Physics of Music, Lecture 5: Human Perception of Sound

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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

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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

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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)

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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.

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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.

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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?

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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

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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).

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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)
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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.

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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

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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)

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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

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