The first overtone of a closed organ pipe is in unison with the fundamental frequency of an open organ pipe. The ratio of the length of the closed pipe to the length of the open pipe is:

Step-by-step solution

The fundamental frequency of an open pipe of length L_o is given by f_o = v 2L_o . The first overtone of a closed pipe of length L_c corresponds to the third harmonic, which is given by f_c = 3v 4L_c . Given that these two frequencies are equal (in unison): 3v 4L_c = v 2L_o Rearranging to find the ratio of their lengths: L_c L_o = 3 4 2 = 3 2 Thus, the ratio of the length of the closed pipe to the length of the open pipe is 3:2 . Answer: 3:2