How to calculate acoustic impedance?

You multiply the density of a medium by the speed at which sound waves travel through it. The formula is z = ρ x c. In SI units, multiplying the density in kilograms per cubic meter by the speed of sound in meters per second gives an acoustic impedance in Rayls. For example, water has a density of about 1000 kg/m3 and a speed of sound of about 1480 m/s, so its acoustic impedance is about 1,480,000 Rayl or 1.48 MRayl.

What is the unit of acoustic impedance?

The SI unit is the rayl, named after Lord Rayleigh. One rayl is equal to one Pascal-second per meter and also one kilogram per square meter per second. Since acoustic impedance of materials often reaches millions of rayls, it is usually expressed in megarayls (MRayl), where one MRayl equals a million rayls. The acoustic impedance of water is about 1.48 MRayl while that of steel is about 40 MRayl.

Why do sound waves get reflected at the interface between two different materials?

Sound waves are reflected because the acoustic impedance of two different materials is not the same. The amount of sound that is reflected is calculated by squaring the value obtained from dividing (z1 - z2) by (z1 + z2), while the remaining sound energy is transmitted. If the acoustic impedances on both sides are the same, no sound waves will be reflected and all will be transmitted. When there is a large difference between the two values, such as at the interface between air and water, almost all of the sound waves will be reflected, with this amount being about 99.9%.

Why is impedance matching important in ultrasound imaging?

The ultrasound probe sends sound waves into the body and must simultaneously receive the reflected waves. If there is a thin air layer between the probe and skin, almost all of the sound waves will be reflected because the acoustic impedance difference between air and body tissue is large. A coupling gel with an acoustic impedance similar to that of the skin fills this gap, reduces reflection, and allows the sound waves to penetrate into the body unhindered for a clear image.

Acoustic Impedance Calculator

Specific acoustic impedance

Density (rho)

Speed of sound (c)

Specific acoustic impedance (z)

Enter any two of density, speed of sound and acoustic impedance, and the calculator finds the third from z = ρ x c. Then open the boundary section to see how sound reflects and transmits between two materials.

Reflection and transmission at a boundary

Please input values into the fields

Acoustic impedance describes how much a material impedes the propagation of sound waves. When a sound wave hits another material, acoustic impedance determines what portion of the sound is reflected and what portion continues through to the other material.

This calculator allows calculations in both directions. You can enter any two of the following quantities: density, sound velocity and specific acoustic impedance to calculate the remaining quantity. If you add a second material, it is also possible to calculate the reflection and transmission of sound waves at the interface between the two materials.

What is acoustic impedance?

When a sound wave propagates through a medium it causes the particles of that medium to vibrate. The acoustic impedance is the ratio of the sound pressure to the particle motion in the medium caused by this pressure and indicates how easily a medium responds to sound waves.

Materials with high density and stiffness typically have a higher acoustic impedance and impede sound waves more. In media that are easily compressible, such as air, the acoustic impedance is very low. Because of these differences, sound is strongly reflected at some boundaries while it passes through others without hindrance.

Formula for acoustic impedance.

For a plane sound wave, the specific acoustic impedance is the product of the density of the medium and the speed of the sound wave propagating in it.

z = \rho \times c

where z is the specific acoustic impedance, ρ (rho) is the density and c is the speed of sound. In SI units, the unit for density is kilograms per cubic meter, the unit for speed of sound is meters per second, and the resulting unit for the calculated acoustic impedance is rayls.

One rayl is equal to one pascal second per meter or one kilogram per square meter per second. Since the specific acoustic impedance of real materials often reaches millions of rayls, it is usually expressed in megarayls, abbreviated as MRayl. One MRayl equals a million rayls.

Example calculation:

What is the specific acoustic impedance of water? The density of water is about 1000 kilograms per cubic meter and the speed of sound waves traveling through it is about 1480 meters per second.

Although the specific acoustic impedance of water is a thousand times that of air, the speed of sound propagation through water is only several times faster than through air.

Instructions for using this calculation tool:

Enter any two of the three values (density, sound velocity, acoustic impedance) and the calculator will calculate the remaining value. If the acoustic impedance is left blank it can be calculated from density and sound velocity. Conversely, density or sound velocity can be calculated from a known acoustic impedance by leaving those fields blank.

For each field you can select the units separately. Enter the density in grams per cubic centimeter and the sound velocity in kilometers per second. The acoustic impedance can be shown in Rayleigh, kilo-Rayleigh or mega-Rayleigh. All conversions are done automatically by the calculation tool.

Density or sound velocity calculation:

Since these three quantities are related by the same equation, if two of them are known then the remaining value can be calculated. By rearranging the equation z = rho*c you get two formulae for calculating the other quantity.

\rho = \dfrac{z}{c} \qquad c = \dfrac{z}{\rho}

If you want to calculate the density from known acoustic impedance and sound speed use the first formula. If you want to calculate the sound speed from known acoustic impedance and density use the second formula. Leave empty the field corresponding to the value you want to calculate and the calculator will automatically select the right formula.

Typical values for specific acoustic impedance of materials:

The following table shows typical values. Acoustic impedance is the product of density and sound velocity, so it can be directly derived from the data in adjacent columns. Published data for human tissues show slight variations due to differences in temperature and measurement methods.

