Reflection, Transmission, and Wave Impedance
At a junction, continuity conditions determine reflection and transmission amplitudes through the characteristic impedances of the two media; reflected displacement reverses phase when the second medium presents the larger effective impedance.
Why this shows up in the exam
Joined-string reflections · Open- and closed-end pulse reflection · Energy sharing at material boundaries
Learn the idea
A boundary divides a wave into reflected and transmitted parts, with phase reversal controlled by impedance contrast. A wave meeting a heavier or more constrained region reflects like a fixed end, while a lighter or freer region reflects without displacement inversion; frequency remains unchanged.
🧠 Memory hook: Higher impedance reflects displacement upside down.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- r = (Z1 - Z2)/(Z1 + Z2) — displacement-amplitude reflection coefficient for a string junction under a consistent convention
- t = 2 Z1/(Z1 + Z2) — corresponding displacement transmission coefficient convention
- Z_string = sqrt(T mu) — characteristic transverse-wave impedance of an ideal string
How to approach it
- 1Identify the incident side and both impedances
- 2Apply boundary continuity with a stated sign convention
- 3Check limiting cases of a free end and a rigid end
Common slip-ups that cost marks
- •Using amplitude coefficients as energy fractions
- •Changing frequency at the boundary
- •Applying a fixed-end phase reversal to every reflection
🌟 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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