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:  http://www.phys.unsw.edu.au/jw/flutes.v.clarinets.html http://www.phys.unsw.edu.au/jw/flutes.v.clarinets.html  http://www.phys.unsw.edu.au/jw/pipes.html http://www.phys.unsw.edu.au/jw/pipes.html  (Kundt’s Tube) http://www.youtube.com/watch?v=qUiB_zd9M0k http://www.youtube.com/watch?v=qUiB_zd9M0k  http://www.mediacollege.com/audio/microphones/condenser.html

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