An organ pipe closed at one end produces 5^ th overtone of an air column. It is found that air in the pipe is vibrating with x nodes and y antinodes. The value of x and y is

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For an organ pipe closed at one end, the fundamental mode ( 0^ th overtone) consists of 1 node and 1 antinode. The n^ th overtone corresponds to the (2n+1)^ th harmonic. The number of nodes in the n^ th overtone is n + 1 . The number of antinodes in the n^ th overtone is n + 1 . For the 5^ th overtone, n = 5 . Number of nodes, x = 5 + 1 = 6 . Number of antinodes, y = 5 + 1 = 6 . Answer: x = 6 and y = 6