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

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Presentation on theme: "Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes Physics of Music, Spring 2014."— Presentation transcript:

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

3 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

4 Kundt’s Tube: Standing waves in wind instruments

5 P + ½  V 2 = constant Bernoulli’s Equation for Fluids  Pressure goes up, velocity goes down (and vice- versa)  Energy is divided into random (pressure) and ordered motion (kinetic energy) pressure densityvelocity

6 Open-open Tube Always “clamped” at atmospheric pressure

7 Closed-open Tube Always “clamped” at atmospheric pressureZero net flow of air molecules

8 Reflections Phase Change No Phase Change

9 Harmonic Series Open-Open Open-Closed

10 Harmonics: Velocity vs Pressure

11 Harmonic Scale Flute Clarinet (missing even harmonics)

12 Kundt’s Tube

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

14 Condenser Microphone

15 Sources  Univ. of New South Wales Acoustics Research Group:    (Kundt’s Tube) 

16 Acoustic Impedance Z =  P/u How much pressure it takes to induce a certain amount of air to flow


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