| a (dB/MHz\" . cm) | | (kg/m3) 1.21 1789 1039 952 1420 1051 1041 1000 | Materia
ID: 1769937 • Letter: #
Question
| a (dB/MHz" . cm) | | (kg/m3) 1.21 1789 1039 952 1420 1051 1041 1000 | Material Air Bone Blood Fat Honey Liver Muscle Water@ 20°C c (m/s) 343 3360 1550 1450 2030 1570 1580 1482 b Z (MegaRayls) 0.0004 6.00 1.61 1.38 2.89 1.65 1.645 1.482 3.54 0.14 0.6 0.9 1.21 0.45 0.57 0.00217 1.05 2.0 Q2. [3096] An ultrasonic wave propagates from muscle into bone: (a) Determine the pressure reflection coefficient seen by the wave. (b) Design a matching layer to reduce the reflection to a minimum. (c) What are the pressure reflection and transmission coefficients seen by the wave with the matching layer in place?Explanation / Answer
For an ultrasonic wave propagating from muscle to bone, ( taking density as p)
(a) Pressure Reflection Coefficient : R = p2c2 - p1c1/ p1c1 + p2c2 , since the wave propagates from muscle to bone p1 = 1041 kg/m3 , p2 = 1789 kg/m3 , c1(speed of sound in the medium) = 1580 m/s , c2 = 3360 m/s
R = p2c2 - p1c1/p1c1 + p2c2 = 6011040 - 1644780/1644780 + 6011040 = 4366260/7655820 = 0.57
(b) To design a layer which reduces the reflection to minimum, this will be the case of perfect matching, which means total transmission and zero refelction, now for this we will take two the impedences of muscle and bone and relate them as
Z0 = (Z1Z2)1/2 , the perfect matching is achieved when a quarter - wavelength matching layer of acoustic impedence Z0 is applied at the interface. Therefore, Z0 = (1041 x 1789)1/2 = 1364.67 MegaRayls
(c) Now for this matching the pressure reflection coefficient is zero since it is perfect matching, for the transmission coefficient T = 1 - (r - 1)2/ 4r, where r = Z2/Z1 denotes the impedence ratio between the two media to be matched. The formula also includes the delta which cos(k0 d), but since the data is not given for that i am not including it in the formula, r = Z2/Z1 = 1780/1041 = 1.71, and putting the value of r in the formula, so T will be equal to
T = 1 - (1.71 - 1)2/ 4 x 1.71 = 1 - (0.71)2/ 6.84 = 0.0731.
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