BMET433 WK4 HW Chapter 10 The Physics of Ultrasound
Wave Propagation
10.8 (a) Solve Equations (10.25) and (10.26) to find the expressions for pressure reflectivity R and
pressure transmittivity T given by Equations (10.27) and (10.28), respectively.
10.11 (a) Derive the intensity reflectivity and transmittivity from the pressure reflectivity and
transmittivity.
(b) Show that T-R=1
(c) Find a concise relationship between TI and RI.
Ultrasound Field Pattern
10.15 An ultrasound imaging system is equipped with two square transducers. One operates at 5MHz,
and the other operates at 12MHz. The 5MHz transducer is 2.0 cm by 2.0 cm and the 12MHz one is 0.4
cm by 0.4 cm. The imaging system is tested in a medium having a speed of sound of 1560 m/s at both
frequencies.
(a) What are the absorption coefficients X5MHz and X12MHz of the medium at the frequencies of the
transducers?
(b) What ranges are considered as far field for each transducer?
Chapter 11 Ultrasound Imaging Systems
Ultrasound Transducer Array
11.6 Consider the linear array in Figure 11.15. Suppose we want to image a cross section of a patient as
shown in Figure P11.2, acquiring a scan line every ∆ θ =1. Assume there are 101 transducers operating at a frequency of 2MHz and c=1540 m/s and d=0.6mm.
(a)Find an expression for the time delay of the ith transducer as a function of angle of the transmitted
plane wave.
(b) How long does it take to scan the entire FOV assuming R=20cm?
Ultrasound Imaging System Design and Image Quality
11.12 An ultrasound imaging system is equipped with two square transducers. One operates at 5 MHz
and the other at 12 MHz. The 5 MHz transducer is 2.0 cm by 2.0 cm and the 12MHz one is 0.4 cm by 0.4
cm. The imaging system is tested in a medium having a speed of sound of 1560 m/s at both frequencies.
The amplitude attenuation factor of the medium satisfies
ENTER EQUATION BMET433 WK4 HW We want to image objects at ranges up to 20 cm.
(a) Find the system sensitivities L5MHz and L12MHz.
(b) What are the widths of the main lobes at the range of 20 cm? (Use the simple 3 dB model of
field pattern)
(c) c
(d) Suppose the transducers were scanned back and forth to obtain a B-mode image. What is the
maximal frame rate if 128 lines are used to form and image?
(e) What will happen to the B-mode image is the speed of sound in the medium is nonuniform but
we still use a uniform speed assumption?

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