State what the acoustic impedance $Z$ of a medium means.
Two media have acoustic impedances $Z_1$ and $Z_2$. The intensity reflection coefficient $\alpha$ at the boundary between the two media is given by $\alpha = \frac{(Z_2 - Z_1)^2}{(Z_2 + Z_1)^2}$. Describe what happens to the transmission of ultrasound through a boundary when the acoustic impedances of the two media differ greatly.
The data for acoustic impedance $Z$ and absorption coefficient $\mu$ for fat and muscle are given in Fig. 10.1. The thickness $x$ of the fat layer on an animal, shown in Fig. 10.2, is to be studied using ultrasound.
The intensity of the parallel ultrasound beam incident on the surface $S$ of the fat layer is $I$. The beam is reflected from the boundary between fat and muscle. The intensity of the reflected ultrasound detected at the surface $S$ of the fat is $0.012\,I$. Calculate the intensity reflection coefficient at the boundary between the fat and the muscle.
Calculate the thickness $x$ of the fat layer.