Derive Green’s theorem for a fluid medium with variable density, where the wave equation is of the form given in (2.14).

1. Make a computer code for computing the magnitude and phase of the planewave reflection coefficient at an interface separating two fluid halfspaces.

a. As a test of your code reproduce the results of

b. Discuss in physical terms the grazing angle dependence of the results.

c. Add a second fluid layer in the bottom and then add frequency as an independent variable to your computer program. Contour your reflection results as a function of angle and frequency. Discuss the resulting structure of the contoured output.