
Threshold of hearing 0 dB Motorcycle (30 feet) 88 dB
Rustling 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.

25. 25
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

26. 26
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
 
For plane progressive waves;
Hold true also for spherical
waves far away from source
Reference Intensity Iref =10-12 Watt/m2

27. 27

28. 28
Effect of multiple sound sources
Lp1
Lp2
2 2 2
1 2
tot
p p p
 
1
2
1 10
2
10
p
L
ref
p
p

1 2
2 2 10 10
10 10
p p
L L
tot ref
p p
 
 
 
 
 
1 2
2
10 10
10 10
2
10log 10log 10 10
p p
L L
tot
ref
p
p
 
 
 
 
 
   
   
10
10
1
10log 10
n
Lp
N
tot
n
Lp

 
  
 

2
1
10 2
10 rms
ref
p
SPL Log dB
p


29. 29
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

30. 30
Correlated and uncorrelated sources

31. 31
Which source to
first take care?

32. 32
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

33. 33
Musical
Instrument
For multiple frequency composition sound, frequency spectrum is
obtained through Fourier analysis
Pure tone
Frequency Composition of Sound

34. 34
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

35. 35
Octave Filters

36. 36

37. 37
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

38. 38

39. 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/pressure
Level
Inverse Square Law
2
2 2
0
4 4 Watt
p
W r I r
c
 

 
Point Source (Monopole)

40. 40
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

 
 
  
 
 
20log 8
P
L L r dB

   Vs 20log 11
P
L L r dB

  
For source not on
ground
Pressure level gets
doubled at the same point

41. 41
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
10log 5
P
L L r dB

  

42. 42
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
power from the sound pressure
VALIDITY OF POINT SOURCE

43. 43
Directivity of Sound Source

44. 44
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

45. 45
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

46. 46
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) in free space
If source is sufficiently above the ground this effect is reduced
EFFECT OF HARD REFLECTING GROUND

47. 47

48. 48
Measurements made in semi-reverberant and free field conditions
are in error of 2dB

49. 49
2
4
I r

  
2
12 12
10log 10log 10log4 10log
10 10
I r

 
   
11 20log
I
L L r
   
20log 11
P
L L r dB
    I P
with L L

20log 8
I
L L r dB
   
If hemisphere surface is used then the above
equation changes to
Sound Power Estimation from
Pressure level measurements

50. 50
Measurement of Power in
Reverberant Room
10 2
4
10log
4
p
Q
L L
r R



 
  
 
 
 
1
avg
avg
S
R




Which is called room
constant team used to
describe acoustic
characteristic of a room
Alternatively,
Lπ = Lp + 10 log V – 10 log T60 - 14

51. 51
Semi-reverberant field technique
When sound field is
neither free nor
completely diffuse.
Use calibrated sound
source with known power
spectrum.
Then use
Lπ = Lπ’r - Lp’r + Lp

52. 52
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
L
 Lpd + 10log10 (2d2)
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)½
Background noise < 10dB
r

53. 53
What we learnt
• Sound Pressure, Intensity and Power
• dB levels
• Multiple Sound Sources
• Types of Sound Sources
• Directivity

54. 54
Thanks !!