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 $(2 n + 1)^{th}$ 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 $y = 6$

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