The Physics of Sound

1
The Physics of Sound

• Sound begins with a vibration of an object
• Vibrating object transfers energy to air medium
• All complex vibration patterns seen as a
  combination of many simple vibration patterns
• Simple harmonic motion
• Elastic restoring force
• Move object from equilibrium point, force returns
  it to equilibrium point
• Force is proportion to distance from equilibrium
  Displacement

2
Simple Harmonic Motion

• Harmonic oscillations, or sinusoid (sine) curves

3
Simple Harmonic Motion, cont

• Amplitude Maximum displacement from one extreme
  to resting position
• Periodic vibration Wave repeats itself
• Frequency (F) Number of cycles per sec (Hz)
• Period (T) Time (sec) to complete one cycle
• F 1 / T
• Phase Progression of wave through one cycle
  (measured in degrees)

4
Simple Harmonic Motion, cont

• Decay of harmonic motion

5
Additivity and Superposition of Sine Waves
6
Additivity and Superposition of Sine Waves, cont
7
Fourier Decomposition or Fourier Analysis
8
Fourier Decomposition, cont

• Systems for Naming Frequency Components
•  
• Freq. Harmonics Overtones Partials
• f0 Fundamental Fundamental 1st Partial
•  
• 2f0 2nd Harmonic 1st Overtone 2nd Partial
•   
• 3f0 3nd Harmonic 2st Overtone 3nd Partial
•   
• 4f0 4nd Harmonic 3st Overtone 4nd Partial

9
Fourier Decomposition, cont
10
The Perception of Pitch
The physiology of the ear
11
The Perception of Pitch, cont

• The place theory of pitch perception
• The basilar membrane as a set of independently
  tuned resonators
• Tone of single frequency causes corresponding
  place on basilar membrane to vibrate

12
The Perception of Pitch, cont

• The frequency theory of pitch perception
• Basilar membrane vibrates to match frequency
• Because of refractory period, nerve fibers cannot
  encode high frequency
• Volley principle nerve fibers working together
  can encode high frequencies

13
The Perception of Pitch, cont

• The psychophysics of frequency
• The Mel Scale Perceived pitch as a function of
  frequency
• Non-linear relation between frequency and pitch

14
The Perception of Pitch, cont

• The Cognitive-Structural approach
• Octave equivalence
• Tones in a 21 frequency ratio have a special
  relation
• Evidence for octave equivalence
• The harmonic series
• The musical pitch set

15
The Perception of Pitch, cont

• The Cognitive-Structural approach
• Psychological evidence for octave equivalence
• Deutsch (1973)
• Standard Intervening
  Sequence Comparison

16
The Perception of Pitch, cont

• The Cognitive-Structural approach
• Psychological evidence for octave equivalence
• Octave-scramble nursery rhymes

17
The Perception of Pitch, cont

• A bi-dimensional approach
• Tone / Pitch Height A continuous dimension that
  increases with frequency
• Tone / Pitch Chroma Circular component
  representing tones with 21 freq. ratio
• The pitch helix

18
The Perception of Pitch, cont

• A bi-dimensional approach
• Shepard / Circular tones
• Single tones
• Continuous glide
• Tritone paradox

19
The Perception of Loudness

• The psychophysics of loudness
• Audibility curves

20
The Perception of Loudness, cont

• The psychological scale of loudness
• Sones scale

21
The Perception of Timbre

• The steady state component approach
• Components that remain the same over time
• Problems with the steady state view of timbre

22
The Perception of Timbre, cont

• The importance of transient components
• Onset rapidity Rate of onset of the tone
• Noise bursts Amount/type of noise in beginning
  of tone
• Spectral energy shift Changes in relative
  intensity of harmonics over time

23
The Perception of Timbre, cont

• The perceptual similarity of musical timbre
• John Greys studies of musical timbre