Answer
The new frequency will be $~1000~Hz$
Work Step by Step
We can write an expression for the initial frequency:
$f_1 = \frac{1}{2\pi~\sqrt{L_1~C}}$
We can find the new frequency:
$f_2 = \frac{1}{2\pi~\sqrt{L_2~C}}$
$f_2 = \frac{1}{2\pi~\sqrt{4L_1~C}}$
$f_2 = \frac{1}{2}\times \frac{1}{2\pi~\sqrt{L_1~C}}$
$f_2 = \frac{1}{2}\times f_1$
$f_2 = \frac{1}{2}\times (2000~Hz)$
$f_2 = 1000~Hz$
The new frequency will be $~1000~Hz$