Question

"Trideco" antenna tower array at the US Navy's Naval Radio Station Cutler in Cutler, Maine, USA. The central mast is the radiating element, while the star-shaped horizontal wire array is the capacitive top load. About 1.2 miles in diameter, it communicates with submerged submarines at 24 kHz at a power of | 1.8 megawatts, the most powerful radio station in the world. Submarine communication by NATO, the US, Russia, China and the Indian and Japanese Navies uses very low frequencies (VLF) operating around 22 kHz. These signals can be detected at surface half way around the world In the tropics, sea conductivity O is 4.6 S/m and /ɛn is about 70. If at surface the 20 kHz field strength was 10 nT/s, and the submarine with its underwater antenna could detect a signal of 10 fT/s, how close to surface would the submarine have to be to use its antenna to detect the signal? [14] In the Baltic sea, the conductivity is only 1.9 S/m (lower water temperature and fresh water runoff). How much deeper would the signal be detectable there? [6]

Answer 1

The NLE radio waves travelling as Electromagnetic waves will try to benetrate the sea. But the salt water of sea acts like a conductor with grien strengths for conductivity in the problem. So a general EM wave travelling inside such a medium can be givers as - Elzit) - u e ilke-ut) where your usual propagations vector is no longer only a real wave number, but is a complex quantity raktik. And it is this t, the altenuation factor, which will decrease the strength of field upen surface penetration . This imaginary compensent of wave number is given as k z w CEI CUTE 2 -1]? det's calculate I , 4-6 slm > 0.33 X 1U Ew 70*8.85 x 1012 ffm x 22 x 3 H4 1 so attenuation has no so y 1 >NIME* 195* *- alvo (die E39 140 (+ => kowe see aj opis peligente com o con 2 for foresent set up, So if we just look at the field strength then I Ēlalfole Re as eelke-ut) in a phase terms with magnitude f. So for po 4.68M" -> ke some . 1685-85x102 = 25.21x10?m? for bolig Smit -> ks jope 2 782. 83 416-2 2 22,92 x 16.21 X10 – Prill kw

So for the first-case the field strength 10nt/s attenuaty to 1067/s. - 10 ft/s alonlls eke is our required depth loxios, loxius ekz ekz 2 106 ) -Kq 2 In 15% -6 ln 10a-6x 2.302 Kz z 13.81 ) 7 2 13.81 x 10²m = 54. 8m 25.21 for the second case of baltic sea, G21.gs/m, again field strengten attenuates with same degree. So, loxios, loxiug eRzt a ekzZz 100 -R₂7 a -6 lu 2 z koz z 13.81 z 72 13.81 x 10²m 16.21 Z ? 85.24 m These are the depths by which signals will be delectable by the Submarines