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Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes. Physics of Music, Spring 2014. 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
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Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes Physics of Music, Spring 2014
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
Bernoulli’s Equation for Fluids P + ½rV2 = constant density velocity pressure • Pressure goes up, velocity goes down (and vice-versa) • Energy is divided into random (pressure) and ordered motion (kinetic energy)
Open-open Tube Always “clamped” at atmospheric pressure
Closed-open Tube Zero net flow of air molecules Always “clamped” at atmospheric pressure
Reflections No Phase Change Phase Change
Harmonic Series Open-Open Open-Closed
Harmonic Scale Flute Clarinet (missing even harmonics)
Brass Instruments How the valves on a trumpet work? Why does pushing down a valve change the note that sounds?
Condenser Microphone - + - + - +
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 How much pressure it takes to induce a certain amount of air to flow Z = DP/u