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Longitudinal Standing Waves and Harmonic Series in Open
and Closed TubesPhysics 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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P + ½ rV2 = constant
Bernoulli’s Equation for Fluids
Pressure goes up, velocity goes down (and vice-versa) Energy divided random and chaotic
pressure density velocity
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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 tubes Closed-open tubes
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Harmonic Scale
Flute
Clarinet (missing even harmonics)
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Brass InstrumentsHow 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/pipes.html (Kundt’s Tube) http://www.youtube.com/watch?v=qUiB_zd9M0k http://www.mediacollege.com/audio/microphones/condenser.html
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Acoustic Impedance
Z = DP/u
How much pressure it takes to induce a certain amount of air to flow