Physics - Sound Wave Question with Solution | TestHub

For an open-ended pipe, the $p^{th}$ harmonic contains $p$ nodes and $p+1$ antinodes.

For the $5^{th}$ harmonic of the open-ended pipe, the number of nodes is $n=5$.

For a pipe closed at one end, only odd harmonics are present. The $q^{th}$ harmonic (where $q$ is an odd integer) contains $\frac{q+1}{2}$ nodes and $\frac{q+1}{2}$ antinodes.

For the $9^{th}$ harmonic of the closed pipe, the number of nodes is $m=\frac{9+1}{2}=5$.

The ratio of the number of nodes is $\frac{n}{m}=\frac{5}{5}=1$.