Thank you for reporting, we will resolve it shortly
Q.
The fundamental frequency of sonometer wire increases by $9 \,Hz$, if its tension is increased by $69\, \%$, keeping the length constant. The frequency of the wire is
We know that, frequency of vibration of a stretched string is given by
$v=\frac{1}{2l} \sqrt{\frac{T}{m}}$
where, $T=$ tension in string
$m=$ mass $/$ length
and $l=$ length of string.
New frequency,
$v'=v+9=\frac{1}{2l} \sqrt{\frac{T+(69 / 100)}{m}}$
$\Rightarrow \frac{v}{v'}=\sqrt{\frac{T}{169} T}$
$\Rightarrow \frac{v}{v+9}=\sqrt{\frac{100}{169}}=\frac{10}{13}$
$\Rightarrow 13 v=10 v+90$
$v=30 Hz$