Alexander Engman asked . 2022-01-18

Underwater soundwave for different starting angles

      function dZ=undervatten(x,Z)
      p=[5.8796 14.4874 257.1923];
      c=@(z) 4800+p(1)+(p(2)*z/1000)+(p(3)*exp(-z/1000));
      c0=c(2000);
      dZ=zeros(2,1);
      dZ(1)=Z(2);
      dZ(2)=-(c0/cosd(7.8))^2*(((-p(3)/1000)*exp(-Z(1)/1000))+p(2)/1000)/...
              (4800+p(1)+p(2)*Z(1)/1000+p(3)*exp(-Z(1)/1000))^3;
      end

This is my function using the information from the assignment and I have confirmed that it is correct. The value cosd(7.8) comes from the starting angle 7.8 degrees. I am then calling this function like this:

clear all, close all, clc

x=0:0.5:6076*25;
n=7.8;
[X,Z]=ode45(@undervatten,x,[2000 tand(n)]);
plot(X,Z(:,1),'-r')
xlabel('distance')
ylabel('depth')
axis ij

sound wave , image processing , matlab