Physics Question on sound

Question

In an experiment with sonometer a tuning fork of frequency $256\, Hz$ resonates with a length of $25\, cm$ and another tuning fork resonates with a length of $16\, cm$ . Tension of the string remaining constant the frequency of the second tuning fork is :

Answer 1

Solution

For sonometer $n \propto \frac{1}{l}$
$\therefore \, \, \frac{n_1}{n_2} = \frac{l_2}{l_1} \Rightarrow \frac{256}{n^2} = \frac{16}{25}$
$n_2 = \frac{256 \times 25}{16}$
$= 400 \, Hz$