basics of noise
TRANSCRIPT
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Hearing by numbers
Dr Max Graham
Faculty of Advanced TechnologyUniversity of Glamorgan
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First principles: Generation of a sound wave from a vibrating source
A simple plane progressive wave
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Relationship between velocity (v), frequency (f), wavelength () and period (T)
V = f m/s
T = 1/f s
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Some velocities of sound
MEDIUM VELOCITY (m/s)
AIR 340
WATER 1500
STEEL 5200
RUBBER (HARD)
RUBBER (SOFT)
1400
50
SAND 95200
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Frequency range of human hearing
Roughly between 20 Hz and 20 kHz
Below 20 Hz is known as infrasound
Above 20 kHz is known as ultrasound Perception of maximum loudness is
around 4 kHz
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Equal loudness contours (humans)
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Frequency ranges of animals
Species Frequency range (Hz)
Dog 5045 000
Cat 4565 000
Horse 5034 000Sheep 10030 000
Mouse 100091 000
Bat 2000110 000
Whale 1000123 000
Goldfish 203000
Tuna 501000
Bullfrog 1003000
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Noise measurement:
Single and third octave band centre frequencies
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Noise spectrum based on single octave band frequency analysis
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Wavelengths of frequency limits of
human hearing
V = f m/s, so = V/f m = 340/f m
At 20 Hz, =340/20 = 17 m
At 20 kHz, =340/20 000 = 17 mm And beyond..
At 20 MHz, =340/20 000 000 = 0.017 mm
(less than the thickness of a human hair)
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A wavelength of 100 mm
Frequency = V/= 340/0.1 = 3400 H z
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Measurement of sound levels?
Decibels (dB)
But what are they?
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Range of sound powers
Acoustic power
(watts)
Sound power
level (dB)
Typical source
100 000 000 200 Rocket
10 000 160 Boeing 707full power
100 140 75 piece orchestra
1 120 Chain saw
0.001 90 Motor car
0.000001 60 Normal voice
0.000000001 30 Whisper
0.000000000001 0 Threshold ofhearing
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Range of sound pressures
Threshold of hearing: 2 x 10-5N/m2or Pa
Threshold of pain: 200 Pa
Atmospheric pressure = 101325 N/m2
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A linear scale?
Adopting a linear scale for say sound
power over the range from the threshold
of hearing (10-12W) to the threshold of
pain (100 W)
A scale of 1014increments
If each increment was represented by an
atom (typical diameter 10-10m), the scale
would stretch for 10 km!
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A logarithmic scale
By definition:
if logab = c,
then ac= b
Number Common
logarithm
1 0
10 1
100 2
1000 3
. .
. .
1000 000 6 etc
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The deci-Bel (dB) scale
The Bel scale was too limited. It is opened
up by a factor of 10 to provide the decibel
scale:
LW= 10 log (W/Wo) dB re Wo = 10-12W
We now have a more realistic range ofbetween 0 dB (threshold of hearing) and
140 dB (threshold of pain)
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Alternative decibel scales
Power (W) of a noise source is expressed as the
sound power level (dB)
Intensity (W/m2) at some distance is expressedas the sound intensity level (dB)
Pressure (N/m2
) at some distance is expressedas the sound pressure level (dB)
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Definition of decibel (dB)
parameters
Sound power level (LW)
LW= 10 log (W/Wo) dB re Wo = 10-12W
Sound intensity level (LI) LI= 10 log (I/Io) dB re Io = 10
-12W/m2
Sound pressure level (Lp)
Lp = 20 log (P/Po) dB re 2 x 10-5N/m2(Pa) or 20 Pa
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Sound pressure level (Lp)
Where does the 20 come from?
P = Iz N/m2 or P2= Iz
Remember log xn= n logx
Z is the characteristic impedance of the medium through whichthe sound is travelling
Z = density of the medium (kg/m3) x velocity of sound throughit (m/s)
Zair = 1.2 x 340 = 408 kg/m2
s (Rayls), roughly 400 Rayls Consider reference values:
Po = Ioz = 10-12x 400 = 4 x 10-10= 2 x 10-5N/m2
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What are the limits?
How quiet can we go?
How loud can we go?
