1. Resonant Waves in A Vibrating Column of Air For a tube open at both ends:

2. Resonant Waves in A Vibrating Column of Air When air is blown across one end, the pressure disturbance moves through the tube to the other end, and a resonance is set up: For a tube open at both ends:

3. Resonant Waves in A Vibrating Column of Air When air is blown across one end, the pressure disturbance moves through the tube to the other end, and a resonance is set up: For a tube open at both ends: Low pressure High pressure

4. Resonant Waves in A Vibrating Column of Air Max Particle Displacement Min Particle Displacement Low pressure High pressure

5. Resonant Waves in A Vibrating Column of Air L

6. L = 2L

7. Resonant Waves in A Vibrating Column of Air L = 2L

8. Resonant Waves in A Vibrating Column of Air L = 2L = L

9. Resonant Waves in A Vibrating Column of Air L = 2L = L

10. Resonant Waves in A Vibrating Column of Air L = 2L = L = 2L/3

11. Resonant Waves in A Vibrating Column of Air = 2L = 2L/1 = L= 2L/2 = 2L/3= 2L/3 = L/2= 2L/4 = 2L/5= 2L/5

12. Resonant Waves in A Vibrating Column of Air Fundamental (1 st Harmonic) 2 nd Harmonic 3 rd Harmonic 4 th Harmonic 5 th Harmonic n = 1 n = 2 n = 3 n = 4 n = 5

13. Resonant Waves in A Vibrating Column of Air where: Resonant wavelength formula For two fixed ends and two open ends: where: Resonant frequency formula

14. Resonant Waves in A Vibrating Column of Air For tubes resonating in air the velocity will always be the speed of sound (~340 m/s)

15. Resonant Waves in A Vibrating Column of Air Displacement of Molecules Pressure Distribution (dark – high pressure)

16. Resonant Waves in A Vibrating Column of Air For tubes with one end closed: Fraction of wave One full wavelength L

17. Resonant Waves in A Vibrating Column of Air For tubes with one end closed: Fraction of wave One full wavelength ¼ sine L

18. Resonant Waves in A Vibrating Column of Air For tubes with one end closed: Fraction of wave One full wavelength ¼ sine L 4L

19. Resonant Waves in A Vibrating Column of Air For tubes with one end closed: Fraction of wave One full wavelength ¼ sine L 4L ¾ sine

20. Resonant Waves in A Vibrating Column of Air For tubes with one end closed: Fraction of wave One full wavelength ¼ sine L 4L ¾ sine 4L/3

21. Resonant Waves in A Vibrating Column of Air For tubes with one end closed: Fraction of wave One full wavelength ¼ sine L 4L ¾ sine 4L/3 sine

22. Resonant Waves in A Vibrating Column of Air For tubes with one end closed: Fraction of wave One full wavelength ¼ sine L 4L ¾ sine 4L/3 sine 4L/5

23. Resonant Waves in A Vibrating Column of Air Trend? 4L 4L/3 4L/5

24. Resonant Waves in A Vibrating Column of Air Trend? 4L 4L/3 4L/5 Resonant wavelength formula for one fixed end and one open end

25. Resonant Waves in A Vibrating Column of Air Resonant wavelength formula For One Closed End/One Open End: Resonant frequency formula

26. Resonant Waves in A Vibrating Column of Air Human voice: