Two identical square transducers with width 1 cm face each other. The first one is located at the origin and points in the +x direction; the second one is located at (10 cm, 0, 0) and points toward the origin. The first one will be used to image the second one. Assume a homogeneous medium with Ï_{0} = 1, 000 kg/m^{3}, c = 1, 500 m/s, and Î± = 1 dB/cm. Assume that the first transducer fires a perfect geometric beam with peak transmit acoustic pressure measured at its face of 12.25 N/cm^{2}; assume that the second transducer is a perfect reflector.

(a) Sketch the A-mode signal. Label the axes carefully and identify the time-of-return and peak-height (as an acoustic pressure at the face) of the returning pulse.

(b) At time t = 2 s the second transducer begins to move back-andforth along the x-axis with x position x(t) = 10 + sin 2Ï€(t âˆ’ 2) cm, t â‰¥ 2 seconds. Sketch the M-mode plot for 0 â‰¤ t â‰¤ 5 seconds. Label the axes carefully; identify key points on your plot.

(c) Now suppose the second transducer stops at its original position and we allow the first transducer to move along the y axis. Sketch the resulting B-mode image. Label the axes carefully; identify key points on your plot. Make a sketch of the peak-height of the returning pulse as a function of the y position of the first transducer.