2. Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes Physics of Music, Spring 2015

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. Analogy to Transverse Waves Pressure waves are sine waves – just like a standing wave on a string instrument!

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

6. P + ½  V 2 = constant Bernoulli’s Equation for Fluids  Pressure goes up, velocity goes down (and vice-versa)  Energy divided random and chaotic pressure densityvelocity

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

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

9. Reflections Phase Change No Phase Change

10. The Fipple: Divides Airstream http://homepages.ius.edu/kforinas/S/12Tubes.html

11. Harmonic Series Open-Open Open-Closed

12. Harmonics: Velocity vs Pressure Open-open tubesClosed-open tubes

13. Harmonic Scale Flute Clarinet (missing even harmonics)

14. Kundt’s Tube

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

16. Condenser Microphone + + - - + -

17. 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

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