Resonance Column and End Correction
In a narrow resonance tube closed by water, the effective air-column length is L+e and resonances obey L_n+e=(2n-1)lambda/4, so consecutive observed lengths differ by lambda/2.
Why this shows up in the exam
Measuring sound speed · Finding end correction · Predicting later resonant lengths
Learn the idea
Successive resonant lengths in a one-open-end column differ by half a wavelength, cancelling the end correction. The open end behaves slightly beyond the tube, shifting every resonance by nearly the same amount; subtracting successive lengths removes that unknown shift.
🧠 Memory hook: Subtract resonant lengths to make end correction disappear.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- L_n + e = (2n-1)lambda/4 — resonance condition with one open end
- lambda = 2(L_next - L_prev) — wavelength from successive resonances
- e approximately 0.6r — common narrow-tube end-correction estimate
How to approach it
- 1Confirm the tube has one effective closed end
- 2Label the resonance order
- 3Use differences first, then recover end correction if required
Common slip-ups that cost marks
- •Treating each observed length as exactly lambda/4
- •Using diameter where the correction formula expects radius
- •Assuming non-successive resonances differ by lambda/2
🌟 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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