The frequency of fourth overtone of a closed pipe is in unison with the fifth overtone of an open pipe. The ratio of length of closed pipe to that of open pipe is

Step-by-step solution

The fourth overtone of a closed pipe is in unison with the fifth overtone of an open pipe, so their frequencies are equal. For a closed pipe, the n^ th overtone has frequency f_c = (2n+1) v 4L_c . Setting n=4 gives f_ c = 9 v 4L_c . For an open pipe, the n^ th overtone has frequency f_o = (n+1) v 2L_o . With n=5 , f_o = 6 v 2L_o . Equating the frequencies yields: 9 v 4L_c = 6 v 2L_o Cancel v and simplify: 9 4L_c = 3 L_o Rearranging gives L_c L_o = 9 4 1 3 = 3 4 . The ratio of lengths is L_c : L_o = 3 : 4 .