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

For an open pipe, the \( k^{\text{th}} \) harmonic has \( k+1 \) nodes. For \( 5^{\text{th}} \) harmonic, \( n=6 \). For a closed pipe, the \( k^{\text{th}} \) harmonic (where \( k \) is odd) has \( (k+1)/2 \) nodes. For \( 9^{\text{th}} \) harmonic, \( m=(9+1)/2 = 5 \). Thus \( n/m = 6/5 \)... wait, checking the options, \( 9/5 \) is option 2.