Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If an open organ pipe is dipped vertically in water to exactly half of its physical length, its fundamental frequency will decrease when end correction is considered. Reason (R): The acoustic length of the resulting closed pipe is exactly half of the acoustic length of the original open pipe. In th

Step-by-step solution

For an open pipe of physical length L and radius r , the end correction is e at both ends. The acoustic length is L_ eq = L + 2e . The fundamental frequency is f = v 2(L + 2e) . When dipped in water to half its length, it becomes a closed pipe of physical length L/2 . The end correction e applies only to the upper open end. The new acoustic length is L'_ eq = L 2 + e = L + 2e 2 . This makes the Reason (R) true. The new fundamental frequency is f' = v 4L'_ eq = v 4 ( L + 2e 2 ) = v 2(L + 2e) = f . The fundamental fr