What is the lateral resolution (FWHM) of this transducer at a range z = 10 cm?

Consider a single, flat, square, ultrasound transducer whose sides have lengths of 0.5 cm and whose resonant frequency is 2.5 MHz. Suppose it is embedded in a homogeneous medium whose density ρ is 920 kg/m3 and whose acoustic impedance Z is 1.35 × 106 kg/m2s.

(a) What range zf characterizes the range at which the far field begins for this transducer in this medium?

(b) For a typical system (i.e., make appropriate assumption(s) about the system), what does the absorption coefficient α of this medium have to be if the depth of penetration is 20 cm.

(c) What is the lateral resolution (FWHM) of this transducer at a range z = 10 cm?

(d) Assume that this transducer could be scanned (slid) rapidly in the x direction and repetitively pulsed in order to create a rectangularshaped B-mode image. It is desired to obtain A-mode data separated by 1 mm in the x direction and to scan a 12 cm wide region. Ignoring any potential mechanical problems with scanning the transducer, what is the maximum frame rate that can be achieved for the depth of penetration given in (b)?

(e) Suppose there is an interface at range 10 cm, normal to the transducer’s axis, and assume that the second medium (beyond 10 cm) has density 1,070 kg/m3 and acoustic impedance 1.7 × 106 kg/m22s. If the acoustic pressure of the initial pulse has amplitude A0 and the absorption coefficient is α = 1.5 dB/cm in the first medium, what is the amplitude of the reflected acoustic pressure pulse when it arrives at the transducer?

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