A closed organ pipe and an open organ pipe have the same physical length of 30 cm and the same radius of 5 cm . Taking the end correction into account, what is the ratio of the fundamental frequency of the closed pipe to that of the open pipe? (Assume the end correction e = 0.6r , where r is the radius of the pipe)

Step-by-step solution

For a closed organ pipe, the end correction is applied at one end. Effective length of the closed pipe, L_ c = L + 0.6r L_ c = 30 + 0.6(5) = 33 cm For an open organ pipe, the end correction is applied at both ends. Effective length of the open pipe, L_ o = L + 2(0.6r) = L + 1.2r L_ o = 30 + 1.2(5) = 36 cm The fundamental frequency of a closed pipe is given by f_ c = v 4L_ c f_ c = v 4 33 = v 132 The fundamental frequency of an open pipe is given by f_ o = v 2L_ o f_ o = v 2 36 = v 72 The ratio of their fundamental