Question

If the tension in the string is increased by $5kgwt$ the frequency of the fundamental tone increases in the ratio $2:3$. What was the initial tension in the string?

Answer 1

$l_n=\frac{n}{2L}\sqrt{\frac{F}{\mu }}$
$n=1$ for fundamental
$\frac{l_1}{l_2}=\frac{\frac{1}{2L}}{\frac{l}{2L}}=\frac{\sqrt{\frac{F_1}{\mu }}}{\sqrt{\frac{F_2}{\mu }}}$
$\frac{2}{3}=\sqrt{\frac{F_1}{F_2}}$
$\frac{2}{3}=\sqrt{\frac{F_1}{F_1+5}}$
$\frac{4}{g}=\frac{F_1}{F_1+5}$
$4F_1+20=g{F}_2$
$\frac{20}{5}=F_2=4N$