A wire of density $7\times {10}^{3}kg/m^3,$ length 1m and diameter $1\text{mm}$ is stretched by weight of $11\text{kg}$ . Calculate the frequency of the fundamental note

Density $d=7\times {10}^3{\text{kg/m}}^{\text{3}}$ 

Length $l=1\text{m}$

Diameter $d=1\text{mm}$

Radius $r=0.5\times {10}^{-3}m\Rightarrow 5\times {10}^{-4}m$

Weight $\text{m=11}\text{kg}$

Frequency $n=?$

$n=\frac{1}{2l}.\sqrt{\frac{T}{\mu }}$

     $=\frac{1}{2l}\sqrt{\frac{mg}{\pi r^2.d}}$

$=\frac{1}{2\times 1}\sqrt{\frac{11\times 9.8}{\frac{22}{7}\times 5^2\times {10}^{-8}\times 7\times {10}^3}}$

$=70\text{Hz}$