1. Physics 1251 The Science and Technology of Musical Sound
Unit 3
Session 27 MWF
Flutes and Flags,
Fipples and Fingering

2. 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 T=20 C.]
Only odd harmonics in stopped pipe:
f1 = 344/4 L = 344 /(4 ‧ 0.30) = Hz
f3 = 3 f1 = 3(286.7) = 860 Hz
f5 = 5 f1 = 5(286.7) = 1424 Hz

3. 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.

4. 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
♩ ♪ ♫
f1 f2 f3 f4 fn ~
Feedback

5. Physics 1251 Unit 3 Session 27 Flutes et cetera
The Flute:
Head Joint
Body
Foot Joint

6. 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

7. 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.

8. 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

9. 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.

10. Physics 1251 Unit 3 Session 27 Flutes et cetera
Fluid Flow Instability
Undulation velocity u = 0.4 vjet
vjet

11. 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.
Bernoulli’s Principle tells us that the faster the flow, the lower the pressure.
Therefore, the left-flowing stream will bend back to the right

12. 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?

13. Physics 1251 Unit 3 Session 27 Flutes et cetera.
So why does a flag wave?

14. 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

15. 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

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

17. 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, n=2 or 3.

18. 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

19. 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
Leff

20. 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. ♩ ♩ ♯♩ ♯♩ ♩ ♩

21. 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 ′

22. 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.