Problem I. $(34$ points$)$

You have a very difficult job: to get a signal from a Transmitter to a Receiver whose line of sight goes through $3$ different mediums on its way:

Transmitter:

Directional antenna:

You will analyze various aspects to determine the best approach. Here is what you know to start: Problem I. $(34$ points$)$ Continued:

a$)$ Tests have indicated that the soil stays dry because the local drainage is very efficient with significant fresh water run$-$off. Seawater and freshwater have about the same dielectric properties but the conductivity of the mix is not known.

Experiments to determine the ratios of conduction to displacement current density values have yielded the following results:

Determine the conductivity of the seawater$/$freshwater mix $($round to nearest whole number$),$ then check your answer for consistency

b$)$ In the air: determine the wave parameters at both frequencies: $10$ kHz and $10$ THz

i$.$ Propagation constant $\backslash (\backslash$beta $\backslash )$

ii$.$ Wavelength $\backslash (\backslash$lambda $\backslash )$ Problem I. $(34$ points$)$ Continued:

c$)$ In the dry soil:

i$.$ First determine the loss tangent at both frequencies: $10$ kHz and $10$ THz

ii$.$ Then determine the wave parameter: Propagation constant

iii. Did the Propagation constant change significantly between the air and the dry soil for either frequency?

iv$.$ At this point, identify the frequency that you think you should use to leave the dry soil and $($possibly$)$ reach the submarine Problem I. $(34$ points$)$ Continued:

d$)$ In the seawater mix:

i$.$ First determine the loss tangent at your selected frequency using your conductivity value from part a$)$

ii$.$ Next determine the attenuation coefficient $\backslash (\backslash$alpha $\backslash )$

iii. Now determine the penetration depth $\backslash (\backslash$delta $\backslash ),$ first in $\backslash ($ m $\backslash )$ and then convert to inches

iv$.$ How easy will it be to communicate with the submarine if it is submerged?