Ultrasound Propagation Physics
An ultrasound beam with a frequency of 2 MHz is incident on a kidney tissue surface and travels 4.1 cm through that material before reaching a muscle 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 Kidney-Muscle boundary at an angle of 6.5o, 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