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Physics of Music, Lecture 5: Human Perception of Sound

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Auditory Nerve, Brain, Mind. Pitch & Timbre Sensation. Right-Left synthesis ... Each auditory nerve cell fires on/off in phase with sound stimulus provided the ... – PowerPoint PPT presentation

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Title: Physics of Music, Lecture 5: Human Perception of Sound


1
Physics of Music, Lecture 5 Human Perception of
Sound
  • Prof. Charles Hyde-Wright
  • Reference materials
  • The Physics of Sound, R.E. Berg, D.G. Stork
  • The Science of Sound, T.D. Rossing

2
Laboratory Projects in sound perception
discrimination
  • Just Noticeable differences in pitch
  • Temporal sequence
  • Right-Left, or Superposition
  • Pitch perception
  • Shortest duration sound
  • Missing fundamental
  • Masking noise
  • Psycho-perceptual scale of intensity
  • Direction and distance perception (of sound)
  • Right-left time difference
  • Right-left intensity difference
  • Reverb

3
PeripheralAuditory System
  • Outer Ear Sound Collection
  • Middle Ear Mechanical Transducer
  • Inner Ear (Cochlea)
  • Frequency to position (fourier analysis)
  • Mechanical vibration to nerve impulse
  • Auditory Nerve, Brain, Mind
  • Pitch Timbre Sensation
  • Right-Left synthesis
  • Sound Identification (danger, music, speech)

4
Middle Ear, Ossicles
  • Hammer (attached to ear-drum), Anvil, and Stirrup
    (terminated on Oval Window of Cochlea).
  • Lever system converts low pressure--large
    amplitude vibrations of eardrum to large
    pressure--small amplitude vibrations of cochlear
    fluid.

5
Cochlea Conversion of mechanical vibrations to
nerve impulses
  • Fluid filled tube, divided in half longitudinally
    by Basilar Membrane.
  • Sound vibrations in fluid cause the basilar
    membrane to vibrate.
  • The Basilar Membrane is tapered in width and in
    thickness along 3.5 cm length.
  • Waves on a string v F/s1/2.
  • Basilar Membrane, Tension and density change
    with position
  • Narrow, stiff near Oval Window. Large and floppy
    at Helicotrema
  • Simple sound oscillations produce
  • localized vibration
  • Low Frequencies near Helicotrema.
  • High Frequencies near Oval Window.

6
Project Proposal for Math Students
  • Study Cochlea physiology and mechanics in a
    little more detail
  • Use math packages on computer (e.g. MathCad) to
    solve Wave Equation of simplified model of
    Basilar Membrane
  • Can you demonstrate localization of pure tones?

7
Musical Pitch C C D D E F F G G A A B C
  • Each Octave is a factor of 2 change in frequency
    (Not an equal additive change)
  • A 55 Hz, 110 Hz, 220 Hz, 440 Hz, 880 Hz,
    1760 Hz, 3520 Hz,
  • Musical Third is a 1.251.0 ratio
  • e.g. AF 220176, 440352,
  • Equal Tempered Tuning
  • Twelve equal half steps in an octave
  • CC DC DD CB
  • Twelve equal factors make 21 for one octave
  • Musical half step 21/12 1.0595

8
Localization of Vibration on Basilar Membrane
  • B. Membrane contains 30,000 hair/nerve cells
    along 35 mm length
  • Each octave is an ? equal shift of ? 3.5 mm
  • Each pure tone is localized to a Critical Band of
    ? 1.2 mm.
  • Each pure tone excites ? 1300 hair cells covering
    a 15 frequency range (lt minor third).

9
Auditory Processing
  • Each auditory nerve cell is a little oscillator,
    tuned to respond to vibrations in a narrow
    frequency band corresponding to the nerves
    position on the Basilar Membrane.
  • Each auditory nerve cell fires on/off in phase
    with sound stimulusprovided the amplitude of
    vibration of the hair/nerve is above threshold.
  • Brain receives frequency phase information from
    firing of nerves and frequency information from
    pattern of which nerves fire.
  • Expect brain can resolve position and width of
    pure tone distribution to 1/20 of full width
    0.06 mm ? frequency ratio 1.01 ? 29 cents

Just Noticeable Difference (JND)
10
Exponential Thinking (Powers of 10)
  • Professors teaching Phys 332 1 100
  • Students in Class 15 1.5x101
  • Students enrolled at ODU 17,000 1.7x104
  • Population of South Hampton Roads
  • 1 Million People 106
  • Population of India
  • 1 Billion People 109
  • U.S. Federal Budget
  • 1 Trillion Dollars 1012
  • Any number is a mantissa (value between 1 and 10)
    times a power of 10.

11
Exponents dont have to be integers
  • 2 100.3010
  • 4 2 x 2 ? 100.3 x 100.3 100.30.3 100.6
  • 8 2 x 2 x 2 ? 100.9
  • We like to work with powers of 2
  • Inches, ½, ¼, 1/8,
  • Coins Currency
  • 1 , 5 , 10 , 25 , 50 , 1, 2?, 5, 10
  • Euro

12
Euro Coins Currency
  • European Currency
  • 1c, 2c, 5c,
  • 10c, 20c, 50c
  • 1E, 2E, 5E
  • 10E, 20E, 50E
  • Repeating pattern of factors of 2 (or 2.5)

13
deciBell Scale of Sound Intensity Ratios
  • A intensity ratio I/I0 is measured in deciBells
    by
  • deciBell scale 10 Log(I/I0)
  • (I/I0) 10(deciBell value/10)
  • 3dB factor of 2 intensity change
  • deciBells multiply
  • 6db 2 factors of 2 factor of 4 intensity
    ratio
  • 10dB factor of 10 intensity ratio
  • 20dB factor of 10(20/10) 102 100 intensity
    ratio
  • 70dB factor of 107

14
Sound Intensity vs Frequency and deciBell Scale
(log-log scale)
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