Acoustic Impedance Calculator

Created by Gabriela Diaz
Reviewed by Hanna Pamuła, PhD candidate and Steven Wooding
Last updated: Feb 15, 2022
Table of contents:

Our acoustic impedance calculator will help you find the specific acoustic impedance of a material (z) and determine the intensity coefficients of reflection and transmission of a sound wave at the boundary of two materials. The wide range of applications of acoustic impedance from ultrasound, tympanometries, architectural acoustics, soundproofing, aeronautical noise control, etc., makes it an important property.

Keep reading to learn what acoustic impedance is, the terms in the acoustic impedance equation, reflection and transmission of the sound wave, and some materials' acoustic impedance.

What is acoustic impedance?

If we recreated a sound from the same source in a room filled with air and underwater in a pool, will it behave the same? 🤔 Sound is a wave of pressure that requires a medium to propagate, and the properties of each material affect the speed and intensity of the wave.

The speed of sound in a given medium (gas, liquid or solid) depends primarily upon how compressible it is. In solids and liquids, which are less compressible than gases and with a higher modulus of elasticity, the speed of sound is faster.

The acoustic impedance (Z) is a material's property that affects how sound travels through it. It represents the medium's resistance to the propagation of the sound, affecting its intensity. The higher the value of Z, the greater is the opposition to the transmission of the sound.

The acoustic impedance (Z) is particular for a geometry and a material, given by the wave's acoustic pressure to flow ratio. Similarly, the specific acoustic impedance (z) is an intensive material's property that relates the wave's pressure and the medium's velocity.

For plane waves, the specific acoustic impedance formula is expressed in terms of density of the medium ($\rho$) and the speed of the sound wave in that particular material ($c$):

$\quad z=\rho\times c$

From our initial question, and using the specific acoustic impedance equation, let's compare the z of water and air at the same temperature:

• Water with a density of 1000 kg/m3 and speed of sound of 1480 m/s, has a z of 1.48 MRayl.
• Air has a density of 1.225 kg/m3 and speed of 343 m/s, has a z of 0.0004 MRayl.

Notice that even though sound moves 4.3 times faster in water than in air, the intensity of the sound wave is 3700 times higher in air than in the water!

💡 The specific acoustic impedance unit is often denoted as Pa⋅s/m × 106 or MRayl (106 Rayleigh).

Intensity reflection and transmission coefficients

The acoustic impedance helps us understand what happens to the sound when it travels from one medium to another. At the boundary of two materials, a fraction of the sound intensity is reflected, and the rest is transmitted. This is why we can hear music playing next room 🎵

To quantify how much is reflected and how much is transmitted, we compare the specific acoustic impedances of the two materials. When a sound wave impacts normally (perpendicular) on a boundary, the intensity reflection (R) and transmission (T) coefficients are expressed in terms of the impedances as:

\quad\begin{aligned} R &= (z_1- z_2)^2/(z_1+z_2)^2 \\\\ T &= 4z_1z_2/(z_1+z_2)^2 \end{aligned}

From these expressions we can see that:

• If $z_1 = z_2$, there’s no reflection $(R=0)$ and all the sound is transmitted $(T=1)$;
• When $z_1$ and $z_2$ are similar, there’s little reflection and most is transmitted $(T>R)$; and
• Otherwise if $z_1$ and $z_2$ are very different, most of the sound is reflected $(R>T)$.

Notice how combining different materials results in different fractions of sound being reflected or transmitted. This effect has a practical application:

• For example, in architecture, for soundproofing of buildings, it's common to combine layers of different materials to reduce the intensity of the sound that comes from the streets or rooms within the facility 🏠
• In contrast, in ultrasound scanning, the goal is that most of the wave transmits into the body. This is why a gel with an acoustic impedance similar to the skin is used, allowing a small reflection of the wave. This is known as acoustic impedance matching.

Specific acoustic impedance of some materials

In the tables of this section, you can find the specific acoustic impedance of everyday materials, ranging from gases, liquids, solids to body tissues and organs.

Specific acoustic impedance of common gases and liquids:

Material

Speed (m/s)

Density (kg/m3)

Spec. acoustic impedance z (MRayl)

Air (20 °C/68 °F)

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/68 °F)

1522

1024

1.56

Water (0 °C/32 °F)

1402

1000

1.40

Water (20 °C/68 °F)

1482

998

1.48

Specific acoustic impedance of solids. Here, you'll find the specific acoustic impedance of steel and other common construction materials:

Material

Speed (m/s)

Density (kg/m3)

Spec. acoustic impedance z (MRayl)

Brick

4300

1700

7.4

Concrete

3100

2600

8.0

Copper

3735

8960

33.6

Glass

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

Specific acoustic impedance of body tissues and organs. In medicine and ultrasounds, these specific acoustic impedances are the most commonly used:

Material

Speed (m/s)

Density (kg/m3)

Spec. acoustic impedance z (MRayl)

Blood (37 °C/98.6 °F)

1570

1060

1.61

Bones

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

Source: /

How to use the acoustic impedance calculator

The acoustic impedance calculator will help you find the specific acoustic impedance of a given material from a list or for a custom material. This tool also determines the intensity reflection and transmission coefficients:

• To find the specific acoustic impedance from a listed material:
1. From the Find menu, choose: Acoustic impedance of chosen material.
2. In the Choose material list, select the material that you'd like to know the specific acoustic impedance.
3. The calculator will display the Specific acoustic impedance (z).
• In order to get the specific acoustic impedance of a custom material with the acoustic impedance formula:
1. From the Find menu, choose: Acoustic impedance of custom material.
2. Enter values of density and speed of sound of the material.
3. The calculator will give you the Specific acoustic impedance (z) value.
• To calculate the intensity reflection (R) and transmission (T) coefficients:
1. From the Find menu, choose: Intensity reflection and transmission coef..
2. Indicate the materials that you'd like to study.
3. The calculator will show the values for the intensity coefficients R and T.
Gabriela Diaz
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Acoustic impedance of chosen material
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Specific acoustic impedance (z)
MRayl
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