Physics 1251 The Science and Technology of Musical Sound Unit 2 Session 13 MWF Sound Intensity Level...

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Unit 2Unit 2

Session 13 MWFSession 13 MWF

Sound Intensity Level Sound Intensity Level and dBand dB

Unit 2Unit 2

Session 13 MWFSession 13 MWF

Sound Intensity Level Sound Intensity Level and dBand dB

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

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

The Cochlea. Different places on theThe Cochlea. Different places on the Basilar Membrane Basilar Membrane are excited by are excited by different frequencies as revealed by different frequencies as revealed by the Nobel-prize-winning work of the Nobel-prize-winning work of Bekesy.Bekesy.


Anatomy of EarAnatomy of Ear

Outer Outer EarEar

Middle Middle EarEar

Inner Inner EarEar


CCochleaochlea(micrograph)(micrograph)““The SnThe Snail”ail”

• o~ oval windowo~ oval window• r~ round windowr~ round window

2 mm2 mm


Structure of CochleaStructure of Cochlea

1. Spiral cone1. Spiral cone

2. Divided by 2. Divided by Basilar Basilar Membrane Membrane

3. In on top half3. In on top half

4. Out on bottom4. Out on bottom

5. “Sloshing “5. “Sloshing “


Microstructure Microstructure

of Cochleaof Cochlea

Basilar Basilar ——————→ ——————→ MembraneMembrane

↑↑

Organ of Organ of CortiCortiAuditory Nerve Auditory Nerve → →

→→

↑↑


Detail of Hair CellDetail of Hair CellN.B. (Nota Bene):N.B. (Nota Bene):

Hair cells have nothingHair cells have nothingto do with hair that to do with hair that grows in the skin.grows in the skin.

HC s are vibration senseHC s are vibration senseorgans.organs.


Outer Hair Cell in Cross SectionOuter Hair Cell in Cross Section


Cilia Displacement vs Cilia Displacement vs Location on Basilar Location on Basilar

MembraneMembrane

2800 Hz2800 Hz

PositionPosition

Rela

tive

Rela

tive

Resp

on

se

Resp

on

se


Cilia Displacement vs Cilia Displacement vs Location on Basilar Location on Basilar

MembraneMembrane

400 Hz400 Hz

PositionPosition

Rela

tive

Rela

tive

Resp

on

se

Resp

on

se


Peak Frequency of Response vsPeak Frequency of Response vs

Location on Basilar MembraneLocation on Basilar Membrane

Distance from Stapes (cm)Distance from Stapes (cm)

f f [Hz][Hz]


Georg von BGeorg von Béékkéésysy

(1899-1972)(1899-1972)

1961 Nobel Prize in 1961 Nobel Prize in

MedicineMedicine

Demonstrated resonance Demonstrated resonance

of Basilar Membraneof Basilar Membrane


11′ Lecture:′ Lecture:

The objective relative intensity The objective relative intensity level of sound is quantified as level of sound is quantified as the Sound Intensity Level (SIL) the Sound Intensity Level (SIL) and is measured in deciBel and is measured in deciBel (dB), where(dB), where

SIL = 10 Log( I / ISIL = 10 Log( I / Ithreshold threshold ) .) .

80/2080/20The The IntensityIntensity of a sound wave is the of a sound wave is the energy radiated per unit time per unit energy radiated per unit time per unit area. [W/marea. [W/m22]]

FYI: Time Averaged Intensity FYI: Time Averaged Intensity 

 = 0.0012 p = 0.0012 pmaxmax22

For air, with [ p ] = [Pa] and [ I ] = [W/mFor air, with [ p ] = [Pa] and [ I ] = [W/m22]]

= < p= >

= ½ = ½ ppmaxmax22/ / ρvρv


““Resonant” Frequency vsResonant” Frequency vs

Location on Basilar Location on Basilar MembraneMembrane

20 kHz20 kHz

20 20 HzHz

Range of Range of Maximum Maximum SensitivitySensitivity


80/2080/20The frequency range of The frequency range of detectability for humans is detectability for humans is approximately 20 Hz to approximately 20 Hz to

20 kHz.20 kHz.

80/2080/20Humans are most sensitive in the Humans are most sensitive in the frequency range 2 kHz to 5 kHz. frequency range 2 kHz to 5 kHz.


80/2080/20The lowest detectable intensity The lowest detectable intensity (the threshold of hearing I(the threshold of hearing Ithresholdthreshold ) is ) is about 1 pW/m about 1 pW/m 22 or 1x10 or 1x10 -12-12 W/m W/m 22 . .

