For an acoustic field in a waveguide, how would you take advantage of the orthogonality of normal modes to construct a modal, rather than plane-wave beamformer? Use a vertical array.

10.5. Write down an expression in terms of discrete normal modes for the field of a point source received on a vertical array. Take the complex conjugate of this result and use the result to represent a distribution of point sources. With this source distribution and the known Green’s function of this problem, propagate the resulting field outward. (With this range-independent geometry, outward is the same as “backward.”)