Make a direct numerical implementation of the expression in (2.146) for the wavenumber representation of the field in an ideal waveguide. Allow the horizontal wavenumber to be complex.
a. For sound speed 1500 m/s and depth 100 m, compute the wavenumber kernel at
20 Hz for source and receiver both at depth 36 m. Sample the kernel at 200 points
equidistantly placed over the interval 
where kw is the water wavenumber. Let the imaginary value of the horizontal wavenumber be _kw=100 to avoid the modal singularities. Note: Your code will crash!
b. Determine the wavenumber interval for which your code produces a result which is qualitatively consistent with 
c. Describe the nature of the numerical problem, and rewrite (2.146) into a form which remedies the problem. Implement it and compare your result to (qualitatively).
