If n 1 , n 2 and n 3 are the fundamental frequencies of three segments into which a string is divided, then…

For first segment we have,

$n_1=\frac{1}{2l_1} \sqrt{\frac{T}{\mu }}$

For second segment we have,
$n_2=\frac{1}{2l_2} \sqrt{\frac{T}{\mu }}$

For third segment we have,
$n_3=\frac{1}{2l_3}\sqrt{\frac{T}{\mu }}$

For the whole string we have,
$n=\frac{1}{2l} \sqrt{\frac{T}{\mu }}$

Total length of the string is,
$l=l_1+l_2+l_3$

Thus, the fundamental frequency for the whole string is,
$\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$