lecture 18
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Lecture 18Lecture 18Sound LevelsSound Levels
November 1, 2004November 1, 2004
Whutshappenin?Whutshappenin? Examinations have been graded and Examinations have been graded and
returned.returned. Next exam is in THREE WEEKS!!!Next exam is in THREE WEEKS!!!
Then, only one week of lectures Then, only one week of lectures followed by the FINAL EXAMINATIONfollowed by the FINAL EXAMINATION– There will be NO make-up exam for the There will be NO make-up exam for the
final.final.– The only acceptable reason for missing the The only acceptable reason for missing the
exam is that you are dead or almost dead.exam is that you are dead or almost dead.
ITEM DATE WEIGHT (%)
Exam #1 Friday, 9/24 15%Exam #2 Friday, 10/22 15%Exam #3 Monday, 11/22 15%
OP Questions Daily 25%Final Exam Dec. 6th 30%
SCHEDULE REMAININGSCHEDULE REMAINING
More ScheduleMore ScheduleWeek Topic
November 1 Loudness, decibels and hearing
November 8 Room Acoustics, Diffraction and Wave interference
November 15 Simple Electricity and Introduction to Speakers and Microphones
November 22 Examination #3, 1 Lecture this week. Continuation of previous.
November 29 Completion of Electrical Aspects of Music (depends on time)
December 6t FINAL EXAM
ENERGY PER UNIT TIMEENERGY PER UNIT TIME
secJoule1 watt 1
SecondJoulesPOWER
TimeUnit Energy
RecallRecall
Same energy (and power) goes through Same energy (and power) goes through surface (1) as through surface (2)surface (1) as through surface (2)
Sphere area increases with rSphere area increases with r22 (A=4 (A=4rr22)) Power level DECREASES with distance Power level DECREASES with distance
from the source of the sound.from the source of the sound.– Goes as (1/rGoes as (1/r22))
ENERGY
To the ear ….To the ear ….
50m
30 watt
Area of Sphere =r2
=3.14 x 50 x 50 = 7850 m2Ear Area = 0.000025 m2
ContinuingContinuing2
2 /004.0785030/ mw
mwattAreaUnitPower
watts.000000095powerEarAt
000025.0m
watt.004
ear Power to
22
m
Scientific Notation = 9.5 x 10-8
Huh??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 LEFT by 6 places.
REFERENCE: See the Appendix in the Johnston Testand Bolemon, page 17.
Scientific NotationScientific NotationChapter 1 in Bolemon, Appendix 2 in JohnstonChapter 1 in Bolemon, Appendix 2 in Johnston
0.000000095 watts = 9.5 x 10-8 watts
Decibels - dBDecibels - dB The decibel (The decibel (dBdB) is used to ) is used to
measure sound level, but it is measure sound level, but it is also widely used in electronics, also widely used in electronics, signals and communication. signals and communication.
Decibel continued (dB)Decibel continued (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.
?
What the **#& is a What the **#& is a logarithm?logarithm?
Bindell’s definition:Bindell’s definition: Take a big number … like 23094800394Take a big number … like 23094800394 Round it to one digit: 20000000000Round it to one digit: 20000000000 Count the number of zeros … 10Count the number of zeros … 10 The log of this number is about equal to the The log of this number is about equal to the
number of zeros … 10.number of zeros … 10. Actual answer is 10.3Actual answer is 10.3 Good enough for us!Good enough for us!
Back to the definition of dB:Back to the definition of dB:
The dB is proportional to the LOGThe dB is proportional to the LOG1010 of of a ratio of intensities.a ratio of intensities.
Let’s take PLet’s take P11=Threshold Level of =Threshold Level of Hearing which is 10Hearing which is 10-12-12 watts/m watts/m22
Take PTake P22=P=The power level we are =P=The power level we are interested in.interested in.
10 log (P2/P1)
An example:An example: The threshold of pain is 1 w/mThe threshold of pain is 1 w/m22
1201210)10log(1010
1log 10
:PAIN of thresholdfor the rating dB
1212-
Another ExampleAnother Example
01.1010
1100
1:
22
Example
Look at the dB ColumnLook at the dB Column
DAMAGE TO EARDAMAGE 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)
Frequency DependenceFrequency Dependence
Why all of this stuff???Why all of this stuff??? We do NOT hear loudness in a linear We do NOT hear loudness in a linear
fashion …. we hear fashion …. we hear logarithmeticallylogarithmetically!!– Think about one person singing.Think about one person singing.– Add a second person and it gets a Add a second person and it gets a
louder.louder.– Add a third and the addition is not so Add a third and the addition is not so
much.much.– Again ….Again ….
