2. Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes Physics of Music, Spring 2016

3. Key terms  Bernoulli’s Equation  Pressure vs. velocity  Compression vs. rarefaction  Open vs. Closed Tubes  Node vs. anti-node  Even and Odd harmonics  Kundt’s Tube  Rubens’ Tube

4. Standing Waves

5. Analogy: Longitudinal to Transverse Waves Pressure waves are sine waves too!

6. Longitudinal Standing Waves Animation courtesy of Dan Russsell, Grad Prog Acoustics, Penn State

7. What causes the oscillation? FippleReed

8. Fire It Up: Rubens’ Tube  Other good videos:  https://www.youtube.com/watch?v=BbPgy4sHYTw (Utah’s tube, detailed explanation)  https://www.youtube.com/watch?v=gpCquUWqaYw (Portland rubens’ tube, good music)  https://www.youtube.com/watch?v=8f0FcDPUqRk (Brazil, fun starts about 6’30”, really good music)  https://www.youtube.com/watch?v=pWekXMZJ2zM (cycles through resonance frequencies, turn your sound off, you don’t go crazy)

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

10. 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 mass density velocity

11. Time for Reflection Phase ChangeNo Phase Change

12. Open Tube Pressure nodes: Openings always “clamped” at ~P atm (Velocity antinodes)

13. Closed Tube Pressure anti-node (Velocity node) Pressure node (Velocity anti-node)

14. Harmonics: Velocity vs Pressure Open tubes Closed-open tubes

15. Closed Tubes

16. Harmonic Scale Flute (open, all harmonics) Clarinet (closed, missing even harmonics)

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

18. Top Brass

19. Fire It Up: Rubens’ Tube  Other good videos:  https://www.youtube.com/watch?v=BbPgy4sHYTw (Utah’s tube, detailed explanation)  https://www.youtube.com/watch?v=gpCquUWqaYw (Portland rubens’ tube, good music)  https://www.youtube.com/watch?v=8f0FcDPUqRk (Brazil, fun starts about 6’30”, really good music)  https://www.youtube.com/watch?v=pWekXMZJ2zM (cycles through resonance frequencies, turn your sound off, you don’t go crazy)

20. The Fipple: Divides Airstream http://homepages.ius.edu/kforinas/S/12Tubes.html http://www.biophysics.uwa.edu.au/turbulence/animations/Miko_1.gif

21. 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

22. Condenser Microphone + + - - + -

23. Harmonic Series Open-Open Open-Closed

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