$A$ spring of length $l$ and force constant $k$ is attached to a mass $m$ and oscillates with frequency $f_1$. If the spring is cut into two equal parts and one part is attached to the same mass $m$ to oscillate,its frequency becomes $f_2$. Find the relation between $f_1$ and $f_2$.
- A$f_1 = \sqrt{2} f_2$
- B$f_1 = f_2$
- C$f_1 = 2 f_2$
- D$f_2 = \sqrt{2} f_1$
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