1. Music, Math, and Motion with Dr. Arun Chandra & Dr. E.J. Zita The Evergreen St. College Fall week 3 Tuesday 14 Oct. 2008

2. Overview Syllabus for the next two weeks Contact: –Radio waves –21 cm line and its frequency –Estimate the chance of extraterrestrial intelligence Loy Ch.8: –Easier way to derive frequencies –Springs, strings, and pipes –Resonant wavelengths and Q factor

3. Syllabus for the next two weeks

4. Contact –Radio waves –21 cm line and its frequency –Estimate the chance of extraterrestrial intelligence

5. Radio waves and EM spectrum

6. 21-cm line of Hydrogen http://abyss.uoregon.edu/~js/ast122/lectures/lec22.html

7. 21 cm line and its frequency What would be the frequency of radio waves of wavelength = 21 cm?

8. Circular polarization http://www.nsm.buffalo.edu/~jochena/images/circular3.gif

9. Estimate possibility of ETI

11. http://www.activemind.com/Mysterious/Topics/SETI/drake_equation.html

12. Loy Ch.8: Vibrating Systems –Easier way to derive frequencies –Springs, strings, and pipes –Resonant wavelengths and Q factor

13. Simple Harmonic Motion (SHM) Loy p.130 s

14. Kinematics of oscillations

15. Easier way to derive frequencies Compare to p.241-241 in Loy (harder, but same result) for SPRING OSCILLATION:

16. Easier way to derive frequencies F = ma -k x = m  2 x k = m  2  2 = k/m  =  k/m = 2  f

17. Frequency of air in piston What instruments are like this? What is the spring constant k of air? Recall that F = -kx, so the units of k are those of F/x, or (N/m). Recall that Pressure = Force/Area, so P = F/A or F = PA. For air, where  = a constant and l = the length of the chamber in which air is trapped.

18. Springs, strings, and pipes Nodes = still points at equilibrium Antinodes = points of maximum oscillation

19. Springs, strings, and pipes How many waves fit in the length L? Use that to find the resonant wavelengths n and resonant frequencies f n.

20. Springs, strings, and pipes How many waves fit in the length L? Use that to find the resonant wavelengths n and resonant frequencies f n.

21. Conical pipes Displacement must vanish at opening, therefore

22. Resonance: Q factor Sharpness of resonance

23. Galloping Gertie http://www.youtube.com/watch?v=j-zczJXSxnw