Acoustic/Sound Reflection Calculator

Calculate acoustic reflection coefficients, impedance mismatch, and signal loss for NDT and physics.

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.

Medium 1 (Source) Impedance Z1 Medium 2 (Target) Impedance Z2 Interface Boundary Incident (Pi) Reflected (Pr) (Echo) Transmitted (Pt)

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.

  1. 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).
  2. 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).
  3. Check Units: You can use kg/m³ or g/cm³. The calculator automatically converts them for you.
  4. 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

MaterialDensity ($\rho$)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.

Input Parameters

Result

0

Updates in real-time as you type

Energy Reflection (%)
-%
Percentage of sound energy reflected back (Intensity Reflection Coefficient).
Reflection Loss / Return Loss
-dB
The strength of the reflected signal relative to the incident signal in decibels.
Impedance Ratio (Z₂/Z₁)
-
Ratio of acoustic impedances. Large deviations from 1.0 cause stronger reflections.

Note

Range: -1 to +1

Current Inputs

Medium 1 Density (ρ₁):0kg/m³
Medium 1 Sound Speed (c₁):0m/s
Medium 2 Density (ρ₂):0kg/m³
Medium 2 Sound Speed (c₂):0m/s