Physics 1251 The Science and Technology of Musical Sound

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Unit 3Unit 3

Session 27 MWFSession 27 MWF

Flutes and Flags, Flutes and Flags,

Fipples and FingeringFipples and Fingering

Unit 3Unit 3

Session 27 MWFSession 27 MWF

Flutes and Flags, Flutes and Flags,

Fipples and FingeringFipples and Fingering

Physics 1251Physics 1251 Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et cetera

What are the first three harmonics of What are the first three harmonics of a pipe closed on one end that is a a pipe closed on one end that is a length of 0.30 m? [Assume T=20 length of 0.30 m? [Assume T=20 C.]C.]

Only odd harmonics in stopped Only odd harmonics in stopped pipe:pipe:

ff11 = 344/4 L = 344 /(4 = 344/4 L = 344 /(4 ‧ ‧ 0.30) = 0.30) = 286.7 Hz286.7 Hz

ff33 = 3 f = 3 f11 = 3(286.7) = 860 Hz = 3(286.7) = 860 Hz

ff55 = 5 f = 5 f11 = 5(286.7) = 1424 Hz = 5(286.7) = 1424 Hz


11′ Lecture:′ Lecture:• Flutes and flue pipes are driven by Flutes and flue pipes are driven by

fluid flow instabilities at their fluid flow instabilities at their mouth.mouth.

• Standing waves in open air columns Standing waves in open air columns of flutes determine the pitch. of flutes determine the pitch.

• Open holes in the flute tube change Open holes in the flute tube change the effective length of the air the effective length of the air column.column.


The Flute The Flute • The transverse flute is acoustically The transverse flute is acoustically

driven by the fluid flow instabilities driven by the fluid flow instabilities whose frequency is controlled by the whose frequency is controlled by the feedback of the resonances of the pipe.feedback of the resonances of the pipe.

♩ ♪ ♫♩ ♪ ♫ ff1 1 f f2 2 f f3 3 f f44

fn

~~ ~~

Flow InstabilityFlow InstabilityStanding wave frequenciesStanding wave frequencies

FeedbacFeedbackk


The Flute:The Flute:Head JointHead Joint

BodyBody

Foot JointFoot Joint


Transverse FluteTransverse Flute

80/2080/20The flute is driven by air flow The flute is driven by air flow against the edge of the embrochure.against the edge of the embrochure.

EmbrochureEmbrochure

Air Air flowflow


Edge ToneEdge Tone

80/2080/20An air stream striking against an An air stream striking against an edge produces a fluctuating edge produces a fluctuating instability in flow.instability in flow.

Air Air StreamStream

The flow alternates The flow alternates sides.sides.

EdgeEdge


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

Thread in flowThread in flow

Winds Winds in Pacific in Pacific OceanOcean


Foolscap FippleFoolscap Fipple

11. Gently blow air from you mouth as in . Gently blow air from you mouth as in whistling.whistling.

Below a certain velocity the air flow is Below a certain velocity the air flow is stable, but faster than this critical stable, but faster than this critical velocity the air flow oscillates.velocity the air flow oscillates.

2.2. Blow against the edge of a piece of Blow against the edge of a piece of paper.paper.

Blow harder and softer.Blow harder and softer. Move the Move the paper closer and farther away from paper closer and farther away from you lips. Notice the change in the you lips. Notice the change in the sound.sound.


Fluid Flow InstabilityFluid Flow Instability

vvjetjet

Undulation velocity Undulation velocity u = 0.4 v u = 0.4 vjetjet


Why does the stream oscillate?Why does the stream oscillate?

Short answer: Short answer: positive feedback.positive feedback.

• When the stream bends to the When the stream bends to the left, the stream moves faster on left, the stream moves faster on the right side.the right side.

• Bernoulli’s PrincipleBernoulli’s Principle tells us tells us that the faster the flow, the that the faster the flow, the lower the pressure.lower the pressure.

• Therefore, the left-flowing Therefore, the left-flowing stream will bend back to the stream will bend back to the rightright


Bernoulli EffectBernoulli Effect

• 80/2080/20The pressure in a fluid The pressure in a fluid decreases as the velocity increases.decreases as the velocity increases.

Hold the foolscap by the edge and Hold the foolscap by the edge and blow across the top. What do you blow across the top. What do you observe?observe?

Physics 1251Physics 1251 Unit 3 Session 27Unit 3 Session 27Flutes et cetera.Flutes et cetera.

So why does a flag wave?So why does a flag wave?

http://usflag.org/toc.html







Edge ToneEdge Tone

bb

vvjetjet

u = 0.4 vu = 0.4 vjetjet

ffedgeedge = 0.4 v = 0.4 vjet jet / 2 b = 0.2 / 2 b = 0.2

vvjet jet /b/b

uu

bb


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

ffedgeedge = 0.2 v = 0.2 vjetjet /b /b

ffnn = n v/ 2L; f = n v/ 2L; fedgeedge

≈ f≈ fnn


Flue and FippleFlue and Fipple

FippleFipple FlueFlue

Recorder Recorder MouthpieceMouthpiece

Air Air ColumnColumn


RecorderRecorderBaroque FluteBaroque Flute

FippleFipple

LL

What What happens happens when you when you “over “over blow?”blow?”

The The instrument instrument jumps to a jumps to a new register, new register, n=2 or 3.n=2 or 3.

fn = n v/2L


The Problem with Flutes:The Problem with Flutes:

• Only about 1% of the energy of the air Only about 1% of the energy of the air stream produces sound. stream produces sound.

• Playing louder means more air flow.Playing louder means more air flow.• More air flow means higher jet velocityMore air flow means higher jet velocity

• Edge tone goes sharp Edge tone goes sharp • Worse in Recorder than in Transverse Worse in Recorder than in Transverse

FluteFlute• Player must “lip” tone into tunePlayer must “lip” tone into tune


How does one “play” the notes?How does one “play” the notes?

• By effectively changing the length of the By effectively changing the length of the air column.air column.• Opening holes introduces reflections that Opening holes introduces reflections that change the change the standing wave length.standing wave length.

Displacement Displacement wavewave LLeffeff

f f nn′ ′ = n = n ‧ ‧ v/2Lv/2Leffeff


Cross FingeringCross Fingering80/2080/20The position and size of the open holes The position and size of the open holes

modify the effective length of the air modify the effective length of the air column and consequently the pitch.column and consequently the pitch.

♩♩ ♯♯

♩♩♩♩ ♩♩ ♯♯♩♩♩♩


Why does the size of the hole Why does the size of the hole matter?matter?

Z =p/U Z =p/U

Impedance = pressure/flowImpedance = pressure/flow

Z Z ′ ′ ZZ

Displacement Displacement →→Flow Flow U:U:

Physics 1251Physics 1251 Unit 3 Session 27Unit 3 Session 27Flutes et al.Flutes et al.

Summary:Summary:• Flutes and flue pipes are open columns of Flutes and flue pipes are open columns of

air, with fair, with fnn = n v/2L, n = 1,2,3,4…. = n v/2L, n = 1,2,3,4….• Flue pipes are excited by flow instabilities Flue pipes are excited by flow instabilities

of the air steam in the embrochure or of the air steam in the embrochure or fipple.fipple.

• The frequency range is selected by the The frequency range is selected by the edge tone.edge tone.

• The pitch is determined by the effective The pitch is determined by the effective length of the pipe.length of the pipe.

• Open holes determine the effective length Open holes determine the effective length of the pipe.of the pipe.

Physics 1251 The Science and Technology of Musical Sound

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