Calculating the Vertical Wavenumber for a Sonar Transducer

Nicholas Kinar

I am interested in calculating the vertical wavenumber from an acoustic
field radiated by a sonar
transducer. Suppose that I know the pressure p at every point on a 2-D
grid. Is the phase (theta) given by

theta = atan((dp/dy)/(dp/dx))

, where dp/dz is thederivative of the pressure field in the y-direction, and
dp/dx is the derivative of the field in the x-direction? Then, would the
vertical wavenumber (k_x) be given by

k_x = dtheta/dx

, where dtheta/dx is the derivative of the phase with respect to the
x-direction? I have numerically calculated the field of the transducer on a
2-D grid, and I am wondering if the vertical wavenumber can be found uising
the two equations given above.

How would I find the average wavenumber of the transducer in the medium?
Would I average (and take the mean) of all values over the entire grid?

Thank you ever so much for your time and assistance!

Nicholas