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Oscillations and Waves

Oscillations and Waves. Physics 100 Chapt 8. 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. F net = away from equil. N.

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Oscillations and Waves

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  1. Oscillations and Waves Physics 100 Chapt 8

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

  32. 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

  33. Ukuleles, etc l0 = L/2; 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)

  34. Doppler effect

  35. Sound wave stationary source Wavelength same in all directions

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

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

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

  39. surf

  40. Folsom prison blues long wavelengths Short wavelengths

  41. Confined waves

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