An open organ pipe and a closed organ pipe have the same inner radius of 5 cm . The fundamental frequency of the open pipe is found to be equal to the first overtone frequency of the closed pipe. If the physical length of the open pipe is 24 cm , what is the physical length of the closed pipe? (Consider the end correction for the pipes)

Step-by-step solution

The end correction e for a pipe of radius r is given by e = 0.6r . Given r = 5 cm , the end correction is e = 0.6 5 = 3 cm . For the open organ pipe, end correction is applied at both ends. Its effective length is: L_ o, eff = L_o + 2e = 24 + 2(3) = 30 cm . The fundamental frequency of the open pipe is: f_ o,1 = v 2L_ o, eff = v 2 30 = v 60 For the closed organ pipe, end correction is applied at one end only. Its effective length is: L_ c, eff = L_c + e = L_c + 3 The first overtone of a closed pipe corresponds to t