gen-define-phase-and-antiphase-and-give-one-short-worked-example-2488

Define phase and antiphase and give one short worked example.

# Phase and Antiphase ## Definitions **Phase**: Two waves are **in phase** when their crests and troughs align perfectly. They reach their maximum and minimum values at the same time. The phase difference is 0° (or any multiple of 360°). **Antiphase**: Two waves are in **antiphase** (or out of phase) when the crest of one wave aligns with the trough of another. The phase difference is 180° (or any odd multiple of 180°). ## Worked Example Consider two sound waves from speakers: - Wave 1: y₁ = 2sin(ωt) - Wave 2: y₂ = 2sin(ωt + φ) **Case 1 - In Phase (φ = 0°):** - Total displacement: y = y₁ + y₂ = 2sin(ωt) + 2sin(ωt) = 4sin(ωt) - **Result**: Constructive interference - amplitude doubles from 2 to 4 **Case 2 - Antiphase (φ = 180°):** - Wave 2 becomes: y₂ = 2sin(ωt + 180°) = -2sin(ωt) - Total displacement: y = 2sin(ωt) + (-2sin(ωt)) = 0 - **Result**: Destructive interference - waves cancel completely This is why you might find "dead spots" when standing between two speakers playing the same tone - you're at a location where the waves arrive in antiphase.