Physics 1251 The Science and Technology of Musical Sound

1
Physics 1251The Science and Technology of
Musical Sound

• Unit 2
• Session 13 MWF
• Sound Intensity Level and dB

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Foolscap Quiz
• What organ, located in the inner ear, is
  responsible for transforming mechanical
  vibrations into neural impulses? How does it
  discriminate different pitches?

The Cochlea. Different places on the Basilar
Membrane are excited by different frequencies as
revealed by the Nobel-prize-winning work of
Bekesy.
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Anatomy of Ear

Middle Ear
Outer Ear
Inner Ear
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Cochlea
• (micrograph)
• The Snail
• o oval window
• r round window

2 mm
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Structure of Cochlea
• 1. Spiral cone
• 2. Divided by
• Basilar Membrane
• 3. In on top half
• 4. Out on bottom
• 5. Sloshing

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Microstructure
• of Cochlea

Basilar ? Membrane
? Organ of Corti
?
Auditory Nerve ? ?
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Detail of Hair Cell
• N.B. (Nota Bene)
• Hair cells have nothingto do with hair that
  grows in the skin.
• HC s are vibration senseorgans.

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Outer Hair Cell in Cross Section

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Cilia Displacement vs
• Location on Basilar Membrane
• 2800 Hz

Relative Response
Position
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Cilia Displacement vs
• Location on Basilar Membrane
• 400 Hz

Relative Response
Position
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Peak Frequency of Response vs
• Location on Basilar Membrane

f Hz
Distance from Stapes (cm)
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Georg von Békésy
• (1899-1972)
• 1961 Nobel Prize in
• Medicine
• Demonstrated resonance
• of Basilar Membrane

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• 1' Lecture
• The objective relative intensity level of sound
  is quantified as the Sound Intensity Level (SIL)
  and is measured in deciBel (dB), where
• SIL 10 Log( I / Ithreshold ) .

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• 80/20The Intensity of a sound wave is the energy
  radiated per unit time per unit area. W/m2

FYI Time Averaged Intensity lt I gt lt I gt 0.0012
pmax2 For air, with p Pa and I
W/m2 lt I gt lt p ? udisplacement gt ½
pmax2/ ?v
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Resonant Frequency vs
• Location on Basilar Membrane

20 kHz
Range of Maximum Sensitivity
20 Hz
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• 80/20The frequency range of detectability for
  humans is approximately 20 Hz to
• 20 kHz.
• 80/20Humans are most sensitive in the frequency
  range 2 kHz to 5 kHz.

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• 80/20The lowest detectable intensity (the
  threshold of hearing Ithreshold ) is about
  1 pW/m 2 or 1x10 -12 W/m 2 .
• 80/20The intensity at which one experiences pain
  (the threshold of pain) is about 1 W/m
  2 .

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Hair Cell (Stereocilium) is a Neuron

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Hair Cell (Stereocilium) is a Neuron

• Neuron has threshold for simulation
• Neuron fires (is either on or off)
• Firing Neurons inhibit neighbors

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Consequence Threshold
• and Non-linear Response

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Neuronal Response of Hair Cells

Hair Cells in the Basilar Membrane
Neuron fires and neighbors are inhibited
Larger
No increased response
Stimulus
No response
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Neuronal Response of Hair Cells

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Consequence Threshold
• and Non-linear Response

Threshold of Pain1 Watt/m2
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Logarithm of Stimulus vs Response

SIL 10 Log( I/Ithreshold)
Response
Log (Stimulus/ Ithreshold )
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Mathematical Digression ? Peligro ?
• ? Danger ? Logarithms Log(N)
• ? Lebensgefahr ? ? Attention

Logarithm ratio arithmetic Log (x) L,such
that 10 L x.

• The power of 10 that will produce a number x
  when 10 is raised to that power is called the
  Logarithm (on the base 10) of the number.

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• The LOG(x) Function

Log(10) 1
Log(9) 0.95
Log(8) 0.90
Log(7) 0.85
Log(6) 0.78
Log(5) 0.70
Log(4) 0.60
Log(3) 0.48
Log(2) 0.30
Log(1) 0
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Some Useful Facts about Logarithms
• Log( x ? y) Log (x) Log (y)
• Log( x / y) Log (x) Log (y)
• Log( x p) p Log ( x )
• Thus, in scientific notation
• Log ( z ? 10 n) Log ( z ) n

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• 80/20Sound Intensity Level
• SIL 10 Log ( I / I threshold ).
• The Sound Intensity Level is 10 times the
  logarithm of the ratio of the intensity of a
  sound and the threshold of hearing.
• The units of SIL are deciBel or dB.
• I I threshold 10 SIL/10

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• 80/20Just Noticeable Difference (JND) is the
  limen of difference that elicits 75 correct
  answers in a Two Alternative Forced-Choice test
  (2AFC test).

