Q166 / 200 · MHT CET - Medical 2026 (25 April Shift 1) · Physics
An organ pipe closed at one end produces $5^{\text{th}}$ 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
- A$x = 5$ and $y = 6$
- Correct answerB$x = 6$ and $y = 6$
- C$x = 6$ and $y = 5$
- D$x = 5$ and $y = 5$
Solution
For an organ pipe closed at one end, the fundamental mode ($0^{\text{th}}$ overtone) consists of $1$ node and $1$ antinode.
The $n^{\text{th}}$ overtone corresponds to the $(2n+1)^{\text{th}}$ harmonic.
The number of nodes in the $n^{\text{th}}$ overtone is $n + 1$.
The number of antinodes in the $n^{\text{th}}$ overtone is $n + 1$.
For the $5^{\text{th}}$ overtone, $n = 5$.
Number of nodes, $x = 5 + 1 = 6$.
Number of antinodes, $y = 5 + 1 = 6$.
Answer: $x = 6$ and $y = 6$
The $n^{\text{th}}$ overtone corresponds to the $(2n+1)^{\text{th}}$ harmonic.
The number of nodes in the $n^{\text{th}}$ overtone is $n + 1$.
The number of antinodes in the $n^{\text{th}}$ overtone is $n + 1$.
For the $5^{\text{th}}$ overtone, $n = 5$.
Number of nodes, $x = 5 + 1 = 6$.
Number of antinodes, $y = 5 + 1 = 6$.
Answer: $x = 6$ and $y = 6$
Hence, the correct answer is option: 'B'.