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Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes Physics of Music, Spring 2015.

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Presentation on theme: "Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes Physics of Music, Spring 2015."— Presentation transcript:

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2 Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes Physics of Music, Spring 2015

3 Key terms  Bernoulli’s Equation  Pressure vs. velocity  Compression vs. rarefaction  Open tube  Closed tube  Boundary condition—phase change  Node vs. anti-node  Even and Odd harmonics  Kundt’s Tube

4 Analogy to Transverse Waves Pressure waves are sine waves – just like a standing wave on a string instrument!

5 Kundt’s Tube: Standing waves in wind instruments

6 P + ½  V 2 = constant Bernoulli’s Equation for Fluids  Pressure goes up, velocity goes down (and vice-versa)  Energy divided random and chaotic pressure densityvelocity

7 Open-open Tube Always “clamped” at atmospheric pressure

8 Closed-open Tube Always “clamped” at atmospheric pressureZero net flow of air molecules

9 Reflections Phase Change No Phase Change

10 The Fipple: Divides Airstream http://homepages.ius.edu/kforinas/S/12Tubes.html

11 Harmonic Series Open-Open Open-Closed

12 Harmonics: Velocity vs Pressure Open-open tubesClosed-open tubes

13 Harmonic Scale Flute Clarinet (missing even harmonics)

14 Kundt’s Tube

15 Brass Instruments How the valves on a trumpet work? Why does pushing down a valve change the note that sounds?

16 Condenser Microphone + + - - + -

17 Sources  Univ. of New South Wales Acoustics Research Group:  http://www.phys.unsw.edu.au/jw/flutes.v.clarinets.html http://www.phys.unsw.edu.au/jw/flutes.v.clarinets.html  http://www.phys.unsw.edu.au/jw/pipes.html http://www.phys.unsw.edu.au/jw/pipes.html  (Kundt’s Tube) http://www.youtube.com/watch?v=qUiB_zd9M0k http://www.youtube.com/watch?v=qUiB_zd9M0k  http://www.mediacollege.com/audio/microphones/condenser.html

18 Acoustic Impedance Z =  P/u How much pressure it takes to induce a certain amount of air to flow


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