Sound Levels

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Lecture 18

• Sound Levels
• November 1, 2004

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Make Sure that you VOTE!!!
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Whutshappenin?

• Examinations have been graded and returned.
• Next exam is in THREE WEEKS!!!
• Then, only one week of lectures followed by the
  FINAL EXAMINATION
• There will be NO make-up exam for the final.
• The only acceptable reason for missing the exam
  is that you are dead or almost dead.

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SCHEDULE REMAINING
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
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More Schedule
Week 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
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ENERGY PER UNIT TIME
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Recall
ENERGY

• Same energy (and power) goes through surface (1)
  as through surface (2)
• Sphere area increases with r2 (A4pr2)
• Power level DECREASES with distance from the
  source of the sound.
• Goes as (1/r2)

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To the ear .
Area of Sphere pr2 3.14 x 50 x 50 7850 m2
50m
Ear Area 0.000025 m2
30 watt
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Continuing
Scientific Notation 9.5 x 10-8
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Huh??
Move the decimal point over by 8 places.
Scientific Notation 9.5 x 10-8
Another example 6,326,8656.3 x 106
Move decimal point to the LEFT by 6 places.
REFERENCE See the Appendix in the Johnston
Test and Bolemon, page 17.
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Scientific NotationChapter 1 in Bolemon,
Appendix 2 in Johnston
0.000000095 watts 9.5 x 10-8 watts
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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.

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Decibel continued (dB)
?
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What the is a logarithm?

• Bindells 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
10 log (P2/P1)

• The dB is proportional to the LOG10 of a ratio of
  intensities.
• Lets take P1Threshold Level of Hearing which is
  10-12 watts/m2
• Take P2PThe power level we are interested in.

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An example

• The threshold of pain is 1 w/m2

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Another Example
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Look at the dB Column
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DAMAGE TO EAR
Continuous 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 (lt 4min)    109 dB                 
           1.875 min (lt 2min)    112 dB         
                    .9375 min (1 min)    115
dB                              .46875 min (30
sec)
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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 logarithmetically!
• 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 .

We hear Logarithmetically
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Lets 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!
How Loud is this "Symphony"?
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Start at the beginning

• Remember those logarithms?
• Take the number 1000000106
• The log of this number is the number of zeros or
  is equal to 6.
• Lets multiply the number by 1000103
• New number 106 x 103109
• The exponent of these numbers is the log.
• The log of A (106)xB(103)log A log B

6 3
9
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Remember the definition
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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.

A 10 increase in dB!
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Lets think about sizes of things.

• Music is primarily between 50 and 5000 Hz.
• Look at the table

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v344 m/s v344 m/s v344 m/s
frequency 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 ltsize of head
5000 0.0688 size of pinna
10000 0.0344 length of ear canal
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E A R
Helmholtz Resonartor
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C R O S S - S E C T I O N
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The Ear Spread Out
Fluid
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The Cochlea
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The Cochlea Unwound
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The Cochlea Schematic
Frequency Info
Low Frequency
High Frequency
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Resonance in the Basilar Membrane(Computed)
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The Hair Cells
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Simplified Version
Resonance !!
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Damage from very LOUD noises.

• Extreme Acoustic Trauma

Guinea Pig Stereocilia damage (120 dB sound)
Control, not exposed
After Exposure
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The Overall Hearing Process

• Sound is created at the source.
• It travels through the air.
• It is collected by various parts of the ear
  (semi-resonance).
• The tympanic membrane moves with the pressure
  variations.
• The inner ear filters/amplifies the sound.

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Hearing Continued

• The sound hits the membrane at the entrance to
  the cochlea.
• The pressure on the basilar membrane causes it to
  mive up and down.
• The resonant frequency of the membrane varies
  with position so that for each frequency only one
  place on the membrane is resonating.

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Some more on hearing

• There are hair cells along the basilar membrane
  which move with the membrane.
• The motion of the hair cells creates an
  electrical (ionic) disturbance which is wired to
  the brain.
• The disturbance is in the form of pulses.
• The brain somehow relates the number of pulse
  firings per second to tone and ..
• Wallah music!

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Next Stop Room Acoustics