Rayleigh’s principle for one-way wave propagation asserts that the average kinetic energy in the wave must be equal to the average potential energy, i.e.,

1. Assume you are using a long horizontal array for passively detecting a sound source in the ocean. The array characteristics are as follows: To estimate the source

bearing in deep water it is often a good approximation to perform the beam forming assuming the source and the array are at equal depth in an infinite, homogeneous medium with the sound speed equal to the one existing at the array depth (assume 1500 m/s).

a. Under such conditionswrite a linear beamformer algorithmfor estimating source

bearing, and use it to compute the beamformer response to a 10-Hz point source

at bearing 45ı off broadside, at a range of 80 km from the center of the array.

b. Discuss the features of the beamformer response.

c. Compute the corresponding beamformer response at 30Hz, and discuss the result.