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

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) = 286.7 Hz f3 = 3 f1 = 3(286.7) = 860 Hz f5 = 5 f1 = 5(286.7) = 1424 Hz

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.

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

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

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

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.

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

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.

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

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

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?

Physics 1251 Unit 3 Session 27 Flutes et cetera. So why does a flag wave? http://usflag.org/toc.html

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

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

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

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.

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

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

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. ♩ ♩ ♯♩ ♯♩ ♩ ♩

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 ′

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.