Use the data from the table to calculate a value for the density of bone.

The fraction F of the intensity of an ultrasound wave reflected at the boundary between two media having acoustic impedances
Z₁ and Z₂ is given by the following equation.

\[F = \frac{{{{\left( {{Z_1} - {Z_2}} \right)}^2}}}{{{{\left( {{Z_1} + {Z_2}} \right)}^2}}}\]

Determine the fraction F for the boundary between

(i) air and muscle.

(ii) gel and muscle.

Use your answers in (b) to explain the need for a gel on the patient’s skin.

use of Z = ρc;
7.8×10⁶=ρ×4.1×10³
ρ=1900kgm⁻³;

(i) \(F = \frac{{{{\left( {1.4 \times {{10}^6} - 4.3 \times {{10}^2}} \right)}^2}}}{{{{\left( {1.4 \times {{10}^6} + 4.3 \times {{10}^2}} \right)}^2}}}\);
F≈1;

(ii) \(F = \frac{{{{\left( {1.5 \times {{10}^6} - 1.4 \times {{10}^6}} \right)}^2}}}{{{{\left( {1.5 \times {{10}^6} + 1.4 \times {{10}^6}} \right)}^2}}}\);
F=0.0012;

for air-muscle boundary, very little ultrasound is transmitted;
gel permits almost complete transmission;