A portion of a linear array is shown in Figure P10.2. Note that The array is compose...

A portion of a linear array is shown in Figure P10.2. Note that The array is composed of five transducers (called elements), whose faces are contained in the x-y plane and vibrate in the z direction. Assume the far-field (Fraunhofer) approximation in all of the parts below.

(a) What is the far-field pattern q₀(x, y, z) of the central element taken by itself?

(b) Find the range z₀ at which the first zeros of this pattern (in the x direction) coincide with x = −s and x = +s?

(c) What condition must the separation s satisfy in order that z0 is in the far-field of the central element?

(d) Find the far-field pattern q(x, y, z) of the five elements operating in unison.

(e) What is the beamwidth (out to the first zeros) of this pattern at range z₀ in both the x and y directions. (Think carefully about this one before you proceed blindly ahead; it is easier than it appears at first glance.)