State the meaning of the specific acoustic impedance of a medium.
A bone sample has density $1.8\,\text{g cm}^{-3}$ and ultrasound travels through the bone at $4.1 \times 10^{3}\,\text{m s}^{-1}$. Calculate the specific acoustic impedance $Z_{B}$ of the bone sample.
A parallel beam of ultrasound is incident normally on a layer of fat and on a layer of muscle, as shown in Fig. 5.1. The fat has thickness $0.45\,\text{cm}$ and the muscle has thickness $2.1\,\text{cm}$. Data for fat and for muscle are given in Fig. 5.2. The intensity reflection coefficient $\alpha$ at a boundary between two media of specific acoustic impedances $Z_1$ and $Z_2$ is given by the expression $\alpha = \left(\frac{Z_2 - Z_1}{Z_2 + Z_1}\right)^2$. Calculate the fraction of the ultrasound intensity that is transmitted across the fat-muscle boundary.
State the meaning of attenuation of an ultrasound wave.
Linear attenuation coefficients are listed in Fig. 5.2. Find the ratio $\dfrac{\text{intensity of ultrasound transmitted through the medium}}{\text{intensity of ultrasound entering the medium}}$ for the fat layer of thickness $0.45\,\text{cm}$.
Linear attenuation coefficients are listed in Fig. 5.2. Find the ratio $\dfrac{\text{intensity of ultrasound transmitted through the medium}}{\text{intensity of ultrasound entering the medium}}$ for the muscle layer of thickness $2.1\,\text{cm}$.
Use your answers in (b) and (c)(ii) to work out the fraction of the intensity entering the layer of fat that is transmitted through the layer of muscle.