1. Oscillations and Waves
Micro-world Macro-world Lect 5

2. Equilibrium (Fnet = 0)

3. Examples of unstable Equilibrium

4. Examples of Stable equilibrium

5. Destabilizing forces N
Fnet = 0 W

6. Destabilizing forces N
Fnet = away from equil W

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

8. restoring forces N
Fnet = 0 W

9. restoring forces N
Fnet = toward equil. W

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

11. Pendulum N W

12. Mass on a spring

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

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

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

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

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

18. Driven oscillators
natural freq. = f0
f = 0.4f0
f = 1.1f0
f = 1.6f0

19. Resonance (f=f0)

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

24. Harmonic sound wave

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

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. Two waves in same direction with slightly different frequencies
Adding waves
Two waves in same direction with
slightly different frequencies
Wave 1
Wave 2
resultant wave
“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. Two wave sources
constructive
interference
destructive
interference

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

33. Confined waves

34. Allowed frequencies l= 2L f0=V/l = V/2L f1=V/l = V/L=2f0 l=L l=(2/3)L
Fundamental tone
f1=V/l = V/L=2f0
l=L
1st overtone
l=(2/3)L
f2=V/l=V/(2/3)L=3f0
2nd overtone
l=L/2
f3=V/l=V/(1/2)L=4f0
3rd overtone
l=(2/5)L
f4=V/l=V/(2/5)L=5f0
4th overtone

35. Ukuleles, etc l0 = 2L; f0 = V/2L l1= L; f1 = V/L =2f0
l2= 2L/3; f2 = 3f0 L
l3= L/2; f3 = 4f0
Etc…
(V depends on the
Tension & thickness
Of the string)

36. Vocal Range – Fundamental Pitch♩ ♩
1175 Hz ♩
880 Hz ♩
587 Hz ♩
523 Hz ♩
392 Hz
329 Hz
196 Hz
165 Hz
147 Hz
131 Hz
98 Hz
82 Hz
Tenor C2 – C5
SopranoG3 – D6 ♂: ♀:
Mezzo-SopranoE3 – A5
Baritone G2 – G4
Bass E2 – E4
ContraltoD3 – D5
Thanks to Kristine Ayson

37. Doppler effect

38. Sound wave stationary source
Wavelength same in all directions

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

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

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

42. Visible light
Short wavelengths
Long wavelengths

43. receding source  red-shifted
approaching source  blue-shifted

44. Edwin Hubble

45. More distant galaxies have bigger red shifts

46. The universe is expanding!!

48. Use red- & blue-shifts to study orbital motion of stars in galaxies
receding
red-shifted
approaching
blue-shifted

49. A typical galactic rotation curve
NGC 6503

50. Large planets create red-shifts and blue shifts in the light of their star
Use this to detect planets & measure their orbital frequency

51. Planetary motion induced stellar velocity