Title: Physics 1251 The Science and Technology of Musical Sound
1Physics 1251The Science and Technology of
Musical Sound
- Unit 2
- Session 13 MWF
- Sound Intensity Level and dB
2Physics 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.
3Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB
Middle Ear
Outer Ear
Inner Ear
4Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB
- Cochlea
- (micrograph)
- The Snail
- o oval window
- r round window
2 mm
5Physics 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
6Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB
- Microstructure
- of Cochlea
Basilar ? Membrane
? Organ of Corti
?
Auditory Nerve ? ?
7Physics 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.
8Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB
- Outer Hair Cell in Cross Section
9Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB
- Cilia Displacement vs
- Location on Basilar Membrane
- 2800 Hz
Relative Response
Position
10Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB
- Cilia Displacement vs
- Location on Basilar Membrane
- 400 Hz
Relative Response
Position
11Physics 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)
12Physics 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
13Physics 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 ) .
14Physics 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
15Physics 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
16Physics 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.
17Physics 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 .
18Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB
- Hair Cell (Stereocilium) is a Neuron
19Physics 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
20Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB
- Consequence Threshold
- and Non-linear Response
21Physics 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
22Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB
- Neuronal Response of Hair Cells
23Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB
- Consequence Threshold
- and Non-linear Response
Threshold of Pain1 Watt/m2
24Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB
- Logarithm of Stimulus vs Response
SIL 10 Log( I/Ithreshold)
Response
Log (Stimulus/ Ithreshold )
25Physics 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.
26Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB
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
27Physics 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
28Physics 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
29Physics 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).
30Physics 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.
31Physics 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
32Physics 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
33Physics 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
34Physics 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
35Physics 1251 Unit 2 Session 13 Sound Intensity
Level and dB
- The Mob Chorus
- Rhubard!
- Donnybrook!
- Dust up!
36Physics 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
37Physics 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
38Physics 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
39Physics 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
40Physics 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
41Physics 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
42Physics 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
43Physics 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.