b
\(\begin{array}{l} {n_1} = {n_2}\\ T \to Same\\ r \to Same\\ l \to Same \end{array}\) 

Frequency of vibration

\(\mathrm{n}=\frac{\mathrm{p}}{2 l} \sqrt{\frac{\mathrm{T}}{\pi \mathrm{r}^{2} \rho}}\)

As \(\mathrm{T}, \mathrm{r},\) and \(l\) are same for both the wires

\(n_{1}=n_{2}\)

\(\frac{p_{1}}{\sqrt{\rho_{1}}}=\frac{p_{2}}{\sqrt{p_{2}}}\)

\(\frac{p_{1}}{p_{2}}=\frac{1}{2} \quad \because \rho_{2}=4 \rho_{1}\)