Answer
The penetration depth of the $2.4~GHz$ microwaves is $~~1.5~cm$
Work Step by Step
We have the following relationships:
$d \propto \sqrt{\lambda}$
$\lambda \propto \frac{1}{f}$
Therefore:
$d \propto \frac{1}{\sqrt{f}}$
We can find $d_2$, the penetration depth of the $2.4~GHz$ microwaves:
$\frac{d_2}{d_1} = \frac{\sqrt{f_1}}{\sqrt{f_2}}$
$d_2 = \sqrt{\frac{f_1}{f_2}}~d_1$
$d_2 = \sqrt{\frac{27\times 10^6~Hz}{2.4\times 10^9~Hz}}~(14~cm)$
$d_2 = 1.5~cm$
The penetration depth of the $2.4~GHz$ microwaves is $~~1.5~cm$
