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Stage 1 – Page 6 : Wave Equation, Phase & Phase Difference
1️⃣ What is a Wave Equation?
A wave equation describes the displacement of a particle in a wave as a function of position and time.
Standard Progressive Wave Equation:
y(x,t) = A sin (ωt − kx + φ)
2️⃣ Meaning of Each Term
| Symbol | Meaning |
|---|---|
| A | Amplitude (maximum displacement) |
| ω | Angular frequency (2πf) |
| k | Wave number (2π/λ) |
| φ | Initial phase constant |
3️⃣ Direction of Wave Propagation
- y = A sin (ωt − kx) → wave moves in +x direction
- y = A sin (ωt + kx) → wave moves in −x direction
JEE Trick:
Sign of kx decides direction, NOT the sign of ωt
4️⃣ Phase of a Wave
The quantity inside sine/cosine is called the phase.
Phase = (ωt − kx + φ)
Phase tells us the state of vibration of a particle.
5️⃣ Phase Difference Between Two Particles
Phase difference depends on:
- Difference in position
- Difference in time
Phase difference due to distance:
Δφ = (2π / λ) × Δx
Phase difference due to time:
Δφ = (2π / T) × Δt
6️⃣ Special Phase Conditions (Very Important)
| Condition | Phase Difference |
|---|---|
| Same phase | 0, 2π, 4π … |
| Opposite phase | π, 3π … |
| Quarter phase | π/2 |
7️⃣ Relation Between Wave Parameters
v = ω / k = fλ
- Speed depends on medium
- Frequency decided by source
- Wavelength adjusts accordingly
8️⃣ Phase Velocity vs Particle Velocity
- Phase velocity → speed of wave pattern (v = ω/k)
- Particle velocity → speed of medium particle
Common Mistake:
Particle velocity ≠ Wave velocity
9️⃣ JEE Numerical Tip
- Write full wave equation first
- Compare with standard form
- Extract A, ω, k, φ carefully
🔟 Quick Revision Box
- Phase controls vibration state
- Distance controls phase difference
- Direction decided by sign of kx
Stage 1 – Page 6 Completed ✅
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