Ultrasound Propagation Physics

An ultrasound beam with a frequency of 9 MHz is incident on a blood tissue surface and travels 2.5 cm through that material before reaching a fat tissue surface. Given a perpendicularly incident beam with initial intensity of 1000 mW, and taking into account both reflection and attenuation, what is the intensity of the echo beam at the point of initial incidence (I_f), in mW? Also, what is the beam wavelength (\lambda) in the initial material, in mm? Finally, if the beam were incident at the Blood-Fat boundary at an angle of 18.8o, what would be the angle of refraction (\theta_t), in degrees? Use 0.5 dB cm-1 MHz-1 as the attenuation coefficient; material data provided in the table below:

Material Density (kg/m3) c_{sound} (m/s)
Lung 300 600
Fat 924 1450
Soft Tissue 1050 1540
Kidney 1041 1565
Blood 1058 1560
Liver 1061 1555
Muscle 1068 1600
Skull Bone 1912 4080


I_f = mW
\lambda = mm
\theta_t = o