The US Navy talks to submerged submarines by using super low frequencies (SLF) that range from 30 to \(300 \mathrm{~Hz}\).
Electromagnetic waves can penetrate a conducting medium, like seawater, up to a portion of its wavelength called the skin depth or 8. The EM wave attenuates similarly to a time constant. That is, at one 8 , the signal is attenuated by \(1 / e\) or \(68 \%\). The Navy transmits at \(76 \mathrm{~Hz}\), for a \(\delta\) of \(26 \mathrm{~m}\). How long would a quarter-wavelength antenna need to be to broadcast at \(76 \mathrm{~Hz}\) ?