When open pipe is closed from one end then second overtone of closed pipe is higher in frequency by 100 Hz than first overtone of open pipe. The fundamental frequency of open end pipe will be (Neglect end correction)

Step-by-step solution

Let the length of the pipe be L and the speed of sound be v . The fundamental frequency of the open pipe is f_o = v 2L . The first overtone of the open pipe is f_ o1 = 2f_o = v L . When the pipe is closed at one end, its fundamental frequency becomes f_c = v 4L . The second overtone of the closed pipe corresponds to the fifth harmonic, so f_ c2 = 5f_c = 5v 4L . According to the given condition, f_ c2 - f_ o1 = 100 . 5v 4L - v L = 100 v 4L = 100 The fundamental frequency of the open pipe is f_o = v 2L = 2 ( v 4L ) .