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Oscillations and Waves

Oscillations and Waves. Micro-world Macro-world Lect 5. Equilibrium (F net = 0). Examples of unstable Equilibrium. Examples of Stable equilibrium. Destabilizing forces. N. F net = 0. W. Destabilizing forces. N. F net = away from equil. W. Destabilizing forces.

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Oscillations and Waves

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  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 A 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. Harmonic wave 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. 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 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 v 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!!

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

  48. A typical galactic rotation curve NGC 6503

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

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