The closed and open organ pipe have same length and when they are vibrating simultaneously in first overtone produce 3 beats. The length of open pipe is made ( 1 3 )^ rd and closed pipe is made 3 times the original, the number of beats produced will be neglect end correction

Step-by-step solution

Let the original length of both pipes be L and the speed of sound be v . The frequency of the first overtone of the open pipe is f_ o1 = 2v 2L = v L . The frequency of the first overtone of the closed pipe is f_ c1 = 3v 4L . Given that they produce 3 beats per second: f_ o1 - f_ c1 = 3 v L - 3v 4L = 3 v 4L = 3 v L = 12 When the length of the open pipe is made L 3 , its new fundamental frequency is: f_ o ' = v 2 ( L 3 ) = 3v 2L = 3 2 12 = 18 When the length of the closed pipe is made 3L , its new fundamental frequen