Power receive by submarine Antenna

Hi Guys,

Attached below is a past year paper qns i had. i had figure out most of the qns except the last part... i cant seems to get the answer of 0.068mW.....

Any helps is much appreciated...



A linearly polarised plane wave of frequency 3 KHz travelling in air is incident
normally on seawater having the following constants: σ = 5.2 S/m; ε r = 80 and μ r = 1,
and the associated incident electric field Ei is 10 V/m.


A half-wavelength dipole antenna attached to the submarine is used to receive
maximum signal whilst the sea craft is submerged. Calculate the required dipole
antenna length.

Taking KT0 = 4 x 10-21
J, what is the maximum depth at which the submarine can detect
the signal if its receiver, which is matched to the antenna, has a bandwidth of 50 Hz
with a S/N ratio of 95 dB? How long will it take for the signal to travel from the sea
surface to the submarine?


S = kToB * 10^9.5 = Prx

Preceive = P_incident * { 1 - |rohv|^2) * Ae * e^-2.alpha.d ; alpha = attenuation constant & Ae = ( lamba^2 / 4.pi ) * G ; G = 1.64, half wave dipole


hence d = ln ( Prx / P_incident * { 1 - |rohv|^2) * Ae ) / -2.alpha



If the submarine were to surface with its dipole antenna completely out of the seawater,
obtain an estimate of the power received by the antenna. Briefly comment on the
factors that can affect the validity of your answer.


How am i going to do this part ?

Prx = Pincident * Ae ?