loudness october 18, 2006 what is it?? the process
TRANSCRIPT
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LoudnessLoudness
October 18, 2006October 18, 2006
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What is it??What is it??
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The Process
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At the Eardrum
Pressure wave arrives at the eardrum It exerts a force The drum moves so that WORK IS DONE The Sound Wave delivers ENERGY to the
EARDRUM at a measurable RATE. We call the RATE of Energy delivery a
new quantity: POWERPOWER
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POWER
Wattsecond
Joule
second
energyPower Example: How much energy does a 60 watt light bulb consume in 1 minute?
J 3600 seconds 60second
joules 60
second
joules 60 watt 60
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By the way …..
You BUY Joules from the power company.
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We PAY for Kilowatt Hours
energytimetime
nergyKWH
e
We PAY for ENERGY!!Not Power/
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More Stuff on Power
10 Watt
INTENSITY = power/unit area
10 Watts = 10 Joules per second.
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Intensity
24
:
r
PI
sphereA
PI
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Same energy (and power) goes through surface (1) as through surface (2)
Sphere area increases with r2 (A=4r2) Power level DECREASES with distance from the
source of the sound. Goes as (1/r2)
ENERGY
So….
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To the ear ….
50m
30 watt
Area of Sphere =4r2
=4x3.14 x 50 x 50 = 31400 m2
Ear Area = 0.000025 m2
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Continuing
watts.000000238power
EarAt
000025.0m
watt.00095
ear Power to
22
m
Scientific Notation = 2.37 x 10-7 watts
22
/00095.31400
30/ mw
m
wattAreaUnitPower
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Huh??
Scientific Notation = 9.5 x 10-8
Move the decimal pointover by 8 places.
Another example: 6,326,865=6.3 x 106
Move decimal pointto the RIGHT by 6 places.
REFERENCE: See the Appendix in the Johnston Test
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Scientific NotationAppendix 2 in Johnston
0.000000095 watts = 9.5 x 10-8 watts
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The perception of loudness
The brain is not a “linear animal”. If the ear hears a sound, it sends a certain
“signal” (electrical) to the brain. The brain determines how loud the music is by
the size of this signal. The range of signals in the brain is limited and it
has to go over a huge range of loudness so it has to process the signal to be in a useful range.
It uses something called a logarithm.
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Decibels - dB
The decibel (dB) is used to measure sound level, but it is also widely used in electronics, signals and communication.
It is a very important topic for audiophiles.
It is a LOGARITHMICLOGARITHMIC translation so it does what the brain does.
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Decibel (dB)Suppose we have two loudspeakers, the first playing a sound with power P1, and another playing a louder
version of the same sound with power P2, but
everything else (how far away, frequency) kept the same.
The difference in decibels between the two is defined to be
10 log (P2/P1) dB
where the log is to base 10.
?
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What the **#& is a logarithm?
Bindell’s definition:
Take a big number … like 23094800394 Round it to one digit: 20000000000 Count the number of zeros … 10 The log of this number is about equal to the number
of zeros … 10. Actual answer is 10.3 Good enough for us!
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Back to the definition of dB:
The dB is proportional to the LOG10 of a ratio of intensities.
Let’s take P1=Threshold Level of Hearing which is 10-12 watts/m2
Take P2=P=The power level we are interested in.
10 log (P2/P1)
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An example:
The threshold of pain is 1 w/m2
1201210)10log(1010
1log 10
:PAIN of thresholdfor the rating dB
1212-
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Another Example
01.1010
1
100
1
:
22
Example
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Look at the dB Column
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DAMAGE TO EARContinuous dB Permissible Exposure Time 85 dB 8 hours 88 dB 4 hours 91 dB 2 hours 94 dB 1 hour 97 dB 30 minutes 100 dB 15 minutes 103 dB 7.5 minutes 106 dB 3.75 min (< 4min) 109 dB 1.875 min (< 2min) 112 dB .9375 min (~1 min) 115 dB .46875 min (~30 sec)
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Can you Hear Me???
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Frequency Dependence
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Why all of this stuff???
We do NOT hear loudness in a linear fashion …. we hear logarithmically
Think about one person singing.Add a second person and it gets a louder.Add a third and the addition is not so much.Again ….
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Let’s look at an example. This is Joe the
Jackhammerer. He makes a lot
of noise. Assume that he
makes a noise of 100 dB.
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At night he goes to a party with his Jackhammering friends.
All Ten of them!
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Start at the beginning
Remember those logarithms? Take the number 1000000=106
The log of this number is the number of zeros or is equal to “6”.
Let’s multiply the number by 1000=103
New number = 106 x 103=109
The exponent of these numbers is the log. The log of {A (106)xB(103)}=log A + log B
9 6 3
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Remember the definition
WattP
P
P
P
P
PP
mwattP
P
PdB
2
12
1212
2120
0
10
2)log(
20)log(10
120)log(10100
)10log(10)log(10100
)10log()log(10)10/log(10100
/10
log10
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Continuing On
The power level for a single jackhammer is 10-2 watt.
The POWER for 10 of them is 10 x 10-2 = 10-1 watts.
110)10log(1010
10log10 11
12
1
dB
A 10% increase in dB!