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]
- The SI unit of phase is the radian (symbol rad), which is itself a unitless ratio.
- 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°.
- Adjacent points in phase are separated by one complete cycle, 2π radian, or 360°.
- 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.