Transcript Physics 1251 The Science and Technology of Musical Sound

Physics 1251
The Science and Technology
of Musical Sound
Unit 2
Session 13 MWF
Sound Intensity Level and dB
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-prizewinning work of Bekesy.
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Anatomy of Ear
Middle Ear
Outer Ear
Inner Ear
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Cochlea
(micrograph)
“The Snail”
•
•
o~ oval window
r~ round window
2 mm
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 “
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Microstructure
of Cochlea
Basilar
——————→
↑
Membrane
Organ of
↑
Auditory Nerve → →
Corti
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Detail of Hair Cell
N.B. (Nota Bene):
Hair cells have nothing
to do with hair that
grows in the skin.
HC s are vibration sense
organs.
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Outer Hair Cell in Cross Section
Physics 1251
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Sound Intensity Level and dB
Relative Response
Cilia Displacement vs
Location on Basilar Membrane
Position
2800 Hz
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Relative Response
Cilia Displacement vs
Location on Basilar Membrane
Position
400 Hz
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)
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
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 ) .
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 < I >
< I > = 0.0012 pmax2
For air, with [ p ] = [Pa] and [ I ] = [W/m2]
< I >= < p ‧ udisplacement >
= ½ pmax2/ ρv
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
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.
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 .
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Hair Cell (Stereocilium) is a Neuron
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
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Response (sensation)
Consequence: Threshold
and Non-linear Response
Threshold of Hearing
10 -12 Watt/m2
Desensitization with
greater stimulus
Stimulus (Intensity)
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Neuronal Response of Hair Cells
Hair Cells
in the Basilar Membrane
Larger
Stimulus
Neuron fires and
neighbors are
inhibited
No increased
No response
response
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Neuronal Response of Hair Cells
No larger response
Attenuated response to
because of
much larger
inhibition
stimulus
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Response (sensation)
Consequence: Threshold
and Non-linear Response
Threshold of Pain
1 Watt/m2
Stimulus (Intensity)
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Response
Logarithm of Stimulus vs Response
130
SIL = 10 Log( I/Ithreshold)
120
110
100
90 Ithreshold = 10 -12 W/m2
70
60
50
40
30
20
10
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Log (Stimulus/ Ithreshold )
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.
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Log(x)
The “LOG(x)” Function
1.0
.9
.8
.7
.6
.5
.4
.3
.2
.1
0
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
0
1
2
3
4
5
x
6
7
8
9
10
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
Physics 1251
80/20Sound
Unit 2 Session 13
Sound Intensity Level and dB
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
Physics 1251
80/20Just
Unit 2 Session 13
Sound Intensity Level and dB
Noticeable Difference (JND) is the
limen of difference that elicits 75%
correct answers in a Two Alternative
Forced-Choice test (2AFC test).
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.
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
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
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
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Musical Dynamics
Pianissimo:
Piano:
Mezzopiano:
Mezzoforte:
Forte:
Fortissimo:
Fortississimo:
pp
p
mp
mf
f
ff
fff
very soft:
soft:
medium soft:
medium loud:
loud:
very loud:
Very, very loud:
50 dB
60 dB
66 dB
76 dB
80 dB
90 dB
100 dB
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
The Mob Chorus:
1.
2.
3.
“Rhubard!”
“Donnybrook!”
“Dust up!”
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Musical Dynamics
Pianissimo:
pp
very soft:
50 dB
Piano:
Mezzopiano:
Mezzoforte:
Forte:
Fortissimo:
Fortississimo:
p
mp
mf
f
ff
fff
soft:
medium soft:
medium loud:
loud:
very loud:
Very, very loud:
60 dB
66 dB
76 dB
80 dB
90 dB
100 dB
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:
Mezzoforte:
Forte:
Fortissimo:
Fortississimo:
mp
mf
f
ff
fff
medium soft:
medium loud:
loud:
very loud:
Very, very loud:
66 dB
76 dB
80 dB
90 dB
100 dB
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Musical Dynamics
Pianissimo:
Piano:
pp
p
very soft:
soft:
50 dB
60 dB
Mezzopiano:
mp
medium soft: 66 dB
Mezzoforte:
Forte:
Fortissimo:
Fortississimo:
mf
f
ff
fff
medium loud:
loud:
very loud:
Very, very loud:
76 dB
80 dB
90 dB
100 dB
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Musical Dynamics
Pianissimo:
Piano:
Mezzopiano:
pp
p
mp
very soft:
soft:
medium soft:
50 dB
60 dB
66 dB
Mezzoforte:
mf
medium loud: 76 dB
Forte:
Fortissimo:
Fortississimo:
f
ff
fff
loud:
80 dB
very loud:
90 dB
Very, very loud: 100 dB
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Musical Dynamics
Pianissimo:
Piano:
Mezzopiano:
Mezzoforte:
pp
p
mp
mf
very soft:
soft:
medium soft:
medium loud:
50 dB
60 dB
66 dB
76 dB
Forte:
f
loud:
80 dB
Fortissimo:
Fortississimo:
ff
fff
very loud:
90 dB
Very, very loud: 100 dB
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Musical Dynamics
Pianissimo:
Piano:
Mezzopiano:
Mezzoforte:
Forte:
pp
p
mp
mf
f
very soft:
soft:
medium soft:
medium loud:
loud:
50 dB
60 dB
66 dB
76 dB
80 dB
Fortissimo:
ff
very loud:
90 dB
Fortississimo:
fff
Very, very loud: 100 dB
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Musical Dynamics
Pianissimo:
Piano:
Mezzopiano:
Mezzoforte:
Forte:
Fortissimo:
pp
p
mp
mf
f
ff
very soft:
soft:
medium soft:
medium loud:
loud:
very loud:
50 dB
60 dB
66 dB
76 dB
80 dB
90 dB
Fortississimo:
fff
Very,very loud:100 dB
Physics 1251
Unit 2 Session 13
Sound Intensity Level and dB
Summary:
•
The objective sound level is measured
by 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.