80/2080/20The intensity at which one The intensity at which one experiences pain (the threshold of experiences pain (the threshold of pain) is about 1 W/m pain) is about 1 W/m 22 . .


Hair Cell (Stereocilium) is a Hair Cell (Stereocilium) is a NeuronNeuron


Hair Cell (Stereocilium) is a Hair Cell (Stereocilium) is a NeuronNeuron

• Neuron has threshold Neuron has threshold for simulationfor simulation

• Neuron “fires” (is Neuron “fires” (is either on or off)either on or off)

•Firing Neurons inhibit Firing Neurons inhibit neighborsneighbors


Consequence: Threshold Consequence: Threshold

and Non-linear Responseand Non-linear Response

Stimulus (Intensity)Stimulus (Intensity)Resp

on

se (

sen

sati

on

)R

esp

on

se (

sen

sati

on

)

Threshold of Threshold of Hearing Hearing 10 10 -12-12 Watt/m Watt/m22

Desensitization Desensitization with greater with greater stimulusstimulus


Neuronal Response of Hair CellsNeuronal Response of Hair Cells

Hair Cells Hair Cells in the Basilar Membranein the Basilar Membrane

StimulusStimulus No responseNo responseLargerLarger

Neuron fires and Neuron fires and neighbors are neighbors are inhibitedinhibited

No increased No increased responseresponse


Neuronal Response of Hair CellsNeuronal Response of Hair Cells

No larger responseNo larger responsebecause ofbecause of

inhibition inhibition

Attenuated Attenuated response to response to much larger much larger

stimulusstimulus


Consequence: Threshold Consequence: Threshold

and Non-linear Responseand Non-linear Response

Stimulus (Intensity)Stimulus (Intensity)Resp

on

se (

sen

sati

on

)R

esp

on

se (

sen

sati

on

)

Threshold of Threshold of PainPain1 Watt/m1 Watt/m22


Logarithm of Stimulus vs ResponseLogarithm of Stimulus vs Response

Log (Stimulus/ Log (Stimulus/ IIthreshold threshold ))

Resp

on

se

Resp

on

se

20

70

110

010

30405060

90100

120130

3 6 90 1 2 4 5 7 8 10 11 12 13

SIL = 10 Log( SIL = 10 Log( I/II/Ithresholdthreshold))

IIthreshold threshold = 10 = 10 -12-12

W/mW/m22


Mathematical Digression Mathematical Digression ☠ ☠ PeligroPeligro ☠ ☠

☠☠ Danger Danger ☠☠ Logarithms Logarithms Log(N)Log(N)

☠ ☠ Lebensgefahr Lebensgefahr ☠ ☠ ☠ ☠ Attention Attention

Logarithm = “ratio arithmetic”Logarithm = “ratio arithmetic”

Log (x) = L,Log (x) = L,such that 10 such that 10 L L = x.= x.

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


The “LOG(x)” FunctionThe “LOG(x)” Function

Log(1) =0

Log(2) =0.30

Log(3) =0.48Log(4) =0.60

Log(5) =0.70Log(6) =0.78Log(7) =0.85

Log(8) =0.90Log(9) =0.95Log(10) =1

3 6 90 1 2 4 5 7 8 10

.3

.6

.9

0.1.2

.4

.5

.7

.8

1.0

xx

Log

(x)

Log

(x)


Some Useful Facts about Logarithms:Some Useful Facts about Logarithms:

Log( x Log( x ‧ y) = Log (x) + Log (y)‧ y) = Log (x) + Log (y)

Log( x / y) = Log (x) – Log (y)Log( x / y) = Log (x) – Log (y)

Log( x Log( x pp) = p Log ( x )) = p Log ( x )

Thus, in scientific notation:Thus, in scientific notation:

Log ( z Log ( z ‧ ‧ 10 10 nn) = Log ( z ) + n) = Log ( z ) + n


80/2080/20Sound Intensity Level:Sound Intensity Level:

SIL = 10 Log ( I / I SIL = 10 Log ( I / I threshold threshold ).).

The Sound Intensity Level is 10 times The Sound Intensity Level is 10 times the logarithm of the ratio of the the logarithm of the ratio of the intensity of a sound and the threshold intensity of a sound and the threshold of hearing.of hearing.

The units of SIL are deciBel or dB.The units of SIL are deciBel or dB.

