Free Acoustic Impedance Calculator

Acoustic impedance is a fundamental property that determines how sound energy propagates through a medium. This acoustic impedance calculator enables you to compute the specific acoustic impedance of any material, evaluate the intensity reflection coefficient and sound transmission coefficient at a boundary, and select from a database of common materials. With applications spanning ultrasound imaging, architectural acoustics, noise control, and material science, knowing the acoustic impedance of a material is key to predicting sound behavior.

Understanding Specific Acoustic Impedance

The specific acoustic impedance ($z$) of a material is defined as the product of its density ($\rho$) and the speed of sound ($c$) within that material:

$$z = \rho c$$

This relation describes the resistance the medium offers to the propagation of a sound wave. The SI unit of $z$ is the pascal-second per meter (Pa·s/m), commonly expressed in rayls (1 rayl = 1 Pa·s/m). Because values for common materials span several orders of magnitude, the mega rayl (MRayl = $10^6$ rayl) is frequently used. For instance, air at room temperature has a specific acoustic impedance of about 0.0004 MRayl, while water at 20°C has roughly 1.48 MRayl.

The speed of sound in a medium is influenced mainly by its compressibility and elastic modulus. Dense, stiff solids generally exhibit high sound speeds, leading to large impedance values, whereas gases have low density and high compressibility, resulting in very low impedances.

Intensity Reflection and Transmission at Boundaries

When a sound wave traveling in medium 1 impinges normally on the interface with medium 2, part of the incident intensity is reflected and part is transmitted. The fractions are dictated solely by the specific acoustic impedances of the two media, $z_1$ and $z_2$. The intensity reflection coefficient ($R$) and intensity transmission coefficient ($T$) are given by:

$$R = \left( \frac{z_2 - z_1}{z_2 + z_1} \right)^2$$ $$T = \frac{4 z_1 z_2}{(z_1 + z_2)^2}$$

Because energy is conserved (neglecting absorption), $R + T = 1$. If the impedances are equal, there is no reflection ($R=0$) and all sound passes through. The greater the impedance mismatch, the larger the reflected portion. This principle is exploited in both directions: in soundproofing, layers of dissimilar materials are combined to reflect noise away; in medical ultrasound, a gel with an impedance close to that of the skin is used to minimize reflection and allow the wave to enter the body.

Example: Water–Air Interface

To put the formulas into context, consider an interface between water ($z_1 \approx 1.48$ MRayl) and air ($z_2 \approx 0.0004$ MRayl). Substituting these numbers into the reflection coefficient equation yields $R$ very close to 1, meaning almost all the sound energy is reflected. This is why sounds generated underwater are barely audible above the surface. Conversely, when two media have similar impedances (e.g., water and human tissue), transmission is high.

Acoustic Impedance of Common Materials

The database of this tool comprises many everyday materials, including fluids, solids, and biological tissues. The tables below present their densities, sound speeds, and specific acoustic impedances.

Gases and Liquids

Material	Speed (m/s)	Density (kg/m³)	z (MRayl)
Air (20°C)	344	1.205	0.0004
Ethyl alcohol	1207	806	0.97
Helium	964	1.664	0.0016
Hydrogen	1284	0.838	0.0011
Seawater (20°C)	1522	1024	1.56
Water (0°C)	1402	1000	1.40
Water (20°C)	1482	998	1.48

Solids

Material	Speed (m/s)	Density (kg/m³)	z (MRayl)
Brick	4300	1700	7.4
Concrete	3100	2600	8.0
Copper	3735	8960	33.6
Glass (typical)	5000–6000	2320–2427	11.6
Stainless steel	5900	7890	45.7
Steel	5130	7874	40.3
Wood cork	500	240	0.12
Wood pine	3500	450	1.57

Body Tissues and Organs (Medical Ultrasound)

Material	Speed (m/s)	Density (kg/m³)	z (MRayl)
Blood (37°C)	1570	1060	1.61
Bone	3360–4100	1810	3.2–7.5
Brain	1540	1030	1.58
Eye aqueous humor	1000–1500	1000	1.50
Fat	1500	920	1.38
Gel (ultrasound)	1500	1000	1.48
Kidney	1560	1040	1.62
Muscle	1580	1070	1.65–1.74
Skin	1600	1100	1.53–1.68

Data sources vary; values represent typical ranges found in literature.

How to Use the Acoustic Impedance Calculator

The tool is designed to be intuitive. You can obtain the specific acoustic impedance of a material in two ways:

• Pre‑defined material: From the “Find” menu choose “Acoustic impedance of chosen material”, then pick the material from the list. The impedance value is shown instantly.
• Custom material: Select “Acoustic impedance of custom material” and input the density and sound speed of the substance you are working with.

To compute the reflection and transmission coefficients at an interface, select “Intensity reflection and transmission coef.”, then specify the two media involved. The calculator will display the acoustic impedance of each material together with the calculated $R$ and $T$ values.

Because it handles both lookup and custom entries, this tool serves as a general acoustic impedance calculator and also functions as a dedicated ultrasound impedance calculator for medical applications.

Practical Applications

Knowledge of acoustic impedance is critical in several fields:

• Architectural acoustics and soundproofing: Using materials with vastly different impedances in layers to reflect sound and reduce noise transmission.
• Medical ultrasound: Impedance matching (using a coupling gel) ensures that most of the ultrasound energy enters the body, maximizing image quality.
• Nondestructive testing: Impedance mismatches help identify flaws or inclusions in materials.
• Acoustic design: Selecting materials with appropriate impedance for rooms and studios.

The acoustic impedance formula ($z = \rho c$) and the reflection/transmission coefficients are the pillars of these calculations. With this acoustic impedance calculator, you can quickly run the numbers for any scenario.