use IR / I0 = (Z1 – Z2)2 / (Z1 + Z2)2 for the intensity reflection coefficient of a boundary between two media

Production and Use of Ultrasound

What is Ultrasound?

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.

How Ultrasound is Produced

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.

  • Apply an alternating voltage → crystal expands and contracts.
  • Rapid expansion creates a pressure pulse → a sound wave.
  • By controlling the voltage frequency, we control the ultrasound frequency.

Reflection at a Boundary

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

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.

Intensity Reflection Coefficient

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.

Analogy

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.

Example Calculation

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.

Applications of Ultrasound

  1. Medical ImagingSonography uses reflected echoes to create real‑time images of organs.
  2. Industrial Inspection – Detects cracks or flaws in metal by measuring reflected waves.
  3. Sonar – Ships and submarines map the sea floor by sending and receiving ultrasound.
  4. Non‑Destructive Testing – Checks the integrity of welds and composites.

Exam Tips 🚀

  • Remember the formula: \$IR/I0 = ((Z1 - Z2)/(Z1 + Z2))^2\$. It’s a quick way to calculate reflections.
  • Know that \$Z = \rho c\$. If you’re given density and speed of sound, you can find impedance.
  • Use the reflection analogy to explain why high impedance differences give strong echoes.
  • When asked to compare two media, calculate the ratio of their impedances first.
  • Practice converting units (kg/m³, m/s) to Pa·s/m to avoid calculation errors.