The fundamental frequency of a closed pipe of length L is equal to the second overtone of a pipe open at both the ends of length (XL). The value of X is (Neglect end correction)

Step-by-step solution

The fundamental frequency of a closed pipe of length L is given by f_c = v 4L . For an open pipe of length L' , the second overtone occurs at f_ o,2nd = 3v 2L' . Equating the frequencies with L' = XL yields: v 4L = 3v 2XL Canceling v and L from both sides gives 1 4 = 3 2X . Solving for X produces 2X = 12 , so X = 6 . The value of X is 6 , corresponding to option C .