A 1 cm × 1 cm ultrasound transducer is placed on the z = 0 plane and pointed in the +z direction. Its sides are parallel to the x and y axes, and its center is at the origin. The transducer is submerged in a homogeneous medium with speed of sound c = 1, 540 m/s. The working frequency is 2.5 MHz. A line scatterer parallel to y-axis passing through the point (0, 0, 5) cm is being imaged.

(a) Write down an expression for the scatterer in mathematical form.

(b) What is the estimated reflectivity?

(c) If a second line scatterer parallel to the first one is placed at the same range, what is the minimal distance between them for the system to distinguish them?

(d) Repeat parts (b) and (c) when the scatterer is at range z = 20 cm.