Acoustic Impedance Calculator
Enter the density and speed of sound of a material to compute its specific acoustic impedance. Switch to the two-material mode to find the intensity reflection and transmission coefficients at a boundary. Use the material preset dropdown to load known values instantly, or type your own. All three solve modes (Z, density, speed of sound) are supported.
Formula
Worked example
Water: rho = 998 kg/m3, c = 1480 m/s. Z = 998 x 1480 = 1,477,040 Pa-s/m = 1.477 MRayl. At an air-water boundary: R = ((1.48 - 0.0004)/(1.48 + 0.0004))^2 = 0.999 - nearly total reflection.
What is acoustic impedance?
Acoustic impedance (symbol Z) describes how strongly a medium resists the propagation of sound. It is defined as the product of the medium's mass density and the speed of sound through it: Z = rho x c. The SI unit is the pascal-second per metre (Pa-s/m), but in practice the megaRayl (MRayl) is used because most useful materials fall between 0.0004 MRayl (air) and 46 MRayl (steel). One MRayl equals one million Pa-s/m, honouring Lord Rayleigh who laid the foundations of acoustic theory. Acoustic impedance is the acoustic analogue of electrical impedance: just as electrical impedance determines how much a circuit resists current, acoustic impedance determines how much a boundary resists sound energy transfer.
Reflection and transmission at a boundary
When a sound wave strikes the interface between two media of different acoustic impedances, it partially reflects and partially transmits. The intensity reflection coefficient R = ((Z2 - Z1) / (Z2 + Z1))^2 gives the fraction of incoming intensity that bounces back; the transmission coefficient T = 1 - R gives the fraction that crosses. If both media have the same impedance, R equals zero and all sound passes through. If the mismatch is extreme (air meeting steel, for example), R approaches 1 and almost all energy is reflected. This principle governs sonar, medical ultrasound, non-destructive testing (NDT), room acoustics, and the design of noise barriers. The pressure reflection coefficient r = (Z2 - Z1) / (Z2 + Z1) can be negative when Z2 < Z1, indicating a phase reversal at the boundary - important in waveform analysis but not in energy calculations, where R = r^2 is always positive.
Impedance matching and quarter-wave layers
Transmitting maximum acoustic power between two mismatched media requires an impedance matching layer. The optimal strategy is a quarter-wavelength-thick layer whose impedance equals the geometric mean of the two outer impedances: Zm = sqrt(Z1 x Z2). At the design frequency, destructive interference of the reflections from both surfaces of the layer results in perfect transmission. This is the mechanism used in medical ultrasound probes (where polymer or epoxy layers couple the piezoelectric element to human tissue) and in underwater sonar transducers. The required thickness is t = c_layer / (4 x f), where c_layer is the wave speed in the layer and f is the operating frequency. For a 1 MHz probe with a 2720 m/s layer, this comes to about 0.68 mm.
Practical applications
Acoustic impedance governs a wide range of everyday and industrial phenomena. In medical imaging, ultrasound gel is applied between the transducer and skin because the air gap (0.0004 MRayl) would reflect more than 99.9 % of the sound, while the gel (similar impedance to tissue) allows almost all energy to enter. In non-destructive testing, a water or oil couplant is used for the same reason. In room acoustics and noise control, a wall material with high impedance (concrete, brick) provides better sound insulation than a low-impedance material (foam). In the sea, sonar engineers must account for the impedance contrast at the seabed, between water and different sediment types. In musical instruments, the acoustic impedance of the air column inside a pipe or horn determines which frequencies resonate and which do not.
Acoustic impedance of common materials
| Material | Density (kg/m³) | Speed of sound (m/s) | Z (MRayl) |
|---|---|---|---|
| Air (20 °C) | 1.204 | 343 | 0.0004 |
| Water (20 °C) | 998 | 1480 | 1.48 |
| Seawater | 1025 | 1522 | 1.56 |
| Human fat | 950 | 1450 | 1.38 |
| Human brain | 1040 | 1520 | 1.58 |
| Human blood | 1060 | 1570 | 1.66 |
| Human muscle | 1070 | 1580 | 1.69 |
| Human bone (avg) | 1900 | 3500 | 6.65 |
| Rubber | 1200 | 1600 | 1.92 |
| Wood (pine) | 550 | 3313 | 1.82 |
| Concrete | 2300 | 3475 | 7.99 |
| Brick | 1800 | 4000 | 7.2 |
| Glass | 2500 | 5640 | 14.1 |
| Aluminum | 2700 | 6420 | 17.33 |
| Copper | 8900 | 3560 | 31.68 |
| Steel (mild) | 7800 | 5850 | 45.63 |
| Stainless steel | 7900 | 5790 | 45.74 |
| PZT-5H piezo ceramic | 7500 | 4350 | 32.63 |
Values at room temperature (~20 °C) unless noted. 1 MRayl = 10⁶ Pa·s/m.
Frequently asked questions
What is the unit of acoustic impedance?
The SI unit is the pascal-second per metre (Pa-s/m), also called the Rayl in honour of Lord Rayleigh. In practice, most materials have impedances in the millions of Rayls, so the megaRayl (MRayl = 10^6 Pa-s/m) is the standard working unit. Air is approximately 0.0004 MRayl; water is about 1.48 MRayl; steel is about 45 MRayl.
Why does ultrasound gel matter?
Air has an acoustic impedance of roughly 0.0004 MRayl, while soft tissue is about 1.5 MRayl. The intensity reflection coefficient at an air-tissue boundary is approximately 99.9 %, meaning almost no sound energy would enter the body without coupling. Ultrasound gel has an impedance close to tissue (~1.5 MRayl), so the reflection coefficient drops to nearly zero and the wave transmits efficiently.
What is the difference between specific and characteristic acoustic impedance?
Specific acoustic impedance (Z = rho x c) is a bulk material property and is what this calculator computes. Characteristic acoustic impedance sometimes refers to the same quantity for plane waves in a loss-free medium, which is numerically identical. Both equal the product of density and wave speed. The term "characteristic" is borrowed from transmission-line theory and is used more in engineering contexts.
How do reflection and transmission coefficients add up?
The intensity reflection coefficient R and the intensity transmission coefficient T always sum to exactly 1 (100 %), reflecting the conservation of energy. This is only true for the intensity coefficients - the pressure reflection and transmission coefficients do not sum to 1 in the same simple way, because they account for sign changes and impedance ratios.
Can acoustic impedance be negative?
The acoustic impedance Z = rho x c is always positive (density and wave speed are both positive). The pressure reflection coefficient r = (Z2 - Z1)/(Z2 + Z1) can be negative when Z2 < Z1 (a wave going from a denser to a less-dense medium), which signifies a phase inversion of the reflected pressure wave. However, the intensity reflection coefficient R = r^2 is always positive.