Use the Fresnel approximation to plot the axial pressure for a square source with sides 2L for the cases
kL = 1, 3 and 10 for distances out to twice the Rayleigh distance. Compare the solution to that obtained by
The angular spectrum code for the case of a square transducer.
The exact solution for a circular transducer.
Comment on differences between the curves.
For a focused source, with the same parameters as in HW 7 (f=2e6; a=10e-3; c0=1500; roc=60e-3) compare O'Neil's exact axial result with that for a Gaussian beam in the Fresnel approximation. Desribe the differences in the shape of the fields. Do the same thing for the pressure amplitude in the focal plane.
Consider a plane wave incident on a rigid scatterer. Plot the amplitude of the scattered field in the far-field as a function of ka varying from 0.3 to 4. Use a semi-log plot with the amplitude being on the log scale. Do this for 4 angles: 0, 48, 90 and 180 degrees. Comment on natures of the curves, in particular their relative amplitudes for small ka and large ka. At what value of ka does the forward scattering amplitude (0 degrees) become larger than the backscatter amplitude (180 degrees)? Over what range of ka does the backscatter amplitude drop below that of the side scatter (90 degrees)