A tuning fork of frequency 280Hz produces 10 beats per sec when sounded with a vibrating sonometer string (in fundamental mode).  When the tension in the string increases slightly, it produces 11 beats per sec.  The original frequency of the vibrating sonometer string in Hz is:

Given frequency of tunning fork  $\vartheta =280\text{\hspace{0.17em}Hz}$
Let the original frequency of the sonometer is ${\vartheta }_s$
Since number of beats produced is 10
$\begin{array}{l}\Rightarrow \left|280-{\vartheta }_S\right|=10\\ \Rightarrow {\vartheta }_S=280+10\\ \therefore {\vartheta }_S=290\mathrm{Hz}\\ \text{The frequency of the wire will be 290 Hz as its frequuency is increasing with increase in tension and producing more number of beats}.\end{array}$