Physics 1251 The Science and Technology of Musical SoundPhysics 1251 Unit 3 Session 27 Flutes et ceteraSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Physics 1251 Unit 3 Session 27 Flutes et cetera.Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Physics 1251 Unit 3 Session 27 Flutes et al.Physics 1251Physics 1251The Science and The Science and Technology of Musical Technology of Musical SoundSoundPhysics 1251Physics 1251The Science and The Science and Technology of Musical Technology of Musical SoundSoundUnit 3Unit 3Session 27 MWFSession 27 MWFFlutes and Flags, Flutes and Flags, Fipples and FingeringFipples and FingeringUnit 3Unit 3Session 27 MWFSession 27 MWFFlutes and Flags, Flutes and Flags, Fipples and FingeringFipples and FingeringPhysics 1251Physics 1251Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et ceteraWhat 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 Hzff33 = 3 f = 3 f11 = 3(286.7) = 860 Hz = 3(286.7) = 860 Hzff55 = 5 f = 5 f11 = 5(286.7) = 1424 Hz = 5(286.7) = 1424 HzPhysics 1251Physics 1251Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et cetera11′ 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.Physics 1251Physics 1251Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et ceteraThe 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 frequenciesFeedbacFeedbackkPhysics 1251Physics 1251Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et ceteraThe Flute:The Flute:Head JointHead JointBodyBodyFoot JointFoot JointPhysics 1251Physics 1251Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et ceteraTransverse FluteTransverse Flute80/2080/20The 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.EmbrochureEmbrochureAir Air flowflowPhysics 1251Physics 1251Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et ceteraEdge ToneEdge Tone80/2080/20An 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 StreamStreamThe flow alternates The flow alternates sides.sides.EdgeEdgePhysics 1251Physics 1251Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et ceteraFlow instabilities appear from the small to Flow instabilities appear from the small to the very large.the very large.Thread in flowThread in flowWinds Winds in Pacific in Pacific OceanOceanPhysics 1251Physics 1251Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et ceteraFoolscap FippleFoolscap Fipple11. 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.Physics 1251Physics 1251Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et ceteraFluid Flow InstabilityFluid Flow InstabilityvvjetjetUndulation velocity Undulation velocity u = 0.4 v u = 0.4 vjetjetPhysics 1251Physics 1251Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et ceteraWhy 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 rightrightPhysics 1251Physics 1251Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et ceteraBernoulli 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 1251Unit 3 Session 27Unit 3 Session 27Flutes et cetera.Flutes et cetera.So why does a flag wave?So why does a flag wave?http://http://usflagusflag.org/.org/toctoc.html.htmlPhysics 1251Physics 1251Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et ceteraEdge ToneEdge Tonebbvvjetjetu = 0.4 vu = 0.4 vjetjetffedgeedge = 0.4 v = 0.4 vjet jet / 2 b = 0.2 / 2 b = 0.2 vvjet jet /b/buubbPhysics 1251Physics 1251Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et ceteraFeedback 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 wavewaveffedgeedge = 0.2 v = 0.2 vjetjet /b /b