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Simple Harmonic Motion

Simple Harmonic Motion. Simple harmonic motion (SHM) refers an oscillatory, or wave-like motion that describes the behavior of many physical phenomena: a pendulum a bob attached to a spring low amp. waves in air, water, the ground vibration of a plucked guitar string.

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Simple Harmonic Motion

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  1. Simple Harmonic Motion

  2. Simple harmonic motion (SHM) refers an oscillatory, or wave-like motion that describes the behavior of many physical phenomena: • a pendulum • a bob attached to a spring • low amp. waves in air, water, the ground • vibration of a plucked guitar string

  3. Objects undergoing SHM trace out sine waves where the d is pos and neg with time.

  4. Simple Pendulum

  5. displacement– time graph w worksheet

  6. Velocity and acceleration in SHM • The position of an object undergoing SHM changes with time, thus it has a velocity • The velocity of an object is the slope of its graph of position vs. time. Thus, we can see that velocity in SHM also changes with time, and so object is accelerating:

  7. Vibrations & Waves

  8. Energy Transfer by Waves Waves are an energy disturbancepropagates through material or empty space.

  9. Waves Transfer EnergyMatter is not transferredEx: Cork on water or buoy

  10. Waves start with vibration

  11. Some Types of Energy that travel as Waves • Sound – vibrating tuning fork, string, wood etc. • Light (EM) – vibrating charges. • Earthquake – vibration of Earth’s crust

  12. How can we prove that waves transfer energy? Can waves do work? Give examples.

  13. Mechanicalwaves need medium through which to travel. Mediums include: Gasses - air liquids/water Solids - wood Ex: Sound/Earthquake waves

  14. Non mechanical – no medium required!Electromagnetic Waves (EM) need no medium*EM waves can also propagate through a medium

  15. P8 Ended Lesson Here

  16. Two Main Types of WavesTransverse (all EM waves), seismic S wavesLongitudinal (Compressional)Sound, seismic P waves

  17. Transverse Wave Pulse One disturbance

  18. Transverse Periodic WavePulses Pass atRegular Intervals Particles vibrate perpendicular to energy transport. Trace out sine wave.

  19. Particle motion transverse wave.

  20. Longitudinal/Compressional WaveParticles compressed and expanded parallel to energy propagation.

  21. Another View

  22. Sound Waves ex of mechanical wave. Need medium to propagate. Vibrations in air molecules from vibrating tuning fork or vibrating string.

  23. Eardrumsound waves do work on eardrum

  24. Water WavesCombination of 2 Types

  25. Parts of a WaveWavelength (l) = distance btw Crests or TroughsMidpoint = Equilibrium Position

  26. Crests l

  27. Wave Pulse • Single disturbance Periodic Wave • Many pulses with regular l and period

  28. 1. State the difference between a mechanical and non-mechanical wave.

  29. Longitudinal Wave Parts

  30. Transverse & Longitudinal Waves can be represented by sine waves. Longitudinal Waves can be graphed as density of particles vs time. Then will graph as sine wave.

  31. Period (T) & Frequency (f) Period = time to complete one cycle of wave crests or troughs. Time for disturbance to travel 1l. Usually measured in seconds. T = 0.5 s/cycle.

  32. Frequency = Number of cycles in unit time. Inverse of period.Usually number per second called Hertz (Hz)Ex: 3 crests or cycles per second = 3s-1 or 3 hz

  33. f = how often T = how longf = a rate T = a time T & f are inversef = 1/T or T = 1/f.

  34. 2. A wave has a period T of 5.0 seconds. What is its frequency? 0.2 hz

  35. 3. A wave has a frequency of 100 Hz. What is its period? 0.01 s.

  36. 4. The wave below shows a “snapshot” that lasted 4.0 seconds. What is the frequency of the wave? 4.0 seconds 2 cycles/4 s = 0.5 Hz

  37. Wave Speed Speed/Velocity = d/t If a crest (or any point on a wave) moves 20m in 5 sec, v = 20m/5s = 4 m/s.

  38. Relationship of wave speed to wavelength(l) and frequency(f).v = d/t but for waves d = 1l occurs in time T (1period)so v = l/Tsince freq f =1/Tv =lf

  39. 5. A piano emits from 28 Hz to 4200 Hz. Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 m/s. l = 0.081 m to 12 m

  40. What determines wave speed? Only the medium through which it travels! • Wave speed is constant if medium is uniform. • Air at constant T and P. • Homogenous solids. • Water with constant T.

  41. In class pg 457 # 4.

  42. Velocity depends on medium’s properties: -EM waves all travel at c in a vacuum.- EM waves slower through materials. -Vibrations travel faster on tighter strings - slower on loose strings.-v sound constant in air but depends on temp/density of air.

  43. What causes the frequency?

  44. Wave song http://www.youtube.com/watch?v=EzU79Egl3-c

  45. Example Problems & Hwk.Read Text 12 - 3 • Read Text Chap 12-3 • Do pg 470 #23- 32, 35. • Write all out will collect.

  46. Do Now Text Pg 457 #2

  47. Quiz • 1. What is only factor that determines wave speed. • 2. Give a real life example of: • A longitudinal wave • A transverse wave. • Sketch a transverse wave. Label the • Wavelength • Amplitude • Equilibrium

  48. Wave Behaviors & Interactions Boundary Behavior & Wave Superposition

  49. When a wave enters a material with new properties it: • Goes through it without noticing • Slows down • Speeds up • Changes speed somehow.

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