Physics%201251%20The%20Science%20and%20Technology%20of%20Musical%20Sound

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Physics 1251The Science and Technology of
Musical Sound

• Unit 3
• Session 27 MWF
• Flutes and Flags,
• Fipples and Fingering

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Physics 1251 Unit 3 Session 27 Flutes et cetera

• What are the first three harmonics of a pipe
  closed on one end that is a length of 0.30 m?
  Assume T20 C.

Only odd harmonics in stopped pipe f1 344/4
L 344 /(4 ? 0.30) 286.7 Hz f3 3 f1
3(286.7) 860 Hz f5 5 f1 5(286.7) 1424 Hz
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Physics 1251 Unit 3 Session 27 Flutes et cetera

• 1' Lecture
• Flutes and flue pipes are driven by fluid flow
  instabilities at their mouth.
• Standing waves in open air columns of flutes
  determine the pitch.
• Open holes in the flute tube change the effective
  length of the air column.

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Physics 1251 Unit 3 Session 27 Flutes et cetera

• The Flute
• The transverse flute is acoustically driven by
  the fluid flow instabilities whose frequency is
  controlled by the feedback of the resonances of
  the pipe.

Standing wave frequencies
Flow Instability
Feedback
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Physics 1251 Unit 3 Session 27 Flutes et cetera

• The Flute

Head Joint
Body
Foot Joint
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Physics 1251 Unit 3 Session 27 Flutes et cetera

• Transverse Flute
• 80/20The flute is driven by air flow against the
  edge of the embrochure.

Air flow
Embrochure
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Physics 1251 Unit 3 Session 27 Flutes et cetera

• Edge Tone
• 80/20An air stream striking against an edge
  produces a fluctuating instability in flow.

Air Stream
Edge
The flow alternates sides.
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Physics 1251 Unit 3 Session 27 Flutes et cetera

• Flow instabilities appear from the small to the
  very large.

Winds in Pacific Ocean
Thread in flow
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Physics 1251 Unit 3 Session 27 Flutes et cetera

• Foolscap Fipple
• 1. Gently blow air from you mouth as in
  whistling.
• Below a certain velocity the air flow is stable,
  but faster than this critical velocity the air
  flow oscillates.

• Blow against the edge of a piece of paper.
• Blow harder and softer. Move the paper closer and
  farther away from you lips. Notice the change in
  the sound.

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Physics 1251 Unit 3 Session 27 Flutes et cetera

• Fluid Flow Instability

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Physics 1251 Unit 3 Session 27 Flutes et cetera

• Why does the stream oscillate?

Short answer positive feedback.

• When the stream bends to the left, the stream
  moves faster on the right side.
• Bernoullis Principle tells us that the faster
  the flow, the lower the pressure.
• Therefore, the left-flowing stream will bend
  back to the right

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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.

Hold the foolscap by the edge and blow across the
top. What do you observe?
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Physics 1251 Unit 3 Session 27 Flutes et
cetera.

• So why does a flag wave?

http//usflag.org/toc.html
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Physics 1251 Unit 3 Session 27 Flutes et cetera

• Edge Tone

fedge 0.4 vjet / 2 b 0.2 vjet /b
u 0.4 vjet
b
b
vjet
u
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Physics 1251 Unit 3 Session 27 Flutes et cetera

• Feedback from the acoustic standing wave locks
  the frequency of the oscillation if the edge tone
  is near the fundamental frequency.

fedge 0.2 vjet /b fn n v/ 2L
fedge fn
Displacement wave
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Physics 1251 Unit 3 Session 27 Flutes et cetera

• Flue and Fipple

Recorder Mouthpiece
Flue
Fipple
Air Column
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Physics 1251 Unit 3 Session 27 Flutes et cetera

• Recorder
• Baroque Flute

fn n v/2L
Fipple
L
What happens when you over blow?
The instrument jumps to a new register, n2 or 3.
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Physics 1251 Unit 3 Session 27 Flutes et cetera

• The Problem with Flutes
• Only about 1 of the energy of the air stream
  produces sound.
• Playing louder means more air flow.
• More air flow means higher jet velocity
• Edge tone goes sharp
• Worse in Recorder than in Transverse Flute
• Player must lip tone into tune

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Physics 1251 Unit 3 Session 27 Flutes et cetera

• How does one play the notes?

• By effectively changing the length of the air
  column.

• Opening holes introduces reflections that change
  the standing wave length.

Displacement wave
f n' n ? v/2Leff
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Physics 1251 Unit 3 Session 27 Flutes et cetera

• Cross Fingering
• 80/20The position and size of the open holes
  modify the effective length of the air column and
  consequently the pitch.

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Physics 1251 Unit 3 Session 27 Flutes et cetera

• Why does the size of the hole matter?
• Z p/U
• Impedance pressure/flow

Displacement ?Flow U
Z '
Z
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Physics 1251 Unit 3 Session 27 Flutes et al.

• Summary
• Flutes and flue pipes are open columns of air,
  with fn n v/2L, n 1,2,3,4.
• Flue pipes are excited by flow instabilities of
  the air steam in the embrochure or fipple.
• The frequency range is selected by the edge tone.
• The pitch is determined by the effective length
  of the pipe.
• Open holes determine the effective length of the
  pipe.