Superposition and Phasor Addition
The superposition principle states that in a linear medium the net disturbance equals the algebraic sum of individual disturbances; equal-frequency sinusoids combine through vector addition of their complex amplitudes.
Why this shows up in the exam
Resultant amplitude and phase · Combining several harmonic sources · Separating carrier and envelope forms
Learn the idea
Overlapping linear waves add displacement by displacement, including their relative phases. Represent each same-frequency sinusoid by an arrow; vector addition of those arrows gives the resultant amplitude and phase without expanding every trigonometric term.
🧠 Memory hook: Add phase arrows, not amplitudes blindly.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- A_R² = A1² + A2² + 2 A1 A2 cos(delta) — resultant amplitude for two same-frequency waves
- tan(phi) = A2 sin(delta)/(A1 + A2 cos(delta)) — resultant phase relative to the first wave
How to approach it
- 1Confirm equal angular frequencies
- 2Choose one wave as phase reference
- 3Add components and place the resultant in the correct quadrant
Common slip-ups that cost marks
- •Adding amplitudes when phases differ
- •Adding intensities for coherent sources
- •Using the two-wave formula for different frequencies
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A mass of 1 kg is attached to a spring of force constant 100 N/m. Find the angular frequency of small oscillations.
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