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Lesson 06
Lesson 06
Interference
When waves meet, their relative phase determines the result.
When two waves occupy the same region, their effects combine. Waves that are aligned reinforce one another. Waves that are opposed can reduce or cancel one another.
Wave A · amp 1.00Wave B · amp 1.00Combined · peak 0.00
ΔΦ = 0°
Live explanation
What is happening?
The waves are opposed and strongly cancel.
Controls
Shape the waves
0°
1.00
1.00
2.0
What to notice
- Aligned waves reinforce one another.
- Opposed waves can cancel.
- Cancellation is complete only when amplitudes match.
- Relative phase determines the combined result.
- Interference does not destroy the original waves.
Show the maths
Optional — the intuition already covers the important ideas.
y₁ = A₁ sin(k x − ω t)
y₂ = A₂ sin(k x − ω t + ΔΦ)
y = y₁ + y₂
y₂ = A₂ sin(k x − ω t + ΔΦ)
y = y₁ + y₂
For equal amplitudes the combined peak has magnitude A_result = 2A cos(ΔΦ / 2) — zero when ΔΦ = 180°, maximum when ΔΦ = 0°.
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