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NEETPhysicsWaves and Sound

Match List-I with List-II for organ pipes of length L . List-I (Mode of vibration) List-II (Wavelength ) (A) Fundamental mode of a closed pipe (I) L (B) Fundamental mode of an open pipe (II) 4L 3 (C) First overtone of a closed pipe (III) 2L (D) First overtone of an open pipe (IV) 4L Choose the correct answer from the options given below:

Options

  1. A(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
  2. B(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
  3. C(A)-(IV), (B)-(III), (C)-(II), (D)-(I)
  4. D(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

Correct answer

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

Step-by-step solution

For a closed pipe of length L , the allowed wavelengths are given by L = n 4 where n = 1, 3, 5, For the fundamental mode ( n = 1 ), = 4L . For the first overtone ( n = 3 ), = 4L 3 . For an open pipe of length L , the allowed wavelengths are given by L = n 2 where n = 1, 2, 3, For the fundamental mode ( n = 1 ), = 2L . For the first overtone ( n = 2 ), = L . Therefore, the correct matching is (A)-(IV), (B)-(III), (C)-(II), (D)-(I). Answer: (A)-(IV), (B)-(III), (C)-(II), (D)-(I)

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