Material	Density (kg/m3)	Speed of sound (m/s)	Impedance (MRayl)
Air (20 C)	1.2	343	0.0004
Fat	920	1450	1.33
Water (20 C)	1000	1480	1.48
Ultrasound gel	1000	1500	1.50
Soft tissue (average)	1060	1540	1.63
Blood	1060	1570	1.66
Muscle	1070	1580	1.69
Bone	1810	4080	7.4
Aluminium	2700	6320	17.1
Steel	7870	5130	40.4

Reflection and transmission at interfaces:

When a sound wave reaches an interface between two different materials, part of it is reflected while the rest is transmitted. How the energy of the sound is split depends only on the acoustic impedances of the two materials. In the case of normal incidence, the fraction of the sound energy that is reflected is:

R = \left(\dfrac{z_1 - z_2}{z_1 + z_2}\right)^2

And the fraction of sound energy transmitted to the second medium is:

T = \dfrac{4\,z_1\,z_2}{(z_1 + z_2)^2}

The sum is always equal to one and if you add T to R it will be 1. This is because sound energy is always transmitted somewhere. If the acoustic impedances on both sides are the same there will be no reflection and all of the sound waves will pass through. When the difference between the two values is large almost all of the sound waves will be reflected.

Here's why a person underwater can barely hear screams from the surface of the water: The acoustic impedance of air and water differ by about a factor of 1000. This means that about 99.9% of the sound is reflected at the surface, while only a tiny fraction makes it into the water.

Impedance matching and ultrasound

Impedance matching means to match the acoustic impedances on both sides of a boundary surface as closely as possible in order to allow sound waves to pass efficiently without reflecting them. In sound transmission from one material to another, impedance matching is essential.

A typical example is medical ultrasound. When the probe is placed directly on the skin, the thin air layer between the transmit and receive elements reflects almost all of the sound waves, resulting in poor image quality. A coupling gel has an acoustic impedance similar to that of the skin, fills the gap, reduces reflection, and allows the sound waves to penetrate into the body and return to the probe with little loss.

The same principle is used in the design of loudspeakers and transducers, sonar systems, and soundproofing. Soundproof constructions sometimes use materials with different acoustic impedances on purpose to block rather than transmit sound.

Specific acoustic impedance and characteristic acoustic impedance.

Two closely related quantities are involved. The specific acoustic impedance is a property of the material itself and corresponds to the ratio between sound pressure and particle velocity of the medium, i.e., the value z = ρ*c used in this calculator.

The acoustic impedance of a particular acoustic system also depends on geometric conditions such as the cross-section of a tube or horn structure through which the sound wave propagates. In plane waves in open media these two quantities are equal, so it is most natural to start with values for the material itself.

Applications of acoustic impedance:

In the medical field, acoustic impedance is fundamental to ultrasound imaging. The reflections that occur at interfaces between different tissues are combined to create an image and also explain why contrast is particularly high in areas with bone or gas.

In engineering, acoustic impedance is often used for non-destructive testing. Defects inside a material can be detected by the reflections caused by cracks. It also has applications in sonar systems, architectural acoustics and speaker and microphone design. When sound enters from one medium into another, the acoustic impedances of both materials determine how it propagates.

This tool is for general education and solving everyday problems. For applications in medical, engineering or other important fields the results should be checked against specific requirements and material data for the particular application.

Frequently asked questions

What is acoustic impedance?: Acoustic impedance describes how much a material impedes the propagation of sound waves. For a plane sound wave, acoustic impedance is the product of the density of the material and the speed at which the sound wave propagates in it, i.e., z = ρ x c, where the unit is rayl. Materials with high acoustic impedance, such as steel, impede sound more strongly, while media with low acoustic impedance, like air, affect sound less strongly. The difference in acoustic impedance between two materials determines the reflection rate of sound waves at the interface.
How to calculate acoustic impedance?: You multiply the density of a medium by the speed at which sound waves travel through it. The formula is z = ρ x c. In SI units, multiplying the density in kilograms per cubic meter by the speed of sound in meters per second gives an acoustic impedance in Rayls. For example, water has a density of about 1000 kg/m3 and a speed of sound of about 1480 m/s, so its acoustic impedance is about 1,480,000 Rayl or 1.48 MRayl.
What is the unit of acoustic impedance?: The SI unit is the rayl, named after Lord Rayleigh. One rayl is equal to one Pascal-second per meter and also one kilogram per square meter per second. Since acoustic impedance of materials often reaches millions of rayls, it is usually expressed in megarayls (MRayl), where one MRayl equals a million rayls. The acoustic impedance of water is about 1.48 MRayl while that of steel is about 40 MRayl.
Why do sound waves get reflected at the interface between two different materials?: Sound waves are reflected because the acoustic impedance of two different materials is not the same. The amount of sound that is reflected is calculated by squaring the value obtained from dividing (z1 - z2) by (z1 + z2), while the remaining sound energy is transmitted. If the acoustic impedances on both sides are the same, no sound waves will be reflected and all will be transmitted. When there is a large difference between the two values, such as at the interface between air and water, almost all of the sound waves will be reflected, with this amount being about 99.9%.
Why is impedance matching important in ultrasound imaging?: The ultrasound probe sends sound waves into the body and must simultaneously receive the reflected waves. If there is a thin air layer between the probe and skin, almost all of the sound waves will be reflected because the acoustic impedance difference between air and body tissue is large. A coupling gel with an acoustic impedance similar to that of the skin fills this gap, reduces reflection, and allows the sound waves to penetrate into the body unhindered for a clear image.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Acoustic impedance
Definition of specific and characteristic acoustic impedance, the rayl unit, and reflection at boundaries.
NDT Resource Center: Acoustic Impedance
How impedance governs the reflection and transmission of sound in non-destructive testing.
Wikipedia: Rayl
The rayl and megarayl units of specific acoustic impedance.