Musical Sounds

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Musical Sounds

• Physics 1010
• Dr. Don Franceschetti
• November 2, 2006

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Musical sound is different from noise

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Attributes of Musical Sound

• Pitch Frequency
• Loudness Intensity
• Quality - Timbre

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Pitch

• Strange as it seems, our musical scale is based
  on the twelfth root of 2 1.059463...
• E/C is almost 5/4
• G/C is almost 3/2
• Some modern scales use finer divisions

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Remember

• Pythagoreans got music going by noting that
  strings with lengths in the ratio small whole
  numbers sounded nice together.
• Kepler (1571-1630) Harmonies of the World related
  planetary distances to musical tones
• Today, string theory

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Standing waves on a string

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More generally

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Pitch

• Wind instruments (brass or wood) determined by
  length of air column.
• Stringed instruments determined by length and
  tension of string.
• Percussion determined by plate or drumhead
  vibration.
• Most music below 4000 hertz.

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Intensity

• Ear is very sensitive but can hear over wide
  range
• Threshold of hearing 10-12 W/m2, defined as 0 bel
  
• 10 times intensity is 1 bel or 10 decibels
• 2 bels is 10 times intensity for 1 bel,
• And so on up through 120 decibels, the threshold
  of pain
• 140 decibels or 100 W/m2, jet engine
• Webers Law The change in stimulus intensity
  that can just be discriminated is a constant
  fraction of the starting intensity of the stimulus

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Loudness

• Is the physiological sensation corresponding to
  pitch
• The study of the relation between stimuli and
  perception is called psychophysics
• Roughly, most of our sense organs are logarithmic
  (Webers law)

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Quality

• Is determined by the mixture of harmonics
• Fundamental frequency harmonics (overtones)
• Fourier analysistakes composite waves and breaks
  them up into frequencies

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Quality

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Ernst Chladni (1756-1827)

• Amateur musician and inventor of musical
  instruments.
• Chladni figures, formed by sand on vibrating
  plates. Key to understanding soundboards and
  percussion.
• Demonstrated before French Academy of Sciences in
  1808, with Napoleon present. Napoleon offers
  prize to scientist who could explain what
  happened.
• Problem solved by Sophie Germain in 1816
• Sand collected on nodes.
• May have inspired Edison to invent phonograph.

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Ernst Chladni
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Chladni figures
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Drum heads

• Different modes have different nodes
• Radial nodes
• Angular nodes
• Electron motions in atoms and nucleon motions in
  nuclei have modes of vibrating ball
• Sun and moon are ringing like a bell
• Was Kepler right?

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Recording Sound

• Phonograph record, sound recorded in analog form.
• How many groves on a record?
• CD waveform coded as numbers. Sampling 44,100
  times a second. Suppresses noise.

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Digital Recording 44,100 times a second

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Digital Playback