Two springs, of force constants $k_1$  and $k_2$  are connected to a mass $m$ as shown. The frequency of oscillation of the mass is  $f$. If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes 

The two springs are in parallel.

$\therefore$Effective spring constant, $k=k_1+k_2$

Initial frequency of oscillation is given by $f=\frac{1}{2\pi }\sqrt{\frac{k_1+k_2}{m}}$              ………. (i)

When both $k_1$ and $k_2$ are made four times their original values, the new frequency is given by 

$f=\frac{1}{2\pi }\sqrt{\frac{4k_1+4k_2}{m}}$
$f\text{'}=\frac{1}{2\pi }\sqrt{\frac{4\left(k_1+k_2\right)}{m}}=2\left(\frac{1}{2\pi }\sqrt{\frac{k_1+k_2}{m}}\right)=fv$