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Decibel manipulation 1
Combination of multiple sources
(equal noise levels)
1 noise source = x dB
2 noise sources = x + 3 dB
L = 10 log(2I/Io)10 log(I/Io) dB
= 10 log 2 = 3 dB 10 noise sources = x + 10 dB
L = 10 log(10I/Io)10 log(I/Io) dB
= 10 log 10 = 10 dB
N noise sources = x + 10 logN dB
L = 10logN dB
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Addition of decibels
A general expression:
L = 10 log(10L1/10+ 10 L2/10+ . 10 Ln/10) dB
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Decibel manipulation 2
Subtraction of decibels
Subtract a noise level L2 from a noise
level L1
New level, L = 10 log(10L!/1010 L2/10) dB
Example: 80 dB + 85 dB = 10 log (108.0 + 108.5) dB = 86.2 dB
86.2 85 dB = 10 log (108.62108.5) dB = 80 dB
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Decibel manipulation 3(Averaging decibels of equal time periods)
If noise levels are sounded over equal time
periods the average noise level over the total
period they have been sounding for is given by:
LAVG= 10 log((10L1/10+ 10L2/10+ 10Ln/10)/n) dB
Example, the average of 80 dB and 100 dB is given by:
LAVG = 10 log((108.0
+ 1010
)/2) dB = 97 dB
NOT (80 + 100) / 2 = 90 dB (the arithmetic average)
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Decibel manipulation 4
(Time weighted averages)
The average noise level (having the same
acoustic energy) for several noise levels
sounding over different time periods can
be calculated and expressed over anytime period (T)
Leq,T = 10 log ((t1 x 10L1/10+ t2 x 10L2/10+.+ tn x 10Ln/10)/T) dB
This can be applied to a single source or any number of sources
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Time weighted averages
An example
A noise level of 90 dB sounds continuously over
a period of one hour.
The noise level this is equivalent to over a period of 15 minutes isgiven by:
L = 10 log ((t x 10L/10)/T dB
= 10 log (60 x 109/15) dB = 96 dB
Similarly, the noise level this is equivalent to over a period of 8 hours
is given by:
L = 10 log(1 x 109/8) dB = 81 dB
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Dont forget your basics
90 dB for 1 hour = 96 dB for 15 minutes
Why?
4 x energy for a quarter of the time
90 dB for 1 hour = 81 dB for 8 hours
1/8 of the energy for 8 x the time
We are equating the energy in all cases.
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Similar principles apply to heat and
light
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The analogy between sound and heat (also applies to light)
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Distribution of energy from airborne sound striking a partition
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Introducing the transmission
coefficient ()
The transmission coefficient () is the
fraction of the acoustic energy which is
transmitted through a partition
TL and are related:
TL = 10 log(1/) dB
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Measures of sound insulation
Transmission loss Transmission
coefficient ()
Zero dB (air gaps) 1
20 dB (single glazing) 0.01
50 dB (cavity brickwork
with ties)
0.00001
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Implications for composite
construction
TL = 10 log (ATOT/(A11+ A22++Ann)) dB
The presence of a relatively small area of
construction with a high transmission coefficientwill seriously reduce the overall sound insulation
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An example
The incorporation of air gaps to the extent
of 1% of the area of a concrete block wall
which should, if properly built, have an
insulation of 50 dB, will reduce this to 20dBthe equivalent of cheaply fitted single
glazing!
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Sound transmission characteristics of a partition:
The mass law
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Resonances
Prediction of resonant frequencies:
F = 0.45Vh((Nx/Lx)2+ (Ny/Ly)2) Hz
F = resonant frequency (Hz)
V = velocity of sound (m/s)
H = thickness of element (m)
Nx, Ny are integers1,2,3 etc Lx = width (m)
Ly = height (m)
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An example
Calculate the lowest resonant frequency
for 6 mm single glazing which is 2 m high
and 1m wide:
F = 0.45x5300x0.006x((1/1)2+ (1/2)2) Hz
= 18 Hz
Second and third resonant frequencies
are: 72 Hz and 161 Hz
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Critical frequency(the lowest frequency at which coincidence occurs)
Critical frequency = VA2/1.8hVL Hz
VA= velocity of sound in air (340 m/s) H = thickness of element (m)
VL = longitudinal velocity of sound through
the element (m/s)
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An example
Calculate the critical frequency for a 100
mm brick wall. The longitudinal velocity of
sound through brickwork is 2350 m/s
Critical frequency = 3402/ (1.8 x 0.1 x 2350) Hz
= 273 Hz
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Thank you