A closed organ pipe is vibrating in a mode that produces exactly 3 nodes and 3 antinodes. The frequency of this mode is equal to the fundamental frequency of an open organ pipe of length 50 cm . The length of the closed organ pipe is ________ cm .

Step-by-step solution

In a closed organ pipe, a standing wave with 3 nodes and 3 antinodes corresponds to the 5^ th harmonic (or 2^ nd overtone). The frequency of this mode is given by: f_c = 5v 4L_c The fundamental frequency of an open organ pipe of length L_o is: f_o = v 2L_o Given that these two frequencies are equal: 5v 4L_c = v 2L_o Substitute L_o = 50 cm : 5 4L_c = 1 2 50 5 4L_c = 1 100 4L_c = 500 L_c = 125 cm . Answer: 125