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Why 75?
• In 2 Alternative Forced Choice
• 50 correct means random choice
• 100 means can always tell the difference.
• Thus, 75 is halfway between random and certainty.

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• 80/20Just Noticeable Difference (JND) is the
  limen of difference that elicits 75 in a Two
  Alternative Forced-Choice test (2AFC test).

The limen of intensity is a ratio of about 1.26
which corresponds to a SIL difference of 1
dB. 10 Log( 1.26 ) 1.0
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Calculator Practice
• Log( 1)
• Log( 10 )
• Log( 100 )
• Log( 2 )
• Log( 20 )
• Log( 200 )

0
1
2
0.301
1.301
2.301
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Calculator Practice
• SIL
• 10 Log( 1)
• 10 Log( 10 )
• 10 Log( 100 )
• 10 Log( 2 )
• 10 Log( 20 )
• 10 Log( 200 )

0 dB
10 dB
20 dB
3.0 dB
13.0 dB
23.0 dB
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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Musical Dynamics
• Pianissimo pp very soft 50 dB
• Piano p soft 60 dB
• Mezzopiano mp medium soft 66 dB
• Mezzoforte mf medium loud 76 dB
• Forte f loud 80 dB
• Fortissimo ff very loud 90 dB
• Fortississimo fff Very, very loud 100 dB

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• The Mob Chorus
• Rhubard!
• Donnybrook!
• Dust up!

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Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Musical Dynamics
• Pianissimo pp very soft 50 dB
• Piano p soft 60 dB
• Mezzopiano mp medium soft 66 dB
• Mezzoforte mf medium loud 76 dB
• Forte f loud 80 dB
• Fortissimo ff very loud 90 dB
• Fortississimo fff Very, very loud 100 dB

37
Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Musical Dynamics
• Pianissimo pp very soft 50 dB
• Piano p soft 60 dB
• Mezzopiano mp medium soft 66 dB
• Mezzoforte mf medium loud 76 dB
• Forte f loud 80 dB
• Fortissimo ff very loud 90 dB
• Fortississimo fff Very, very loud 100 dB

38
Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Musical Dynamics
• Pianissimo pp very soft 50 dB
• Piano p soft 60 dB
• Mezzopiano mp medium soft 66 dB
• Mezzoforte mf medium loud 76 dB
• Forte f loud 80 dB
• Fortissimo ff very loud 90 dB
• Fortississimo fff Very, very loud 100 dB

39
Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Musical Dynamics
• Pianissimo pp very soft 50 dB
• Piano p soft 60 dB
• Mezzopiano mp medium soft 66 dB
• Mezzoforte mf medium loud 76 dB
• Forte f loud 80 dB
• Fortissimo ff very loud 90 dB
• Fortississimo fff Very, very loud 100 dB

40
Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Musical Dynamics
• Pianissimo pp very soft 50 dB
• Piano p soft 60 dB
• Mezzopiano mp medium soft 66 dB
• Mezzoforte mf medium loud 76 dB
• Forte f loud 80 dB
• Fortissimo ff very loud 90 dB
• Fortississimo fff Very, very loud 100 dB

41
Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Musical Dynamics
• Pianissimo pp very soft 50 dB
• Piano p soft 60 dB
• Mezzopiano mp medium soft 66 dB
• Mezzoforte mf medium loud 76 dB
• Forte f loud 80 dB
• Fortissimo ff very loud 90 dB
• Fortississimo fff Very, very loud 100 dB

42
Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Musical Dynamics
• Pianissimo pp very soft 50 dB
• Piano p soft 60 dB
• Mezzopiano mp medium soft 66 dB
• Mezzoforte mf medium loud 76 dB
• Forte f loud 80 dB
• Fortissimo ff very loud 90 dB
• Fortississimo fff Very,very loud 100 dB

43
Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB

• Summary
• The objective sound level is measuredby SIL in
  dB.
• SIL 10 Log (I /Ithreshold) .
• 0 dB corresponds to an intensity of 1 pW/m2.
• The threshold of pain is 120 dB.