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Grade 11 Math Lab: Transcendence & Limits FREE
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Phase Shift & Wave Superposition
Learning Objectives
- Calculate phase shifts
- Add sinusoidal functions
- Analyze beat frequencies
Key Concepts
Phase Shift
Horizontal displacement C in y = sin(x - C)
Superposition
Sum of two waves creates interference patterns
Theory
**Phase shift:** In y = A·sin(B(x - C)):
- C > 0: shift right
- C < 0: shift left
**Superposition:** When waves combine:
- Same phase → Constructive (louder/bigger)
- Opposite phase → Destructive (cancellation)
**Sum-to-product:** sinA + sinB = 2·sin((A+B)/2)·cos((A-B)/2)
Examples
Phase shift of y = sin(2x - π)
Solution: y = sin(2(x - π/2)). Shift right π/2.