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Vibrations and Waves

Vibrations and Waves. Repeating motion. Chapter 5. Vibrations. Just back and forth. pp. 104–106. compression. tension. Structure of Solids. Atoms and molecules connected by chemical bonds Considerable force needed to deform. small stretch. larger stretch. Elasticity of Solids.

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Vibrations and Waves

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  1. Vibrations and Waves Repeating motion Chapter 5

  2. Vibrations Just back and forth pp. 104–106

  3. compression tension Structure of Solids • Atoms and molecules connected by chemical bonds • Considerable force needed to deform

  4. small stretch larger stretch Elasticity of Solids Small deformations are proportional to force Hooke’s Law: uttensio, sic vis(as the pull, so the stretch) Robert Hooke, 1635–1703

  5. Restoring Force • A Hooke’s law force always draws the system back to equilibrium • If you push or pull a mass on a spring away from equilibrium, how will it move after release?

  6. Oscillation • Spring oscillations are repeating motion • So is uniform circular motion • Circular motion concepts are useful in describing any repeating motion • Cycle • Period and frequency • Phase angle • Trigonometric functions

  7. Oscillation amplitude y time period

  8. Oscillation Terms • Period = duration of one repeat • Frequency = repeats per unit time • Unit hertz = Hz = cycle/s • Amplitude = maximum excursion from equilibrium

  9. Period • Stiffness of spring • Mass of load • Not amplitude Determining factors

  10. L q m Simple Pendulum • Restoring force • Approximately Hooke’s law • Determining factors • length L • Gravitational field g • Not mass m!

  11. Waves Travel in space pp. 106–121

  12. Waves and Vibrations • Vibrations: Repeat in time • no net displacement of disturbance • no net displacement of medium • Waves: Repeat in time and space • wave travels • no net displacement of medium

  13. Wave Pulse in a Rope • Why does the pulse move? • What determines its speed? • What is happening inside the rope?

  14. a c b d What are the velocity and acceleration of the string particles at the following positions? Why? • middle (leading edge) • crest • middle (trailing edge) • trough Points to Ponder The particles of the string change their motion as the wave travels. What force accelerates them?

  15. crest l l trough Features of a Wave • Crest: high point • Trough: low point • Wavelength: crest-crest distance (m) • Period: crest-crest-timing (s)

  16. v A Features of a Wave • AmplitudeA: (crest height – trough height) / 2 • Frequencyf: repeats in a given time (cyc/s = Hz) • Velocityv: speed of crest motion (m/s)

  17. Relations between Features • Period T = 1 / f; Frequency f = 1 / T • Velocity v = l / T = lf • Wavelengthl=vT=v / f • Frequencyf = v / l; Period T = l / v

  18. Wave Pulse in a Slinky • Why does the pulse move? • What determines its speed? • What is happening inside the spring?

  19. Types of Waves • Motion of the medium is perpendicular to the direction the wave travels: transverse wave (example: string wave) • Motion of the medium is parallel to the direction the wave travels: longitudinal wave (examples: sound wave, slinky wave) • Animation

  20. Wave Refraction Direction changes to keep wave front continuous Source: University of Southampton, Institute for Sound and Vibration Research

  21. Example u = 1/2 u = 3/4 u = 1

  22. Ocean Wave Refraction

  23. Combining Waves

  24. result Adding Waves Together 3 0 –3

  25. Wave Interference • Constructive: Sum of waves has increased amplitude • Destructive: Sum of waves has decreased amplitude • Two-wave simulation

  26. Wave Refraction Direction changes to keep wave front continuous Source: University of Southampton, Institute for Sound and Vibration Research

  27. Beats • Waves of similar frequency combine to give alternating times of constructive and destructive interference

  28. 2-D Wave Interference • interference patterns • http://www.falstad.com/ripple/

  29. Standing Waves • Add a wave to an identical wave traveling in the opposite direction • (Its reflection) • Medium vibrates, but waves don’t travel • Nodes: positions of zero variation • Antinodes: positions of maximum variation

  30. Sound Longitudinal wave in 3 dimensions pp. 111–121

  31. Pipes: “Closed” and “Open” Tube Modes Source: Halliday, Resnick, and Walker, Fundamentals of Physics, 2003, p 419.

  32. Harmonic Sequence • Western musical scale and harmonies are based on overtone series

  33. Doppler Effect Distance and time § 16.9

  34. Moving Source or Detector • Source: successive wave fronts do not emanate from the same place • Detector: successive wave fronts are not detected at the same place • Simulation: http://physics.bu.edu/~duffy/HTML5/doppler.html

  35. vD vS v 3 2 1 0 D Moving Source or Detector

  36. Two-Dimensional Waves • Ocean waves, earthquake surface waves • Wave types animations • Membrane standing waves animations

  37. Water Waves • Restoring force is gravity • Fastest in deep water, slow in shallow water • Breaking and refractive behavior in shallow water • Speed depends on wavelength • Very complicated behavior!

  38. Shoaling and Breaking • Waves slow in shallows by shore • Wavelength shortens and amplitude rises • Troughs move slower than crests • Crests fall forward

  39. Example u = 1/2 u = 3/4 u = 1

  40. Ocean Wave Refraction

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