Physics 1251 The Science and Technology of Musical Sound

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Physics 1251The Science and Technology of
Musical Sound

• Unit 3
• Session 29 MWF
• Brass Instruments

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Physics 1251 Unit 3 Session 29 Brass
Instruments

• What pitch (frequency) does a clarinet play if
  the length from the reed to a hole is 19.5 cm
  (including end corrections, i.e. L' 0.195 m) at
  20 C?

f v/4L' for a stopped cylinder v 343
m/s f 343/(4 ? 0.195) 440 Hz.
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• 1' Lecture
• Brass instruments are stopped pipes, that have a
  bore that is a combination of cylindrical and
  conical or flared.
• Brass are excited by lip-valves.
• The pitch is determined by feedback from the
  resonances of the pipe.
• The pitch is changed by exciting various
  overtones and by changing the length of the pipe.

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Physics 1251 Unit 3 Session 29 Brass
Instruments

• Brass Instruments of the Orchestra

Euphonium
Piccolo Trumpet
Trumpet
Trombone
French Horn
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• Brass Instruments
• The lips produce a pulsation in the pressure
  admitted to the pipe the pressure standing wave
  feeds back to control the oscillations of the
  plays lips.

Lip-valve pulsations
Standing wave frequencies
Feedback
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• The Origins of Brass

Shofar
Sackbut
Serpent
Ocleidex
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• The Lip Valve
• 80/20Brass instruments are played by the players
  lips.
• Breath pressure, muscle tension and pressure
  feedback from the pipe determine the frequency of
  the opening and closing of the lips.

Louis Armstrong trumpet (1901-1971)
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• Lip Valve

Embouchure
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• Lip Valve
• The lips of the player act as a valve that admits
  pressure pulses into the pipe.
• The frequency is determined by the breath air
  pressure, the lip tension and the resonances of
  the pipe.

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Physics 1251 Unit 3 Session 29 Brass
Instruments

• 80/20Brass Instruments
• are stopped pipes.
• The players lips produce a
  displacement node
  (pressure antinode)
  at the mouthpiece.
• A displacement
  anti-node (pressure node)
  exists at the bell.

Winton Marsalis Trumpet
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• The Mouthpiece

Back Bore
Cup
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• The Mouthpiece

Cup Volume
80/20The Cup Volume and the diameter of the
constriction leading to the back bore are more
important than the shape of the cavity.
Diameter
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• Resonance for Combination Pipes

80/20The Brass mouthpiece lowers the high
frequency resonances.
f
Cone with mouthpiece
Cone
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• The pitch is changed by pipe length and
  excitation of resonances.

By means of slides and valves the length is
changed.
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Physics 1251 Unit 3 Session 29 Brass
Instruments
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• Horns can be played by exciting the
  resonances only.

The Natural Horns No valves
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• Resonance for Combination Pipes

f
Cone/ Cylinder
0/100
25/75
50/50
40/60
20/80
100/0
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• Resonances for Combination Bores
  in Brass Instruments
• 80/20A 50 cylindrical ? 50 conical bore has a
  nearly harmonic series.

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Physics 1251 Unit 3 Session 29 Brass
Instruments

• Cylindrical-Conical Instruments

Cone
French Horn
Trombone
Cylinder
Cornet
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• Trumpet-like Instruments

Various instruments have different lengths of
cylindrical and of conical pipe.
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• The Bell

Exponential Horn
a ao exp(m x) b
80/20m is called the
flare constant. Larger m means more rapid flare.
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• The Bell

Bessel Horns
a ao e-(ex) b
80/20Called Bessel Horns because the standing
wave follows a Bessel Function.
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Physics 1251 Unit 3 Session 29 Brass
Instruments

• Summary
• Brass Instruments are stopped pipes.
• The pipe bore is designed to give resonances that
  are harmonic.
• The pedal tone (the lowest note) is not harmonic.
• The players lips are a soft reed.
• The pitch is changed by changing the length and
  exciting resonances.