A submarine submerged in the ocean (sigma = 4 S/m, elementof_r = 81, mu_r = 1) wants to receive an electromagnetic signal from a ship located at the surface and transmitting at f = omega/2 pi = 30 kHz. a) Calculate the numerical values of the propagation constant gamma = alpha + j beta and intrinsic impedance eta. Use the approximations appropriate for the associated loss tangent sigma/omega elementof. b) How close by must the submarine be located in order to receive at least 1% of the signal amplitude at the surface? c) What is the wavelength lambda = 2 pi/beta = v_p/f of the EM signal at this operating frequency? d) Repeat parts (a-c) for ship transmission at 300 Hz.

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