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Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes

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

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  1. Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes Physics of Music, Spring 2014

  2. 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

  3. Kundt’s Tube: Standing waves in wind instruments

  4. 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)

  5. Open-open Tube Always “clamped” at atmospheric pressure

  6. Closed-open Tube Zero net flow of air molecules Always “clamped” at atmospheric pressure

  7. Reflections No Phase Change Phase Change

  8. Harmonic Series Open-Open Open-Closed

  9. Harmonics: Velocity vs Pressure

  10. Harmonic Scale Flute Clarinet (missing even harmonics)

  11. Kundt’s Tube

  12. Brass Instruments How the valves on a trumpet work? Why does pushing down a valve change the note that sounds?

  13. Condenser Microphone - + - + - +

  14. 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

  15. Acoustic Impedance How much pressure it takes to induce a certain amount of air to flow Z = DP/u

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