Physics of Music: Lecture 7 October 8, 2002

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Physics of Music Lecture 7October 8, 2002

• Sound Recording and Reproduction
• Berg Stork, Chapter 7
• Prof. C.E. Hyde-Wright

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Analog

• The sound amplitude is recorded by a continuously
  varying signal
• Shape of groove cut in wax/plastic on 78/45/33
  rpm record.
• Strength of magnetization on magnetic tape.
• Quantity of electric charge stored on an array of
  capacitors CCD, short term recording only
  (milli-seconds).

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Digital

• Sound amplitude is converted to a numerical
  value, which is then stored (usually in binary
  form)
• Digital Audio Tape
• Magnetization on/off records 0/1, exact value of
  magnetization is unimportant
• Compact Disk
• Pits/flat record 0/1
• The instrument itself is digitized pitch,
  intensity
• Player Piano rolls mixed analog/digital
• A. Rubenstein 19th century digital sound
  editing
• MIDI

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Recording/Playback

• Playback
• Digital or Analog information converted to
  electrical signal
• Signal is amplified
• Impedance matched to speaker
• Microphone
• Sound wave converted to electrical signal
• Recording
• Electrical signal routed to recording device

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Ohms Law

• Flow of waterpumping pressure / Resistance
• Resistance viscosity (length/area)
• Flow of current Voltage of source / Resistance
• I V/R, V I R
• Resistance Resistivity (length/area)
• Oscillating Source
• Current Voltage / Impedance
• Impedance includes idea of phase shift
• Power Force times Velocity
• Electrical power P IV

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Impedance, Power, phase shift

• In an oscillator with no damping, force and
  velocity are 90 degrees out of phase.
• P I V, No net power loss

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Electrical/Audio Circuits

• A source can be described as an ideal voltage
  source in series with a resistance (impedance).
• Microphones, Line-out of CD player, have large
  source (or output) impedance (100k Ohm)
• A hi-fi speaker has low load resistance (8 Ohm)
• Power delivered to load is maximized if output
  impedance of source matches input impedance of
  load.

Vs
Rs
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Microphone

• Magnetic Induction
• As the coil moves, the free electrons in the wire
  experience a magnetic force. This force drives a
  current in the coil
• Electrostatic A voltage source keeps the
  charges separated on the two plates of the
  condenser. As one plate moves, this voltage
  (force) changes.

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Cardioid Directivity

• Cardioid directivity of microphone from
  front/rear cancellation
• Use parabolic reflector to get narrow directivity

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Loudspeaker

• Current in coil in presence of permanent magnet
  induces magnet force on coil
• Large motions required (esp. at low frequency) to
  generate large audio power
• Acoustic baffle eliminates destructive
  interference at low frequency
• Speaker cone has vibration resonance at about 100
  Hz need to dampen and broaden
• Tuned port produces a resonance (bass boost)
  below the mechanical resonance of the cone.

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Stereo LPs (remember them?)

• Mechanical recording of sound
• 19th century grammaphone produced audible sound
  with no amplification

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AM FM Radio

• Amplitude Modulation
• Stations are only allowed 5 kHz of bandwidth
• Not enough for hi-fidelity (20 kHz)
• Frequency Modulation
• Constant amplitude (less interference)
• 200 kHz bandwidth
• Enough for two signals, each with 20 kHz

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Audio Tape (Analog Digital)

• Magnetic material
• microscopic magnetic domains, each a permanent
  magnet, all randomly oriented.
• Read/Write/Erase head
• Coil on non-magnetized iron C
• Erase Strong 100kHz signal randomizes
  magnetization
• Write Strong Audio signal produces magnetic
  alignment proportional to strength of audio
  signal.
• Read Magnetization of tape induces a signal in
  pick-up coil

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Digital Recording

• How many bits?
• 8-bits 0 to 28-1255
• How many samples per second.
• To faithfully record up to 20 kHz signal requires
  sampling frequency just greater than twice 20, or
  40 kHz.
• What does a 40 kHz sampling system do to a 41 kHz
  signal
• Aliasing (shift to low frequency)

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Compact Disk

• A 1 is recorded by a change (either from flat
  to pit, or from pit to flat).
• A 0 is recorded by no change