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Chapter 3 Transverse standing waves Resonance and the Overtone Series Mersenne s laws Longitudinal standing waves Other

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Chapter 3 Transverse standing waves Resonance and the Overtone Series Mersenne s laws Longitudinal standing waves Other

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    1. Chapter 3 Transverse standing waves Resonance and the Overtone Series Mersenne’s laws Longitudinal standing waves Other standing waves and applications

    2. Identical waves moving in opposite directions

    3. Motion of the spring

    4. Motion of point along the spring

    5. Stretched strings End effects

    6. Standing wave representation

    7. Impossible “standing waves”

    8. Standing Waves in a Stretched String

    9. Stretched String Frequencies and Wavelengths f = v / ? N = 1 ? = 2L f = v/2L = f1 N = 2 ? = L f = v/L = 2f1 N = 3 ? = 2L/3 f = 3v/2L = 3f1 N = 4 ? = L/2 f = 2v/L = 4f1 N = 5 ? = 2L/5 f = 5v/2L = 5f1 N = 6 ? = L/3 f = 3v/L = 6f1

    10. Notes of the Overtone Series

    11. Mersenne’s Laws

    12. Mersenne’s First Law f a 1/L F and W constant If L => 2 L then f => ?? If L => L / 2 then f => ??

    18. Rope Wave Example 110 grams => 3 loops (frequency f) What happens with 990 grams?

    21. Nanoguitar

    22. Nanoguitar

    23. Longitudinal Standing Waves

    24. Kundt’s tube

    26. “End Effect” Experiment

    27. End at right “open”

    28. End configurations for tubes 1. Phase change at open and closed ends

    30. Open Tubes

    31. “Open” Tube Frequencies and Wavelengths f = v / ? N = 1 ? = 2Lo f = v/2Lo = fo N = 2 ? = Lo f = v/Lo = 2fo N = 3 ? = 2Lo/3 f = 3v/2Lo = 3fo N = 4 ? = 2Lo/4 f = 4v/2Lo = 4fo N = 5 ? = 2Lo/5 f = 5v/2Lo = 5fo N = 6 ? = 2Lo/6 f = 6v/2Lo = 6fo

    34. Open and Closed Tube Comparison

    35. Tube Quiz

    36. Fundamental Frequency Open and Closed Tubes If Lo = Lc what is fo : fc If Lo = 2Lc what is fo : fc

    37. Closed Tube Resonances

    38. Applications to Musical Instruments

    39. The Flute

    40. The Recorder

    42. The Clarinet

    44. The Saxophone

    45. The Trumpet

    46. Various Standing Waves Flame Tube Aluminum Rod Velocity of Sound in Aluminum Chladni Plates (photos)

    47. Chladni Plates

    48. Violin Body Vibrations

    49. Standing Waves in a Membrane Rectangular Membrane Applet Circular Membrane Applet

    50. Beaker Breaker using sound wave resonance

    51. Tacoma Narrows Bridge Collapse

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