Answer
(a) $f = 1000~Hz$
(b) $f =707~Hz$
(c) $f = 707~Hz$
(d) $f = 1000~Hz$
Work Step by Step
We can write an expression for the resonance frequency:
$f = \frac{1}{2\pi~\sqrt{L~C}}$
(a) The resonance frequency does not depend on the resistance.
$f = 1000~Hz$
(b) If the inductance $L$ is doubled then the resonance frequency is decreased by a factor of $\frac{1}{\sqrt{2}}$
$f = (\frac{1}{\sqrt{2}})(1000~Hz) = 707~Hz$
(c) If the capacitance $C$ is doubled then the resonance frequency is decreased by a factor of $\frac{1}{\sqrt{2}}$
$f = (\frac{1}{\sqrt{2}})(1000~Hz) = 707~Hz$
(d) The resonance frequency does not depend on the peak emf $\epsilon_0$.
$f = 1000~Hz$
