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Published byDominic Casey Modified over 9 years ago
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Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes Physics of Music, Spring 2015
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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
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Analogy to Transverse Waves Pressure waves are sine waves – just like a standing wave on a string instrument!
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Kundt’s Tube: Standing waves in wind instruments
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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
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Open-open Tube Always “clamped” at atmospheric pressure
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Closed-open Tube Always “clamped” at atmospheric pressureZero net flow of air molecules
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Reflections Phase Change No Phase Change
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The Fipple: Divides Airstream http://homepages.ius.edu/kforinas/S/12Tubes.html
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Harmonic Series Open-Open Open-Closed
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Harmonics: Velocity vs Pressure Open-open tubesClosed-open tubes
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Harmonic Scale Flute Clarinet (missing even harmonics)
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Kundt’s Tube
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Brass Instruments How the valves on a trumpet work? Why does pushing down a valve change the note that sounds?
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Condenser Microphone + + - - + -
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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
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Acoustic Impedance Z = P/u How much pressure it takes to induce a certain amount of air to flow
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