The fundamental frequency of vibration $f$ is given by $f=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$
where $l=$ length of the wire
$T=$ tension
= mass per unit length
Thus;
$f\alpha \frac{1}{l}\dots ...(i)$
$f\alpha \sqrt{T}\dots \dots$.(ii)
or $f^2\alpha T$
and $f\alpha \frac{1}{\sqrt{\mu }}\dots$....(iii)
(ii) above is a direct relationship. It means increment in $f$ such as doubling it will result in a geometrical increase in $T$ i.e. $T$ quadruples and increasing $f$ by 4 will increase $T$ by 16 et cetera