For sound waves, if the number of nodes for the $5^{th}$ harmonic of an open-ended pipe is $n$ and that for the $9^{th}$ harmonic of the same pipe with one of its ends closed is $m$, the ratio $\dfrac{n}{m}$ is :

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 $\dfrac{q+1}{2}$ nodes and $\dfrac{q+1}{2}$ antinodes.

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

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