The open end of a pipe is not a perfect antinode. The antinode actually forms a little OUTSIDE the tube, so the real vibrating air column is longer than the measured length. This extra bit is the end correction, e = 0.6r (r = tube radius). Memory hook: "air spills out" — the antinode leaks past the open mouth, so add a little to L. For NEET, use effective length L + e for a closed pipe and L + 2e for an open pipe.
The vibrating antinode of a closed pipe sits a small distance e = 0.6r beyond the open rim, so the effective air column is L + e. Using two resonance lengths lets e cancel, giving an accurate speed of sound.
Your doubts, answered
Why does the antinode form OUTSIDE the open end and not exactly at the rim?
At the open end the air is free to move and pushes a little into the outside atmosphere before it turns around. So the point of maximum vibration (the antinode) sits slightly beyond the physical opening, not exactly at the rim. Because of this the air that actually vibrates is a bit longer than the tube you measured. We correct for this small extra length by adding the end correction e.
What is the formula for end correction and what does it depend on?
For one open end, end correction e = 0.6 r, where r is the radius of the tube (sometimes written e = 0.3 D using diameter D = 2r, since 0.6 r = 0.3 D). It depends ONLY on how wide the tube is, not on its length, not on the frequency, and not on the harmonic. A wider tube has a larger end correction.
How is effective length different for a closed pipe and an open pipe?
A closed (one-end) pipe has just ONE open end, so effective length = L + e. An open (both-ends) pipe has TWO open ends, so you add the correction twice: effective length = L + 2e. Always put the EFFECTIVE length into the frequency formula, not the measured length, when end correction is asked.
How do you cancel end correction using two resonance lengths?
In a resonance tube, the first two resonance lengths (for the same tuning fork) are L1 + e = lambda/4 and L2 + e = 3 lambda/4. Subtract the first from the second: L2 - L1 = lambda/2, so lambda = 2(L2 - L1). The end correction e cancels out. This is why the experiment uses the DIFFERENCE of two lengths to find speed of sound accurately.
⚠️ The NEET trap ✗ Students plug the measured tube length L straight into f = v/(4L) and forget the antinode sits outside the tube. ✓ When end correction is mentioned, use the EFFECTIVE length: closed pipe L + e, open pipe L + 2e, with e = 0.6r. In the two-resonance-length method e cancels, so lambda = 2(L2 - L1). 🧠 Open end = antinode LEAKS OUT. Closed pipe adds e once, open pipe adds e twice.
Real NEET questions
NEET 2016
An air column closed at one end and open at the other resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column that resonates with the same tuning fork is:
A · 66.7 cm
B · 100 cm
C · 150 cm ✓
D · 200 cm
Solution: This is the resonance-column setup where end correction lives (here ideal, e neglected). A closed pipe resonates at odd multiples of lambda/4. Smallest length is the fundamental: lambda/4 = 50 cm, so lambda = 200 cm. Next resonance is the 3rd harmonic at 3 lambda/4 = 3 x 50 = 150 cm. Note: if end correction e were included, both lengths carry +e and the DIFFERENCE 150 - 50 = 100 cm = lambda/2 would give lambda directly with e cancelled.
Solved Waves NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
