d
\(\text { Frequency of } L C \text { oscillation }=\frac{1}{2 \pi \sqrt{L C}}\)

or, \(\frac{f_{1}}{f_{2}}=\left(\frac{L_{2} C_{2}}{L_{1} C_{1}}\right)^{1 / 2}=\left(\frac{2 L \times 4 C}{L \times C}\right)^{1 / 2}=(8)^{1 / 2}\)

\(\therefore \quad \frac{f_{1}}{f_{2}}=2 \sqrt{2} \Rightarrow f_{2}=\frac{f_{1}}{2 \sqrt{2}} \quad\) or, \(\quad f_{2}=\frac{f}{2 \sqrt{2}}\)

\(\left(\because f_{1}=f\right)\)