The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5/x. The value of x i $s______.$
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Question

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5/x. The value of x i $s______.$

Options

G1 Physics · Accepted Answer

For a closed organ pipe, the fifth harmonic frequency is f(closed,5) = 5v/[4L(closed)]. For an open organ pipe, the first harmonic is f(open,1) = v/[2L(open)]. The two frequencies are in unison: 5v/[4L(closed)] = v/[2L(open)]. Cancel v and cross-multiply: 5L(open) = 2L(closed). Therefore, L(closed)/L(open) = 5/2. The question gives L(closed)/L(open) = 5/x. Hence, x = 2. Correct option: B.

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5/x. The value of x i s______.