The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe 2 ~m long. The length of the open pipe is

Step-by-step solution

Let L be the length of the open pipe. The fundamental frequency of the open pipe is given by v= v 2 L , v= velocity of sound in air The second overtone of the open pipe has a frequency 3 v_O= 3 v 2 L_O ~Hz The length of the closed pipe L_C=2 ~m . The fundamental frequency of the closed pipe is given by v= v 4 L The first overtone of the closed pipe has a frequency 3 v_C= 3 v 4 L_C = 3 v 4 2 = 3 v 8 ~Hz Now 3 v_O=3 v_C or 3 v 2 L_O = 3 v 8 or 2 L_O=8 or L_O=4 ~m