JEE Main 2026 · 24 January · evening · Single correct · +4 / −1

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5/x. The value of x is ____

  1. (a) 3
  2. (b) 2
  3. (c) 4
  4. (d) 1
Answer and solution

Answer (b) 2

Solution

Physics sir · 4 steps

Write both frequencies with the right end-correction-free formulas, set them equal, and the speed v cancels.

  1. Closed pipe. A pipe closed at one end has fundamental v/4L_c and only odd harmonics. Since 5 is odd, the fifth harmonic exists and is 5v/4L_c.
  2. Open pipe. A pipe open at both ends has fundamental (first harmonic) v/2Lₒ.
  3. Unison means equal. In unison means the two frequencies are the same. The speed of sound v is the same in both pipes, so it cancels.

    5v/4L_c = v/2Lₒ ⇒ L_c/Lₒ = (5 × 2)/4 = 5/2

  4. So. Comparing 5/2 with 5/x gives x = 2, which is option (b).

The idea to keep. Closed pipe: fₙ = nv/4L with odd n only. Open pipe: fₙ = nv/2L with every n. Set the frequencies equal and the speed of sound drops out.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 60 times in JEE Main since 2020. This question is from 2026.