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Stage 1 – Page 7 : Reflection of Waves (JEE / Intermediate Level)
1️⃣ What is Reflection of a Wave?
Reflection of a wave occurs when a travelling wave strikes a boundary and returns back into the same medium.
The nature of reflection depends on the type of boundary.
2️⃣ Types of Boundaries
- Fixed (Rigid) End
- Free End
3️⃣ Reflection at a Fixed End
At a fixed end, the particle at the boundary cannot move.
- Displacement at fixed end = 0
- Reflected wave undergoes phase change of π (180°)
Important Result:
Crest reflects as trough and trough reflects as crest
Mathematical Insight:
Incident wave: y = A sin (ωt − kx)
Reflected wave: y = −A sin (ωt + kx)
4️⃣ Reflection at a Free End
At a free end, the particle at the boundary is free to move.
- Displacement is maximum at boundary
- No phase change on reflection
Important Result:
Crest reflects as crest and trough reflects as trough
Mathematical Insight:
Incident wave: y = A sin (ωt − kx)
Reflected wave: y = A sin (ωt + kx)
5️⃣ Phase Change Summary (Very Important)
| Boundary | Phase Change | Crest → |
|---|---|---|
| Fixed End | π (180°) | Trough |
| Free End | 0 | Crest |
6️⃣ Velocity & Frequency on Reflection
- Speed of wave remains same
- Frequency remains same
- Wavelength remains same
JEE Reminder:
Only phase and direction change, not speed or frequency
7️⃣ Common JEE Traps
- Assuming phase change at free end ❌
- Mixing up fixed and free end conditions ❌
- Changing wavelength unnecessarily ❌
8️⃣ Practical Examples
- String tied to a wall → Fixed end
- String attached to a ring → Free end
- Water waves at rigid boundary → Fixed type
9️⃣ One-Line Memory Trick
Fixed = Flip (Phase change)
Free = Friendly (No phase change)
🔟 Quick Revision Box
- Fixed end → π phase change
- Free end → No phase change
- Speed & frequency unchanged
Stage 1 – Page 7 Completed ✅
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