Final answer:
Increasing the frequency of a plane electromagnetic wave four times will result in a decrease in the penetration depth into a good conductor due to the skin effect. At higher frequencies, the wave attenuates more rapidly within the conductor.
Step-by-step explanation:
Impact of Increased Frequency on Penetration Depth in Good Conductors
When considering the penetration depth of an electromagnetic wave into a good conductor, it is important to understand that it is related to the skin effect. The skin effect describes how an electromagnetic wave attenuates as it travels through a conductor. As the frequency of the wave increases, the depth of penetration decreases. This is because at higher frequencies, the oscillating electric fields generate more rapid changes in current, which in turn results in greater resistive losses within the conductor. Therefore, increasing the frequency of a plane electromagnetic wave by four times will lead to a reduction in the penetration depth.
For instance, in applications such as ELF (Extremely Low Frequency) radio communication with submarines, lower frequencies are utilized precisely because they can penetrate deeper into water and earth, allowing for communication at extended depths or distances.
In summary, the depth of penetration for an electromagnetic wave incident normally on a good conductor will decrease as the frequency of the wave is increased.