Interference and Superposition

Summary

• Objects made of matter
  • are material, tangible, corporeal, and definite
  • cannot occupy the same place at the same time
  • exchange energy and momentum during collisions
• Waves
  • are immaterial, intangible, incorporeal, and indefinite
  • can occupy the same place at the same time
  • pass through each other without effect
• Principle of Linear Superposition
  • When waves occupy the same place at the same time they interfere or superpose.
  • The resulting disturbance is the sum of the individual disturbances at every point in space and time.
• Phase (φ, the Greek letter phi)
  • The stage of development of a periodic process
  • Two points on a wave with the same phase have the same…
    • quantity of disturbance (ex. displacement)
    • rate of change of disturbance (ex. velocity).

    

    

  • Phase is an angular quantity.
    • The SI unit of phase is the radian (symbol rad), which is itself a unitless ratio.

      [rad = m/m = Pa/Pa = (V/m)/(V/m) = etc.]

    • The degree is a non-SI unit that is acceptable for phase.

      [360° = 2π rad = 1 cycle]

  • Range of phase
    • Adjacent points in phase are separated by one complete cycle, 2π radian, or 360°.
      • Also true for whole number multiples of a cycle, 2π radian, or 360°.
    • Adjacent points out of phase are separated by half a cycle, π radian, or 180°.
      • Also true for odd number multiples of half a cycle, π radian, or 180°.

    

• Range of interference
  • Constructive interference occurs when two waves meet with the same phase (in phase) and a maximum amplitude results.
  • Destructive interference occurs when two waves meet with opposite phase (out of phase) and a minimum amplitude results.

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