instrument ! air ! listener

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• instrument ! air ! listener
• source ! medium ! receptor
• The source emits.
• The medium transmits.
• The receptor detects, registers, or, in general,
  is affected in some specific way.

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Sound waves

• Goldstein, pp. 331 339
• CWE, pp. 182 187
• Levine, pp. 332 338
• Howard Angus, Chapter 1
• Warren, pp. 1 5

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Sound of a physical stimulus pressure changes in
the air
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Sound waves

• are longitudinal waves.
• are alternations of rarefaction and compression
  of an elastic medium (such as water, air, or
  walls) in which they travel.
• are created by rapid movement of a source in
  mechanical contact with this medium.
• can be transmitted for great distances.
• cannot pass through a vacuum.
• The speed of sound varies according to the medium
  in which it travels.

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• Wavelength (?) distance from one peak of the
  wave to the next
• Cycle the completion of a full sequence of air
  rarefaction and compression
• Frequency (f) number of cycles a sound wave
  completes in one second
• Hertz (Hz) unit (cycles per second) used to
  measure frequency of sound waves
• ? v/f (v velocity (m s-1))
• Pressure amplitude measure of the size of the
  variation in air pressure caused by a sound wave

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• Phase the particular point in the
  compression-rarefaction cycle of sound wave at
  one instant of time
• Phase (in phase out of phase how much they are
  out of phase is expressed in terms of phase angle
  ?)

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Pressure amplitude

• Amount by which the wave causes the pressure to
  differ from the normal atmospheric pressure
  (which is 105 N/m2 newtons/meter2)
• Maximum pressure variation the ear can tolerate
  (10 00Hz tone) 30 N/m2
• Minimum pressure variation the ear can detect (10
  00Hz tone) 2 10-5 N/m2

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Sound Pressure Level (SPL)

• The decibel SPL value for a sound with pressure
• LP 20 log (P/P0)
• P sound pressure amplitude being measured
• P0 210-5 N/m2
• (logarithmic scale relative to some reference)

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Relation between sound pressure and decibel
Pressure (p/p0)
dB SPL
1 0
10 20
100 40
1000 60
10 000 80
100 000 100
1 000 000 120
10 000 000 140
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Sound pressure levels (intensity levels) of
various sound sources
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Frequency
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Piano keyboard, showing the frequencies
associated with each note and the ranges of
various other instruments
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Complex sound waves produced by musical
instruments
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Jean-Baptiste Joseph Baron de Fourier1768 - 1830

• Fourier-analysis decomposing complex pattern
  into sine waves
• Fourier-synthesis adding sine waves to create a
  complex pattern

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Gradually adding higher frequency sine waves of
lower amplitude
Gradually adding higher frequency sine waves of
the same amplitude
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Additive synthesis

• Fundamental frequency (or first harmonic)
  starting frequency for a complex sound
• Harmonics pure tones, each of which has a
  frequency that is a multiple of the fundamental

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Fundamental or first harmonic
Frequency spectrum
frequency line's position amplitude line's
height
Second harmonic
Third harmonic