define the specific acoustic impedance of a medium as Z = ρc, where c is the speed of sound in the medium

Specific Acoustic Impedance

The specific acoustic impedance of a medium is defined as \$Z = \rho c\$, where \$\rho\$ is the density of the medium and \$c\$ is the speed of sound in that medium. It tells us how much resistance the medium offers to the propagation of sound waves.

Think of it like a traffic jam on a highway: the denser the traffic (higher \$\rho\$) and the slower the cars move (lower \$c\$), the harder it is for a new car (sound wave) to get through.

In ultrasound, we often use materials with high impedance to reflect sound back to the transducer, creating an image.

Calculating \$Z\$ – Example

Suppose we have water with density \$\rho = 1000 \,\text{kg/m}^3\$ and speed of sound \$c = 1500 \,\text{m/s}\$. Then:

\$Z = \rho c = 1000 \times 1500 = 1.5 \times 10^6 \,\text{kg/(m}^2\text{s)}\$

That’s the impedance of water.

Why Impedance Matters in Ultrasound Imaging

• Reflection occurs where there is a large change in impedance.
• Different tissues have different \$Z\$ values, so we can distinguish them.
• High‑frequency ultrasound (like 10–15 MHz) gives better resolution but penetrates less depth.

Exam Tip Box

🔍 Remember: When you’re given \$\rho\$ and \$c\$, just multiply to find \$Z\$. If you’re asked why a boundary reflects sound, think about the impedance mismatch.

📝 Practice: Calculate the impedance of bone (density ~ 1900 kg/m³, \$c\$ ~ 3000 m/s) and compare it to soft tissue.

Quick Review Quiz

1. What is the formula for specific acoustic impedance?
2. If \$\rho = 800 \,\text{kg/m}^3\$ and \$c = 1200 \,\text{m/s}\$, what is \$Z\$?
3. Which of the following changes would increase \$Z\$?

   • a) Increase density
   • b) Decrease speed of sound
   • c) Both a and b

Answers: 1) \$Z = \rho c\$; 2) \$Z = 9.6 \times 10^5\$; 3) c) Both a and b.

Typical Acoustic Impedance Values