1. Oscillations and Waves Physics 100 Chapt 8

2. Equilibrium (F net = 0)

3. Examples of unstable Equilibrium

4. Examples of Stable equilibrium

5. Destabilizing forces W N F net = 0

6. Destabilizing forces W N F net = away from equil

7. Destabilizing forces W N F net = away from equil destabilizing forces always push the system further away from equilibrium

8. W N F net = 0 restoring forces

9. W N F net = toward equil. restoring forces

10. W N F net = toward equil. restoring forces Restoring forces always push the system back toward equilibrium

11. Pendulum N W

12. Mass on a spring

13. Displacement vs time amplitude period (=T ) Displaced systems oscillate around stable equil. points Equil. point

14. Simple harmonic motion Equil. point T T= period = time for 1 complete oscillation f = frequency = # of oscillations/time = 1/T Pure Sine-like curve

15. Masses on springs Animations courtesy of Dr. Dan Russell, Kettering University

16. Not all oscillations are nice Sine curves A T Equil. point f=1/T

17. Natural frequency f= (1/2  )  g/l f= (1/2  )  k/m

18. Driven oscillators f = 0.4f 0 f = 1.1f 0 f = 1.6f 0 natural freq. = f 0

19. Resonance (f=f 0 )

20. Waves Animations courtesy of Dr. Dan Russell, Kettering University

21. Wave in a string Animations courtesy of Dr. Dan Russell, Kettering University

22. Pulsed Sound Wave

23. Harmonic sound wave

25. Harmonic wave wavelength = Wave speed =v Wave speed = v = distance time wavelength period = = T = f but 1/T=f V=f  or f=V/  Shake end of string up & down with SHM period = T

26. Reflection (from a fixed end) Animations courtesy of Dr. Dan Russell, Kettering University

27. Reflection (from a loose end) Animations courtesy of Dr. Dan Russell, Kettering University

28. Adding waves pulsed waves Animations courtesy of Dr. Dan Russell, Kettering University

29. Adding waves Wave 1 Wave 2 resultant wave Two waves in same direction with slightly different frequencies “Beats” Animations courtesy of Dr. Dan Russell, Kettering University

30. Adding waves harmonic waves in opposite directions incident wave reflected wave resultant wave (standing wave) Animations courtesy of Dr. Dan Russell, Kettering University

31. Confined waves Only waves with wavelengths that just fit in survive (all others cancel themselves out)

32. Allowed frequencies =(2/3)L f 0 =V/ = V/2L f 1 =V/ = V/L=2f 0 = 2L =L =(2/5)L =L/2 f 2 =V/ = V /( 2/3) L=3f 0 f 3 =V/ = V /( 1/2) L=4f 0 f 4 =V/ = V /( 2/5) L=5f 0 Fundamental tone 1 st overtone 3 rd overtone 4 th overtone 2 nd overtone

33. Ukuleles, etc L 0 = L/2; f 0 = V/2L 1 = L; f 1 = V/L =2f 0 2 = 2L/3; f 2 = 3f 0 3 = L/2; f 3 = 4f 0 Etc… (V depends on the Tension & thickness Of the string)

34. Doppler effect

35. Wavelength same in all directions Sound wave stationary source

36. Wavelength in backward direction is longer (frequency is higher) Wavelength in forward direction is shorter (frequency is higher) Sound wave moving source

37. Waves from a stationary source Wavelength same in all directions

38. Waves from a moving source Wavelength in forward direction is shorter (frequency is higher) Wavelength in backward direction is longer (frequency is higher) v

39. surf

40. Folsom prison blues Short wavelengths long wavelengths

41. Confined waves