An air column is of length 17 cm . The ratio of frequencies of 5^ th overtone if the air column is closed at one end to that open at both ends is (velocity of sound in air =340 ~ms ⁻¹ )

Step-by-step solution

Key Concepts For a closed organ pipe, only odd harmonics exist with frequencies f_n = (2n-1) v 4L where n=1,2,3, ; the k^ th overtone corresponds to n = k+1 . For an open organ pipe, all harmonics are present with frequencies f_n = n v 2L , where the k^ th overtone corresponds to n = k+1 . The fifth overtone in a closed pipe gives n=6 , so f_ closed = (2 6-1) v 4L = 11v 4L . The fifth overtone in an open pipe gives n=6 , so f_ open = 6 v 2L = 3v L . The ratio is f_ closed f_ open = 11v 4L 3v L = 11v 4L L 3v = 11 12