The Physics
Hypertextbook
Opus in profectus

# Interference and Superposition

## Summary

• 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) and
• 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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