Physics 1251 The Science and Technology of Musical Sound

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Physics 1251The Science and Technology of
Musical Sound

• Unit 3
• Session 28 MWF
• Clarinets and Other Reeds

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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• What pitch (frequency) does a flute play if the
  length from the embouchure to the finger hole is
  67.5 cm 26½ inches (including end
  corrections) when the temperature in the tube is
  37 C?

f v/2L' v 343 0.6 (T-20C) v 343
0.6(37-20) 343 0.6 (17) 353 m/s f
353/(2 ? 0.675) 262 Hz. With no warm up f '
344/354 f 255. Hz, ?f f ' f 262 255
7 Hz. P 3986 Log (255/262) - 47, 1/4 tone
?
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• With what velocity should the flautist blow to
  produce a stable tone of 262 Hz if the embouchure
  is about 0.01 m?

f 0.2 vjet / b 262 Hz 0.2 vjet /0.01 vjet
262 ? 0.01/0.213.1 m/s ( 30 mph)
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• 1' Lecture
• Reed instruments are stopped pipes.
• The clarinet has a cylindrical bore and is a
  stopped pipe consequently, only odd harmonics
  are significant.
• Conical pipes exhibit all harmonics, even in
  stopped pipes.
• The saxophone, oboe and bassoon?all have conical
  bores.

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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• Comparison
  of Flute and Clarinet Registers
• Overblown flutes jump from a fundamental f1 v/2L
  to an octave f2 2f1 in the second register an
  octave (2x) and a perfect fifth (3/2) f3 3 f1
  3 (v/2L) in the third register.
• Overblown clarinets jump from a fundamental
  f1 v/4L to an octave (2x) and a fifth (3/2
  )?the twelfth? in the second register, because
  only odd harmonics produce standing waves in a
  stopped cylindrical pipe.

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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• Reed Instruments
• The reed produces a pulsation in the pressure
  admitted to the pipe the pressure standing wave
  feeds back to control the oscillations of the
  reed.

Standing wave frequencies
Reed pulsations
Feedback
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• The Clarinet

Reed
Body
Bell
The clarinet has a cylindrical bore.
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• The Single Reed
• 80/20The reed opens and closes like a valve,
  pressurizing the pipe when open, closing due to
  the Bernoulli effect when the air flows.

Reed
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• Hard and Soft Reeds
• 80/20A hard reed is one for which the frequency
  is determined by its stiffness and dimensions.
• A soft reed flexes easily and vibrates at the
  frequency of external pressure fluctuations.

Soft Reeds
Hard Reed Harmonica
Clarinet
Oboe
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• Harmonium or Reed Organ

Hard or soft reed?
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• The Double Reed
• 80/20The reed opens and closes like a valve,
  pressurizing the pipe when open, closing due to
  the Bernoulli effect when the air flows.

Pressure Pulses
Reed Tip
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• Double Reed
• The
  
• Bassoon
• uses a
• double
• reed,
• as does
• the Oboe
• and English
• Horn.

Bassoon Reeds
Reed
Double Reed
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Physics 1251 Unit 3 Session 27 Flutes et cetera

• Bernoulli Effect
• 80/20The pressure in a fluid decreases as the
  velocity increases.

Thus, as the air flows past the reed, it is
forced closed.
Bernoulli Effect
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• 80/20Feedback from the pressure standing wave
  locks the frequency of the oscillation of the
  reed.

f2n-1 (2n-1) v/ 4L'
Pressure wave
L' L 0.3 d
0.3 d
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• Other Bore Shapes
• Conical?

Pressure anti-node
Pressure node
Pressure anti-node
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

80/20For a stopped conical pipe fn n v / 2(L'
c) if c ltlt ? L' L 0.3 d
L'
d
c
0.3 d
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• Why?
• Z changes along the length of the pipe.
• Weighted String Analogy

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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• Other Reed Woodwinds

Saxophone
Conical bore
English horn
Conical bore
Oboe
Conical bore
Bassoon
Conical bore
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• The Reed Pipes of Organs
• Conical
• Voiced
  by Reeds
• Tuned
  by Spring
  

Pipe
Shallot
Reed
Tuning Spring
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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• Reed Pipes

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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• Bicycle Horn

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Physics 1251 Unit 3 Session 28 Clarinets et
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• Edge versus Reed
• Cylinder versus Cone

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Physics 1251 Unit 3 Session 28 Clarinets et
cetera

• Summary
• Reed Instruments are stopped pipes.
• L' L 0.3 d
• f2n-1 (2n-1) v/4L' for stopped cylindrical
  pipes such as the clarinet.
• fn n v/ 2(L'c) for stopped conical pipes such
  as the saxophone, oboe, bassoon, etc.
• Soft reeds act as pressure valves that respond to
  the frequency fed back from the standing waves of
  the pipe.