For wire vibrating under tension, the fundamental frequency is given by

${\mathrm{f}}_1=\frac{1}{2\mathrm{L}}\sqrt[\mathrm{ }]{\frac{\mathrm{T}}{\mathrm{\mu }}}$, Where T is tension and $\mu$ linear mass density of string
It is given that, when it is sounded with a tuning fork of frequency $\mathrm{x}$, $6$ beats per second were heard

$\therefore \mathrm{ }\left(\mathrm{x}-\mathrm{f}\right)=6$

${\mathrm{f}}_1=\frac{1}{2\mathrm{L}}\sqrt{\frac{225}{\mathrm{\mu }}}$

${\mathrm{f}}_2=\frac{1}{2\mathrm{L}}\sqrt{\frac{256}{\mathrm{\mu }}}$ undefined

$\therefore \mathrm{ }\left(\mathrm{x}+6\right)=\frac{16}{15}(\mathrm{x}-6)$

$\therefore \mathrm{ }15\mathrm{x}+90=16\mathrm{x}-96$

$\therefore \mathrm{ }\mathrm{x}=186\mathrm{ }\mathrm{H}\mathrm{z}$