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+// Exa 2.25

+clc;

+clear;

+close;

+// given :

+Em=20 // minimum signal level required for vessel under sea water in microV/m

+Em=20*10^-6 // minimum signal level required for vessel under sea water in V/m

+E=100 // electric intensity of wave in V/m

+v=3*10^8 // speed of light in m/s

+f=4 // frequency in MHz

+f=4*10^6 // frequency in Hz

+omega=2*%pi*f // angular frequency in Hz

+sigma=4 // conductivity of sea water in mho/m

+epsilon_r=81 // relative permittivity

+epsilon_0=8.854*10^-12 // permittivity in free space

+epsilon=epsilon_r*epsilon_0 // permittivity

+mu_r=1 // relative permeability

+mu_0=4*%pi*10^(-7) // permeability in free space

+mu=mu_r*mu_0 // permeability

+k=(sigma)/(omega*epsilon)//ratio

+disp("ratio k is equal to: ")

+disp(k,"ratio:")

+disp("K is >>1 so sea water is a good conductor")

+eta_1=377 // intrinsic impedance in free space in ohm

+alpha_1=0 // attenuation constant in free space in m^-1

+beta_1=omega/v // phase constant in m^-1

+mageta_2=sqrt(omega*mu/sigma) // magnitude of eta_2(intrinsic impedance of sea water in ohm) 

+argeta_2=45 // argument of eta_2 in degrees

+eta_2=mageta_2*cosd(argeta_2)+%i*mageta_2*sind(argeta_2) //intrinsic impedance in complex form (r*cos(theta)+%i*r*sin(theta))

+TC=2*eta_2/(eta_1+eta_2) // transmission cofficient

+Et=abs(TC)*E // transmitted electric field in V/m

+alpha_2=sqrt(omega*mu*sigma/2) // attenuation constant for sea water in m^-1

+// formula: Et*exp(-alpha_2*d)=Es

+d=-(1/alpha_2)*log(Em/Et) // depth in the sea that can be reached by the aeroplane in m

+disp(d,"depth in the sea that can be reached by the aeroplane in m:")

+

+

+// note 1: the value of alpha_2 in book is 7.905 but it is "7.94" exactly calculated by scilab

+//note 2 : The correct answer of the Depth(d) is "1.41094" the answer in the book is wrong.