What is Acoustic Reflection?
When a sound wave traveling through a material encounters a boundary with a different material, part of the wave travels through (Transmission), and part bounces back (Reflection).
The strength of this reflection depends entirely on the difference in Acoustic Impedance ($Z$) between the two materials. This tool helps you calculate that mismatch, which is critical for Ultrasonic Testing (NDT), Medical Imaging, and Sonar.
Visualization: Incident vs. Reflected Wave
The diagram below illustrates the process. Note how the “Impedance Mismatch” determines the size of the reflected arrow.
Fig 1. Schematic of acoustic reflection at a boundary.
How to Use This Calculator
This tool calculates how sound behaves when moving from Medium 1 to Medium 2.
- Enter Medium 1 Properties: Input the Density ($\rho_1$) and Sound Speed ($c_1$) of the material where the sound starts (e.g., the steel part being tested).
- Enter Medium 2 Properties: Input the Density ($\rho_2$) and Sound Speed ($c_2$) of the material the sound hits (e.g., air in a crack, or water).
- Check Units: You can use
kg/m³org/cm³. The calculator automatically converts them for you. - Interpret the Result:
- High Energy %: Means most sound bounced back (Good for finding cracks).
- Low Energy %: Means most sound went through (Good for medical imaging).
The Physics Behind the Tool
1. Acoustic Impedance ($Z$)
Impedance measures how much resistance a material offers to the passage of sound. It is calculated as: $$Z = \rho \cdot c$$
- $\rho$: Density ($\text{kg/m}^3$)
- $c$: Speed of sound ($\text{m/s}$)
2. Reflection Coefficient ($R$)
This tells us the ratio of reflected pressure to incident pressure: $$R = \frac{Z_2 - Z_1}{Z_2 + Z_1}$$
- If $Z_2 > Z_1$ (e.g., Air to Steel): $R$ is Positive (in-phase reflection).
- If $Z_2 < Z_1$ (e.g., Steel to Air): $R$ is Negative (phase inverted).
3. Return Loss (dB)
In engineering (NDT/Sonar), we measure the strength of the echo in Decibels (dB): $$\text{Return Loss} = -20 \log_{10}(|R|)$$
- 0 dB: Total reflection (100% echo).
- High dB: Weak reflection (faint echo).
Application Scenarios
NDT: Finding Cracks in Steel
In ultrasonic testing, we look for cracks.
- Scenario: Sound travels through Steel ($Z \approx 46$ MRayl) and hits an Air-filled crack ($Z \approx 0.0004$ MRayl).
- Result: The impedance mismatch is massive. $R \approx -0.999$.
- Outcome: 99.9% of the energy reflects back to the sensor, creating a clear “spike” on the screen that indicates a defect.
Medical: Why We Use Gel?
Ultrasound probes ($Z \approx 30$) cannot transmit sound directly into Skin ($Z \approx 1.6$) through Air ($Z \approx 0.0004$).
- Without Gel: 99.9% of sound reflects off the skin surface. No image.
- With Gel: The gel matches the impedance of the skin, reducing reflection to nearly zero, allowing sound to enter the body.
Common Material Reference
| Material | Density ($\rho$) | Speed ($c$) | Impedance ($Z$) |
|---|---|---|---|
| Air | $1.2 \text{ kg/m}^3$ | $343 \text{ m/s}$ | $0.0004 \text{ MRayl}$ |
| Water | $1000 \text{ kg/m}^3$ | $1480 \text{ m/s}$ | $1.48 \text{ MRayl}$ |
| Steel | $7850 \text{ kg/m}^3$ | $5900 \text{ m/s}$ | $46.3 \text{ MRayl}$ |
| Bone | $1900 \text{ kg/m}^3$ | $4000 \text{ m/s}$ | $7.6 \text{ MRayl}$ |
FAQ
Q: What does a negative Reflection Coefficient mean? A: It means the reflected wave is Phase Inverted ($180^\circ$). This happens when sound travels from a “hard” material (high impedance) to a “soft” material (low impedance), like from Steel to Air. The amount of energy reflected ($R^2$) is still positive.
Q: Can I use this for non-perpendicular angles? A: No, this calculator assumes Normal Incidence (the wave hits the surface at $90^\circ$). For angled incidence, you would need to calculate Snell’s Law and mode conversion, which is more complex.