Given that a source is at a depth of $1300$ meters is in the Atlantic Ocean with a bottom

depth $5000$ m $.$ The sound speed profile is a Munk profile given by

c$($z$)=$c$\_(1)[1+\backslash$epsi $($z$^(\text{'})-1+$e$^(-$z$^(\text{'})))]$;z$^(\text{'})=2($z$-$z$\_(1))/($B$)$

and with the following parameters

z$\_(1)=1300$m

B$=1300$m

c$\_(1)=1500($m$)/($s$)$

$\backslash$epsi $=7\mathrm{.}37$e$-3$

a$.$ A ray is launched from the source upward to the surface. What is the launch angle

$($grazing angle$)$ of the ray that turns at the surface?

$(5$ points$)$

b$.$ If a ray tube has an area of $10$m$^(2)$ and an intensity of $1($W$)/($m$^(2))$ at one location A $,$ and at

another location B$,$ the same ray tube has an area of $2$m$^(2).$ What is the intensity of the ray

tube at location B$.$

c$.$ In ray theory which of the following best describes the eikonal?

i$.$ the eikonal gives us the amplitude of the ray tube

ii$.$ the gradient of the eikonal provides the propagation direction of the ray

iii. the eikonal provides the image of the ray above the surface

iv$.$ the integral of the eikonal provides the travel time of the ray