Match List-I with List-II regarding the standing waves in organ pipes of length L . List-I List-II (Wavelength ) (A) 1^ st overtone of a closed pipe (I) 4L 5 (B) 2^ nd overtone of an open pipe (II) L (C) 2^ nd overtone of a closed pipe (III) 4L 3 (D) 1^ st overtone of an open pipe (IV) 2L 3 Choose the correct answer from the options given below:

Step-by-step solution

For a closed organ pipe of length L , the allowed frequencies are odd harmonics: f = (2n+1) v 4L , where n = 0, 1, 2, is the overtone number. The wavelength is given by = v f = 4L 2n+1 . (A) 1^ st overtone of a closed pipe ( n=1 ): = 4L 3 . So, (A) matches with (III). (C) 2^ nd overtone of a closed pipe ( n=2 ): = 4L 5 . So, (C) matches with (I). For an open organ pipe of length L , all harmonics are present: f = (n+1) v 2L , where n = 0, 1, 2, is the overtone number. The wavelength is given by = v f = 2L n+1 . (B)