I = I = I I threshold threshold 10 10 SIL/10SIL/10


80/2080/20Just Noticeable Difference (JND) is Just Noticeable Difference (JND) is the the limenlimen of difference that elicits of difference that elicits 75% correct answers in a Two 75% correct answers in a Two Alternative Forced-Choice test Alternative Forced-Choice test (2AFC test).(2AFC test).


Why 75%?Why 75%?

In 2 Alternative Forced Choice:In 2 Alternative Forced Choice:• 50% correct means random choice50% correct means random choice• 100% means can always tell the 100% means can always tell the

difference.difference.

• Thus, 75% is halfway between random Thus, 75% is halfway between random and certainty.and certainty.


80/2080/20Just Noticeable Difference (JND) is Just Noticeable Difference (JND) is the the limenlimen of difference that elicits of difference that elicits 75% in a Two Alternative Forced-75% in a Two Alternative Forced-Choice test (2AFC test).Choice test (2AFC test).

The limen of intensity is a ratio of about The limen of intensity is a ratio of about 1.26 which corresponds to a SIL difference 1.26 which corresponds to a SIL difference of 1 dB.of 1 dB.

10 Log( 1.26 ) = 1.010 Log( 1.26 ) = 1.0


Calculator Practice:Calculator Practice:

Log( 1) = Log( 1) =

Log( 10 ) = Log( 10 ) =

Log( 100 ) = Log( 100 ) =

Log( 2 ) =Log( 2 ) =

Log( 20 ) = Log( 20 ) =

Log( 200 ) =Log( 200 ) =

11

22

0.3010.3011.3011.301

2.3012.301

00


Calculator Practice:Calculator Practice:

SIL:SIL:

10 Log( 1) = 10 Log( 1) =

10 Log( 10 ) = 10 Log( 10 ) =

10 Log( 100 ) = 10 Log( 100 ) =

10 Log( 2 ) =10 Log( 2 ) =

10 Log( 20 ) = 10 Log( 20 ) =

10 Log( 200 ) =10 Log( 200 ) =

10 dB10 dB

20 dB20 dB

3.0 dB3.0 dB13.0 13.0 dBdB23.0 23.0 dBdB

0 dB0 dB


Musical DynamicsMusical Dynamics

Pianissimo:Pianissimo: pppp very soft:very soft: 50 dB50 dB

Piano:Piano: pp soft:soft: 60 dB60 dB

Mezzopiano:Mezzopiano: mpmp medium soft: medium soft: 66 dB66 dB

Mezzoforte:Mezzoforte: mfmf medium loud:medium loud: 76 dB76 dB

Forte:Forte: ff loud:loud: 80 dB80 dB

Fortissimo:Fortissimo: ffff very loud:very loud: 90 dB90 dB

Fortississimo:Fortississimo: ffffff Very, very loud:Very, very loud: 100 dB 100 dB


The Mob Chorus:The Mob Chorus:

1.1. ““Rhubard!”Rhubard!”

2.2. ““Donnybrook!”Donnybrook!”

3.3. ““Dust up!”Dust up!”



Pianissimo:Pianissimo: pppp very soft:very soft: 50 dB50 dBPiano:Piano: pp soft:soft: 60 dB60 dB









Piano:Piano: pp soft:soft: 60 dB60 dBMezzopiano:Mezzopiano: mpmp medium soft: medium soft: 66 dB66 dB









Mezzopiano:Mezzopiano: mpmp medium soft: medium soft: 66 dB66 dBMezzoforte:Mezzoforte: mfmf medium loud:medium loud: 76 dB76 dB









Mezzoforte:Mezzoforte: mfmf medium loud:medium loud: 76 dB76 dBForte:Forte: ff loud:loud: 80 dB80 dB









Forte:Forte: ff loud:loud: 80 dB80 dBFortissimo:Fortissimo: ffff very loud:very loud: 90 dB90 dB









Fortissimo:Fortissimo: ffff very loud:very loud: 90 dB90 dBFortississimo:Fortississimo: ffffff Very, very loud:Very, very loud: 100 dB 100 dB









Fortississimo:Fortississimo: ffffff Very,very loud:Very,very loud:100 dB100 dB


Summary:Summary:• The objective sound level is measuredThe objective sound level is measured

by SIL in dB.by SIL in dB.

• SIL = 10 Log (I /ISIL = 10 Log (I /Ithresholdthreshold) .) .

• 0 dB corresponds to an intensity of 1 0 dB corresponds to an intensity of 1 pW/mpW/m22..

• The threshold of pain is 120 dB.The threshold of pain is 120 dB.

Physics 1251 The Science and Technology of Musical Sound Unit 2 Session 13 MWF Sound Intensity Level...

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