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Published byPauline Gregory Modified over 8 years ago
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Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes Physics of Music, Spring 2016
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Key terms Bernoulli’s Equation Pressure vs. velocity Compression vs. rarefaction Open vs. Closed Tubes Node vs. anti-node Even and Odd harmonics Kundt’s Tube Rubens’ Tube
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Standing Waves
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Analogy: Longitudinal to Transverse Waves Pressure waves are sine waves too!
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Longitudinal Standing Waves Animation courtesy of Dan Russsell, Grad Prog Acoustics, Penn State
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What causes the oscillation? FippleReed
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Fire It Up: Rubens’ Tube Other good videos: https://www.youtube.com/watch?v=BbPgy4sHYTw (Utah’s tube, detailed explanation) https://www.youtube.com/watch?v=gpCquUWqaYw (Portland rubens’ tube, good music) https://www.youtube.com/watch?v=8f0FcDPUqRk (Brazil, fun starts about 6’30”, really good music) https://www.youtube.com/watch?v=pWekXMZJ2zM (cycles through resonance frequencies, turn your sound off, you don’t go crazy)
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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 mass density velocity
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Time for Reflection Phase ChangeNo Phase Change
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Open Tube Pressure nodes: Openings always “clamped” at ~P atm (Velocity antinodes)
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Closed Tube Pressure anti-node (Velocity node) Pressure node (Velocity anti-node)
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Harmonics: Velocity vs Pressure Open tubes Closed-open tubes
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Closed Tubes
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Harmonic Scale Flute (open, all harmonics) Clarinet (closed, missing even harmonics)
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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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Top Brass
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Fire It Up: Rubens’ Tube Other good videos: https://www.youtube.com/watch?v=BbPgy4sHYTw (Utah’s tube, detailed explanation) https://www.youtube.com/watch?v=gpCquUWqaYw (Portland rubens’ tube, good music) https://www.youtube.com/watch?v=8f0FcDPUqRk (Brazil, fun starts about 6’30”, really good music) https://www.youtube.com/watch?v=pWekXMZJ2zM (cycles through resonance frequencies, turn your sound off, you don’t go crazy)
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The Fipple: Divides Airstream http://homepages.ius.edu/kforinas/S/12Tubes.html http://www.biophysics.uwa.edu.au/turbulence/animations/Miko_1.gif
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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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Condenser Microphone + + - - + -
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Harmonic Series Open-Open Open-Closed
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Acoustic Impedance Z = P/V How much pressure it takes to induce a certain amount of air to flow
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