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

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

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB C ochlea (micrograph) “The Sn ail” o~ oval window o~ oval window r~ round window r~ round window 2 mm

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB Structure of Cochlea 1. Spiral cone 2. Divided by Basilar Membrane Basilar Membrane 3. In on top half 4. Out on bottom 5. “Sloshing “

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB Microstructure of Cochlea Basilar ——————→ Membrane ↑ Organ of Corti Auditory Nerve → → ↑

Physics 1251Unit 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 1251Unit 2 Session 13 Sound Intensity Level and dB Outer Hair Cell in Cross Section

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB Cilia Displacement vs Location on Basilar Membrane 2800 Hz Position Relative Response

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB Cilia Displacement vs Location on Basilar Membrane 400 Hz Position Relative Response

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB Peak Frequency of Response vs Location on Basilar Membrane Distance from Stapes (cm) f [Hz]

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB Georg von Békésy ( ) 1961 Nobel Prize in Medicine Demonstrated resonance of Basilar Membrane

Physics 1251Unit 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 / I threshold ).

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB 80/20 The Intensity of a sound wave is the energy radiated per unit time per unit area. [W/m 2 ] FYI: Time Averaged Intensity FYI: Time Averaged Intensity = p max 2 = p max 2 For air, with [ p ] = [Pa] and [ I ] = [W/m 2 ] = = = ½ p max 2 / ρv

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB “Resonant” Frequency vs Location on Basilar Membrane 20 kHz 20 Hz Range of Maximum Sensitivity

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB 80/20 The frequency range of detectability for humans is approximately 20 Hz to 20 kHz. 80/20 Humans are most sensitive in the frequency range 2 kHz to 5 kHz.

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB 80/20 The lowest detectable intensity (the threshold of hearing I threshold ) is about 1 pW/m 2 or 1x W/m 2. 80/20 The intensity at which one experiences pain (the threshold of pain) is about 1 W/m 2.

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB Hair Cell (Stereocilium) is a Neuron

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB Hair Cell (Stereocilium) is a Neuron Neuron has threshold for simulation Neuron has threshold for simulation Neuron “fires” (is either on or off) Neuron “fires” (is either on or off) Firing Neurons inhibit neighborsFiring Neurons inhibit neighbors

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB Consequence: Threshold and Non-linear Response Stimulus (Intensity) Response (sensation) Threshold of Hearing Watt/m 2 Desensitization with greater stimulus

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

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB Neuronal Response of Hair Cells No larger response because of inhibition Attenuated response to much larger stimulus

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB Consequence: Threshold and Non-linear Response Stimulus (Intensity) Response (sensation) Threshold of Pain 1 Watt/m 2

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB Logarithm of Stimulus vs Response Log (Stimulus/ I threshold ) Response SIL = 10 Log( I/I threshold ) I threshold = W/m 2

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

Physics 1251Unit 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 1251Unit 2 Session 13 Sound Intensity Level and dB 80/20 Sound 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 1251Unit 2 Session 13 Sound Intensity Level and dB 80/20 Just Noticeable Difference (JND) is the limen of difference that elicits 75% correct answers in a Two Alternative Forced-Choice test (2AFC test).

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB Why 75%? In 2 Alternative Forced Choice: 50% correct means random choice50% correct means random choice 100% means can always tell the difference.100% means can always tell the difference. Thus, 75% is halfway between random and certainty. Thus, 75% is halfway between random and certainty.

Physics 1251Unit 2 Session 13 Sound Intensity Level and dB 80/20 Just 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 1251Unit 2 Session 13 Sound Intensity Level and dB Calculator Practice: Log( 1) = Log( 10 ) = Log( 100 ) = Log( 2 ) = Log( 20 ) = Log( 200 ) =

Physics 1251Unit 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 ) = 10 dB 20 dB 3.0 dB 3.0 dB 13.0 dB 23.0 dB 0 dB

Physics 1251Unit 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 1251Unit 2 Session 13 Sound Intensity Level and dB The Mob Chorus: 1. “Rhubard!” 2. “Donnybrook!” 3. “Dust up!”

Physics 1251Unit 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 1251Unit 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 1251Unit 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 1251Unit 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 1251Unit 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 1251Unit 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 1251Unit 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 1251Unit 2 Session 13 Sound Intensity Level and dB Summary: The objective sound level is measured by SIL in dB. The objective sound level is measured by SIL in dB. SIL = 10 Log (I /I threshold ). SIL = 10 Log (I /I threshold ). 0 dB corresponds to an intensity of 1 pW/m 2. 0 dB corresponds to an intensity of 1 pW/m 2. The threshold of pain is 120 dB. The threshold of pain is 120 dB.