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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:

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physics 1251 the science and technology of musical sound

Physics 1251The 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
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.

physics 1251 unit 2 session 13 sound intensity level and db1
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 db2
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 db3
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 db4
Physics 1251 Unit 2 Session 13 Sound Intensity Level and dB

Microstructure

of Cochlea

Basilar ——————→

Membrane

Organ of Corti

Auditory Nerve → →

physics 1251 unit 2 session 13 sound intensity level and db5
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.

physics 1251 unit 2 session 13 sound intensity level and db7
Physics 1251 Unit 2 Session 13 Sound Intensity Level and dB

Cilia Displacement vs

Location on Basilar Membrane

2800 Hz

Relative Response

Position

physics 1251 unit 2 session 13 sound intensity level and db8
Physics 1251 Unit 2 Session 13 Sound Intensity Level and dB

Cilia Displacement vs

Location on Basilar Membrane

400 Hz

Relative Response

Position

physics 1251 unit 2 session 13 sound intensity level and db9
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 db10
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 db11
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 db12
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 db13
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 db14
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 db15
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 db16
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 db17
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 db18

Response (sensation)

Threshold of Hearing 10 -12 Watt/m2

Desensitization with greater stimulus

Stimulus (Intensity)

Physics 1251 Unit 2 Session 13 Sound Intensity Level and dB

Consequence: Threshold

and Non-linear Response

physics 1251 unit 2 session 13 sound intensity level and db19
Physics 1251 Unit 2 Session 13 Sound Intensity Level and dB

Hair Cells in the Basilar Membrane

Neuronal Response of Hair Cells

Neuron fires and neighbors are inhibited

Larger

No increased response

Stimulus

No response

physics 1251 unit 2 session 13 sound intensity level and db20

No larger response because of inhibition

Attenuated response to much larger stimulus

Physics 1251 Unit 2 Session 13 Sound Intensity Level and dB

Neuronal Response of Hair Cells

physics 1251 unit 2 session 13 sound intensity level and db21

Response (sensation)

Stimulus (Intensity)

Physics 1251 Unit 2 Session 13 Sound Intensity Level and dB

Consequence: Threshold

and Non-linear Response

Threshold of Pain1 Watt/m2

physics 1251 unit 2 session 13 sound intensity level and db22

130

120

110

100

Ithreshold = 10 -12 W/m2

90

70

60

50

40

30

20

10

0

0

1

2

3

4

5

6

7

8

9

10

11

12

13

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 )

physics 1251 unit 2 session 13 sound intensity level and db23
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 db24

1.0

.9

.8

Log(x)

.7

.6

.5

.4

.3

.2

.1

0

0

1

2

3

4

5

6

7

8

9

10

x

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

physics 1251 unit 2 session 13 sound intensity level and db25
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 unit 2 session 13 sound intensity level and db26
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

physics 1251 unit 2 session 13 sound intensity level and db27
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).

physics 1251 unit 2 session 13 sound intensity level and db28
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 db29
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 db30
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 db31
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 db32
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

physics 1251 unit 2 session 13 sound intensity level and db33
Physics 1251 Unit 2 Session 13 Sound Intensity Level and dB

The Mob Chorus:

  • “Rhubard!”
  • “Donnybrook!”
  • “Dust up!”
physics 1251 unit 2 session 13 sound intensity level and db34
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

physics 1251 unit 2 session 13 sound intensity level and db35
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

physics 1251 unit 2 session 13 sound intensity level and db36
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

physics 1251 unit 2 session 13 sound intensity level and db37
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

physics 1251 unit 2 session 13 sound intensity level and db38
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

physics 1251 unit 2 session 13 sound intensity level and db39
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

physics 1251 unit 2 session 13 sound intensity level and db40
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

physics 1251 unit 2 session 13 sound intensity level and db41
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.
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