Which of the following statements about waves in pipes is correct?

Step 1: Analyze the question We need to pick the true statement about resonance in open and closed pipes.

Step 2: Key concepts

• Closed pipe (one end closed): there is a node at the closed end and an antinode at the open end. Only odd harmonics are possible: f₁, 3f₁, 5f₁, … The frequencies are f = nv/4L, where n = 1, 3, 5, …
• Open pipe (both ends open): there is an antinode at each end. All harmonics are possible: f₁, 2f₁, 3f₁, … The frequencies are f = nv/2L, where n = 1, 2, 3, …
• End correction (e): the antinode forms slightly beyond the open end of the pipe. A closed pipe has one open end, so it has one end correction. An open pipe has two open ends, so it has two end corrections.

Step 3: Check each option

• A. Wrong. An open pipe has two open ends, so it has two end corrections (L + 2e).
• B. Wrong. A closed pipe has only one open end, so it has one end correction (L + e).
• C. Correct. A closed pipe has a node at one end and an antinode at the other, which allows only odd multiples of the fundamental (1st, 3rd, 5th, …).
• D. Wrong. Even harmonics are not possible in a closed pipe.

Answer: C

Tip: Remember "Closed = Corner of odd". Closed pipes give odd harmonics only, while open pipes give all harmonics. Also count the open ends to find the number of end corrections: one open end means one correction, and two open ends mean two corrections.