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