Introduction to Wind Instruments

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Introduction to Wind Instruments

• Acoustics Music
• Semester 2 Week 8

Aims Introduce Principle Mechanisms for
Variety of Wind Instruments Learning
Outcomes Wind instrument types Excitation
Mechanisms Air column as a waveguides
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Principle Components

• Excitation Source (lips and mouthpiece/reed)
• Main oscillator/waveguide (column of air)
• Resonator (body, horn, bell, etc)

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Brass Instruments

• Excited by air flow of through a player's lips
• Lips / Breath
• pressure-controlled valve
• (embouchure) - determines impedance at the
  mouthpiece and hence the boundary condition for
  oscillation
• excites resonance's similar to harmonic series
  0.7f, 2f, 3f,..
• though with pedal note
• Valves control the effective length hence
  together with changes in embouchure musical
  scales can be constructed
• Bell
• efficient radiator of acoustic energy providing a
  gradual transition from high tube impedance to
  lower outside air impedance
• reflects low frequencies back to the mouthpiece
  hence filter
• reflected energy gives positive feedback to the
  player.
• conical shape determines modal response

4
Woodwind Instruments

• single-reed driven instruments (clarinets and
  saxophones)
• double-reed instruments (oboes, bassoons,
  english-horns)
• air-reed instruments (flutes, piccolos, and
  recorders)

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• The reed functions as a pressure-controlled valve
• With single reed player's lips can control input
  impedance
• Toneholes to vary the effective length of the air
  column
• A tonehole lattice acts as a high pass filter,
  reflecting back low frequency components and so
  influencing timbre.
• A register hole (vent) destructively interferes
  with the fundamental resonance of the air column
  so forcing oscillations at the next strongest
  resonance.
• Horn or bell radiates, resonates, filters and
  provides positive feedback

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Air reed
lower pressure at top sucks air upwards, hence
leaves rarefaction that sucks air back

• Flutes

Crumhorn / Modern Sax
Shawn / Modern Oboe
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Cornet
Early cornets used tone holes
Modern version gives a complex array of tubing
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How do we build a scale on a wind instrument?
Consider wave number
Intervals on trumpet, trombone, etc see
tutorial notes
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Wave Equation for Pipe
pressure change
cross-sectional area

• Assumptions
• Friction negligible
• Thermal conductivity negligible
• Ignore Gravity
• Pipe is sufficiently narrow for displacement to
  be the same for all points across it's width.

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Pressure in and out of small section
Fma
Where e is particle displacement (particle is
small volume molecules continuous i.e. density,
temp and pressure effectively constant)
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Consider pressure changes that are too fast for
energy go in and out of system (e.g. acoustic
pressure)

• Adiabatic expansion

P0 atmospheric pressure, V0 volume, ? Adiabatic
gas constant, K constant
So small changes with respect to volume, given by
Substituting for K
Can consider this small change in pressure as
acoustics pressure
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Acoustics Pressure
adiabatic gas constant
atmospheric pressure
Differentiating equation of motion
Substitute
Wave Equation for Pipe
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Solution

• The general harmonic solution for this general
  type of equation is
• or
• Which suggest two waves moving backwards and
  forwards along the pipe in opposite directions
  and stationary modes.

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Application of boundary conditions
Assume high impedance at mouthpiece
Closed/Closed Pipe
1f, 2f, 3f, 4f,
1f, 3f, 5f, 7f,..
Closed/Open Pipe
Realistic
0.7f, 2f, 3f, 4f, 5f