Ultrasound refers to sound waves with frequencies above the upper limit of human hearing (≈20 kHz). Think of it as a “high‑pitched” version of the sounds you hear every day, but invisible to the ear.
Ultrasound is generated by a piezoelectric transducer – a crystal that changes shape when an electric voltage is applied. When the crystal vibrates, it pushes on the surrounding medium (water, air, or body tissue) creating a pressure wave.
When an ultrasound wave meets a boundary between two different materials (e.g., water and bone), part of the wave is reflected back and part is transmitted. The amount reflected depends on the acoustic impedance of each medium.
Acoustic impedance, \$Z\$, is defined as:
\$Z = \rho \, c\$
where \$\\rho\$ is the density of the medium and \$c\$ is the speed of sound in that medium.
The fraction of the incident intensity that is reflected is given by the intensity reflection coefficient:
\$\displaystyle \frac{IR}{I0} = \left(\frac{Z1 - Z2}{Z1 + Z2}\right)^2\$
Here, \$IR\$ is the reflected intensity, \$I0\$ is the incident intensity, \$Z1\$ is the impedance of the first medium, and \$Z2\$ is the impedance of the second.
Imagine throwing a ball at a wall. If the wall is very soft (low impedance), most of the ball’s energy bounces back (high reflection). If the wall is very hard (high impedance), the ball passes through with little bounce (low reflection). Ultrasound behaves similarly at material boundaries.
Suppose ultrasound travels from water (\$Z{\text{water}} = 1.5 \times 10^6 \,\text{Pa·s/m}\$) into bone (\$Z{\text{bone}} = 7.0 \times 10^6 \,\text{Pa·s/m}\$). The reflection coefficient is:
\$\displaystyle \frac{IR}{I0} = \left(\frac{1.5-7.0}{1.5+7.0}\right)^2 \approx 0.28\$
So about 28 % of the ultrasound intensity is reflected back – enough for a clear echo in medical imaging.