In this case,

Stress = $\frac{mg}{A}$

Strain = $\frac{l}{L}$ (where $l$ is extension)

Now, Young's modulus $Y$ is given by

$Y=\frac{\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}}{\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}}=\frac{mg/A}{l/L}$

$m\mathrm{g}=\frac{YAl}{L}$

So, $kl=\frac{YAl}{L}$ ($\because m\mathrm{g}=kl$)

($k$ is force constant)

Now, frequency is given by

$n=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$

$=\frac{1}{2\pi }\sqrt{\left(\frac{YA}{mL}\right)}$