Waves

• 4.24.15 Watch This Doppler
• Read Chapter on waves:  OK look at the pictures!
• 4.17.15 Watch Videos
• Complete Practice pages on superposition
• 16. Harmonic Motion
  The music and mathematics of periodic motion.
  17. Resonance (most important)
  Why a swaying bridge collapses with a high wind, and why a wine glass shatters with a higher octave.
  18. Waves
  With an analysis of simple harmonic motion and a stroke of genius, Newton extended mechanics to the propagation of sound.
   

• Objectives

  After studying the material of this chapter, you should be able to:
  1. State the conditions required to produce SHM.
  2. Determine the period of motion of an object of mass m attached to a spring of force constant k.
  3. Calculate the velocity, acceleration, potential, and kinetic energy at any point in the motion of an object undergoing SHM.
  4. Write equations for displacement, velocity, and acceleration as sinusoidal functions of time for an object undergoing SHM if the amplitude and angular velocity of the motion are known. Use these equations to determine the displacement, velocity, and acceleration at a particular moment of time.
  5. Determine the period of a simple pendulum of length L.
  6. State the conditions necessary for resonance. Give examples of instances where resonance is a) beneficial and b) destructive. Explain how damped harmonic motion can be achieved to prevent destructive resonance.
  7. Distinguish between a longitudinal wave and a transverse wave and give examples of each type of wave.
  8. Calculate the speed of longitudinal waves through liquids and solids and the speed of transverse waves in ropes and strings.
  9. Calculate the energy transmitted by a wave, the power of a wave and the intensity of a wave, across a unit area A.
  10. Describe wave reflection from a barrier, refraction as the wave travels from one medium into another, constructive and destructive interference as waves overlap, and diffraction of waves as they pass around an obstacle.
  11. Explain how a standing wave can be produced in a string or rope and calculate the harmonic frequencies needed to produce standing waves in string instruments.