Find the ratio,  , between the transmit amplitudes of the two systems such that at z = zswitch, assuming a perfect reflection.

Consider the transducer array shown in Figure P11.6, which has elements that alternate in frequency between 3 MHz (white) and 6 MHz (grey). Assume that each transducer is only able to transmit and receive at its own frequency. Assume L = 90 dB and α = af where a = 1 dB/(cm MHz). In the figure below, let d = h = 0.4 mm. Assume the speed of sound is 1,540 m/s

Figure P11.6 See Problem 11.16.

(a) What is the depth of penetration for the two transducer types? Suppose both arrays will fire simultaneously, sending out sound in the direction θ = 20◦. The 6-MHz system will focus at a depth of z = 5 cm, while the 3-MHz system will focus at a depth of z = 10 cm.

(b) Assuming that T0 fires at t = 0, write an expression for the transmit delays  of the 3-MHz system and compute the actual delay  in μs.

(c) Assuming T0 fires at t = 0, write an expression for the transmit delays  of the 6-MHz system and compute the actual delay in μs.

(d) Let  and  be the amplitudes for the 6-MHz and 3-MHz echoes received from range z, assuming a perfect reflection. The displayed A-mode signals will be switched from the 6-MHz echoes to the 3- MHz echoes when  reach a signal loss of 30 dB. At what range, zswitch, does this ‘‘switchover’’ occur?

(e) Find the ratio,  , between the transmit amplitudes of the two systems such that at z = zswitch, assuming a perfect reflection.

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