A 70 cm long sonometer wire is in unison with a tuning fork. If the length of the wire is decreased by 1.0 cm, it produces 4 beats per sec. with the same tuning fork. Find the frequency of the tuning fork 

Let the frequency of the fork be n. In the first case, the length of the wire is 70 cm (0.70 m). Therefore,
$n=\frac{1}{2\times 0.70}\sqrt{\frac{T}{m}}\mathrm{...}\left(1\right)$
On decreasing the length of the wire, its frequency will increase. Hence in the second case when the length is 69 cm = 0.69 m, then
$n+4=\frac{1}{2\times 0.69}\sqrt{\frac{T}{m}}\mathrm{...}\left(2\right)$
dividing equation (1) by (2), we get
$\Rightarrow \frac{n}{n+4}=\frac{0.69}{0.70}$
$\Rightarrow n\times 0.70=(n+4)\times 0.69$