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 that of closed pipe is made 3 times the original, the number of beats produced will be (Neglect end correction)

Step-by-step solution

Beat frequency analysis for organ pipes with length modifications Let v represent the speed of sound in air and L the original length of both pipes. The first overtone for an open pipe is f_ o1 = v/L , while for a closed pipe it is f_ c1 = 3v/4L . The initial beat frequency of 3 Hz gives |v/L - 3v/4L| = 3 , simplifying to v/(4L) = 3 and thus v/L = 12 . After modification, the open pipe length becomes L/3 and the closed pipe length becomes 3L . The fundamental frequencies are now f'_ o = v/(2 L/3) = 3v/(2L) for the