Wave Interference Principles

Overview

This lecture covers the principles of wave interference, focusing on constructive and destructive interference, phase differences, and how path length differences affect resulting wave patterns for any type of wave.

Wave Interference Basics

• Wave interference occurs when two waves overlap in the same medium.
• The total wave at any point is the sum of the individual wave values at that point.

Constructive Interference

• Constructive interference happens when the peaks and valleys of two waves align (in phase).
• The result is a wave with larger amplitude, twice as loud for sound waves.
• Occurs when the path length difference (Δx) is an integer multiple of the wavelength (nλ, where n = 0, 1, 2, …).

Destructive Interference

• Destructive interference happens when a peak from one wave aligns with a valley from the other (180° out of phase or π phase shift).
• The result is cancellation, yielding no wave (silence for sound).
• Occurs when the path length difference (Δx) is an odd half-integer multiple of the wavelength ((2n+1)λ/2).

Phase Shift and Path Length

• A 180° phase shift (π) can be created by swapping the polarity of a speaker's terminals.
• Path length difference (Δx) is the difference in distance traveled by two waves to the same point.
• Moving one source 1/2 a wavelength ahead causes destructive interference; moving it a full wavelength ahead restores constructive interference.
• For sources initially out of phase (π shift), integer wavelength difference causes destructive, and half-integer causes constructive interference (opposite to in-phase case).

General Interference Rules

• Interference rules apply to all types of waves: sound, light, water, etc.
• The combination of path length difference and any phase shift determines constructive or destructive interference.

Key Terms & Definitions

• Interference — the phenomenon when two waves overlap and combine.
• Constructive Interference — when waves add to create a larger amplitude.
• Destructive Interference — when waves cancel each other, producing no amplitude.
• In phase — waves’ peaks and valleys align.
• Out of phase (π or 180° shift) — one wave's peak coincides with another’s valley.
• Path length difference (Δx) — the difference in distance two waves travel to a point.
• Wavelength (λ) — the length of one full cycle of a wave.

Action Items / Next Steps

• Practice identifying constructive vs. destructive interference given path length and phase difference.
• Review applications of interference (e.g., noise-canceling headphones, double slit experiments).
• Prepare examples showing calculation of interference outcomes for test review.