Acoustic Impedance Calculator

Background.

Shout at someone swimming underwater and they will barely hear you. The sound is not soaked up by the water; almost all of it bounces off the surface, because air and water respond to the push of a sound wave in very different ways. That resistance to being set in motion is acoustic impedance, and the mismatch between two materials' impedances decides how much sound crosses the boundary between them and how much is turned back.

For a plane wave travelling through a uniform material, the impedance is simply density times sound speed, Z = ρc. Dense materials in which sound travels fast — steel, glass, bone — have high impedance; light, slow ones such as air have very little. Water comes out at about 1.48 million rayl and air at roughly 413, a ratio of around 3,600 to 1. At a flat surface hit head-on, that mismatch reflects about 99.9% of the sound energy: the swimming-pool problem in numbers.

The same arithmetic runs through a good deal of engineering. A medical ultrasound probe is used with gel because even a thin film of trapped air between transducer and skin would send nearly the whole pulse straight back. Ultrasonic flaw detection works because a crack, which is a thin layer of air inside metal, reflects strongly while sound metal lets the pulse through. Sonar and the matching layers bonded onto transducers are exercises in the same balancing act.

The result here is the characteristic impedance of one material. It assumes a homogeneous medium carrying a longitudinal plane wave, so it says nothing about frequency dependence, attenuation, the complex impedance of absorbent or layered materials, or waves meeting a boundary at an angle. To compare two materials, work out each one separately.

What is acoustic impedance calculator?

Characteristic acoustic impedance is the ratio of acoustic pressure to particle velocity in a plane sound wave travelling through a material. For a lossless homogeneous medium it equals density multiplied by sound speed, so it is a property of the material alone. Its SI unit is the pascal-second per metre, equivalent to kg/(m²·s) and called the rayl; values for liquids and solids are usually quoted in megarayl (MRayl), millions of rayl.

How to use this calculator.

1. 01Enter the material's density in kilograms per cubic metre. Water is close to 1,000; for a gas, use the density at the actual temperature and pressure, since both change it substantially.
2. 02Enter the longitudinal (compressional) sound speed in metres per second, taken at the same temperature as the density. For a solid, use the longitudinal value from a materials table, not the slower shear-wave speed.
3. 03Read the impedance in rayl, and divide by one million to compare it with tables that quote MRayl.
4. 04To estimate reflection at a boundary, work out the impedance of each material in turn and put the two results into the reflection formula given in the questions below.

The formula.

Z = ρ × c, where ρ is the density in kg/m³ and c the longitudinal sound speed in m/s; the product has units of kg/(m²·s), the rayl. The relationship comes from the plane-wave solution of the linear acoustic equations. In such a wave the pressure p and the particle velocity u rise and fall together, with p = ρc × u, so ρc measures how much pressure it takes to drive the material's particles at a given speed. Both inputs enter to the first power, so doubling either doubles Z. Across everyday materials density varies far more than sound speed — air to steel is a factor of several thousand in density but under twenty in speed — which is why gases sit so far below liquids and solids. For a strongly absorbing material the impedance becomes a complex number that depends on frequency, and this simple product no longer describes it.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Kinsler et al., Fundamentals of Acoustics, 4th ed. (PRINT), plane waves.
2. [2]Nondestructive Testing Resource Center, Ultrasonic Testing, Acoustic Impedance.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.