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Match List-I with List-II regarding the number of displacement nodes in different resonant modes of organ pipes. List-I List-II A. 3^ rd overtone of an open pipe I. 6 nodes B. 2^ nd overtone of a closed pipe II. 4 nodes C. 5^ th overtone of a closed pipe III. 2 nodes D. 2^ nd harmonic of an open pipe IV. 3 nodes Choose the correct answer from the options given below:

Options

  1. AA-IV, B-III, C-I, D-II
  2. BA-II, B-III, C-I, D-IV
  3. CA-II, B-IV, C-I, D-III
  4. DA-I, B-IV, C-II, D-III

Correct answer

C. A-II, B-IV, C-I, D-III

Step-by-step solution

For an open organ pipe, the n^ th overtone corresponds to the (n+1)^ th harmonic, which contains (n+1) displacement nodes. For a closed organ pipe, the n^ th overtone corresponds to the (2n+1)^ th harmonic. The number of displacement nodes in the q^ th harmonic is q+1 2 . Therefore, the n^ th overtone has (2n+1)+1 2 = n+1 displacement nodes. A. 3^ rd overtone of an open pipe is the 4^ th harmonic, which has 4 nodes. (A II) B. 2^ nd overtone of a closed pipe is the 5^ th harmonic, which has 5+1 2 = 3 nodes. (B IV) C

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