ELF communication signals ( f < 3 kHz) can more effectively penetrate seawater than VHL signals ( 3 kHz < f < 30 kHz). In practice, an ELF signal used for communication can penetrate and be received at a depth of up to 80 m below the ocean surface.
(a) Find the ELF frequency at which the skin depth in seawater is equal to 80 m. For seawater, use \sigma = 4 S/m^-1, \epsilon_r = 81, and mew = mew_0.
(b) Find the ELF frequency at which the skin depth is equal to half of 80 m
(c) At 100 Hz, find the depth at which the peak value of the electric field propagating vertically downward in seawater is 40 dB less than its value immediately below the surface of the sea. (To calculate a dB value for a wave amplitude use dB = 20*log10 [amplitude] ).
(d) A surface vehicle-based transmitter operating at 1kHz generates an electromagnetic signal of peak value 1 V /m immediately below the sea surface. If the antenna and the receiver system of the submerged vehicle can measure a signal with a peak value of as low as 1 microV/m, calculate the maximum depth beyond which the surface vehicle can no longer communicate with the submarine.