Let’s look at an example.Let’s look at an example. This is Joe the This is Joe the
Jackhammerer. Jackhammerer. He makes a lot He makes a lot
of noise.of noise. Assume that he Assume that he
makes a noise makes a noise of 100 dB.of 100 dB.
At night he goes to a party At night he goes to a party with his Jackhammering with his Jackhammering
friends.friends.All Ten of them!
Start at the beginningStart at the beginning Remember those logarithms?Remember those logarithms? Take the number 1000000=10Take the number 1000000=1066
The log of this number is the number of The log of this number is the number of zeros or is equal to “6”.zeros or is equal to “6”.
Let’s multiply the number by 1000=10Let’s multiply the number by 1000=1033
New number = 10New number = 1066 x 10 x 1033=10=1099
The exponent of these numbers is the log.The exponent of these numbers is the log. The log of The log of {{A (10A (1066)xB(10)xB(1033))}}=log A + log B=log A + log B
9 6 3
Remember the definitionRemember the definition
WattP
PPP
P
PP
mwattP
PPdB
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
Continuing OnContinuing On The power level for a single jackhammer is The power level for a single jackhammer is
1010-2-2 watt. watt. The POWER for 10 of them isThe POWER for 10 of them is
– 10 x 1010 x 10-2 -2 = 10= 10-1-1 watts. watts.
110)10log(101010log10 11
12
1
dB
A 10% increase in dB!
Let’s think about sizes of Let’s think about sizes of things.things.
Music is primarily between 50 and Music is primarily between 50 and 5000 Hz.5000 Hz.
Look at the table:Look at the table:
v=344 m/sfrequency wavelength size
50 6.88
100 3.44
200 1.72 height or a person
500 0.688
1000 0.344 head
2000 0.172 <size of head
5000 0.0688 size of pinna
10000 0.0344 ~length of ear canal
EAR
Helmholtz Resonartor
CROSS-SECTION
The Ear Spread OutThe Ear Spread Out
Fluid
The CochleaThe Cochlea
The Cochlea UnwoundThe Cochlea Unwound
The Cochlea SchematicThe Cochlea Schematic
Rubber Membrane
Low Frequency High Frequency
Frequency Info
Resonance in the Basilar Resonance in the Basilar MembraneMembrane(Computed)(Computed)
The Hair CellsThe Hair Cells
Simplified VersionSimplified Version
Resonance !!
Damage from very Damage from very LOUDLOUD noises. noises.
Extreme Acoustic TraumaExtreme Acoustic Trauma
Control, not Control, not exposedexposed
After After ExposureExposure
Guinea Pig StereociliaGuinea Pig Stereocilia damage (120 dB damage (120 dB sound)sound)
The Overall Hearing ProcessThe Overall Hearing Process Sound is created at the source.Sound is created at the source. It travels through the air.It travels through the air. It is collected by various parts of the It is collected by various parts of the
ear (semi-resonance).ear (semi-resonance). The tympanic membrane moves with The tympanic membrane moves with
the pressure variations.the pressure variations. The inner ear filters/amplifies the The inner ear filters/amplifies the
sound.sound.
Hearing ContinuedHearing Continued The sound hits the membrane at the The sound hits the membrane at the
entrance to the cochlea.entrance to the cochlea. The pressure on the basilar membrane The pressure on the basilar membrane
causes it to mive up and down.causes it to mive up and down. The resonant frequency of the The resonant frequency of the
membrane varies with position so that membrane varies with position so that for each frequency only one place on for each frequency only one place on the membrane is resonating. the membrane is resonating.
Some more on hearingSome more on hearing There are hair cells along the basilar There are hair cells along the basilar
membrane which move with the membrane.membrane which move with the membrane. The motion of the hair cells creates an The motion of the hair cells creates an
electrical (ionic) disturbance which is wired electrical (ionic) disturbance which is wired to the brain.to the brain.
The disturbance is in the form of pulses.The disturbance is in the form of pulses. The brain somehow relates the number of The brain somehow relates the number of
pulse firings per second to tone and ..pulse firings per second to tone and .. Wallah … music!Wallah … music!
Next Stop – Room AcousticsNext Stop – Room Acoustics
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