Acoustic Impedance Calculator
This acoustic impedance calculator finds the characteristic acoustic impedance of a medium, the property that decides how readily a sound wave travels through it and how much reflects at a boundary. Enter the density of the material and the speed of sound in it, and the calculator multiplies the two, Z equals density times speed, to give the impedance in rayl and in the more convenient MRayl used for solids and tissue. Acoustic impedance sits at the heart of ultrasound imaging, sonar, non destructive testing and loudspeaker design, because whenever sound crosses from one medium to another the mismatch between their impedances governs the split between reflected and transmitted energy. A big mismatch, like the one between air and human tissue, bounces almost all the sound straight back, which is exactly why a scanning probe needs a layer of gel to couple into the body. The calculator also shows the reflection coefficient you would get if this medium met air, a quick feel for how reflective the boundary is. Physics and engineering students use it to check impedance values from density and sound speed tables, and to build intuition for why some material pairings transmit sound cleanly while others act like a mirror. Enter SI units, kilograms per cubic metre for density and metres per second for speed, and the impedance comes out in rayl.
1 rayl = 1 Pa.s/m = 1 kg/(m2.s). MRayl is a million rayl. Reflection vs air is the fraction of sound intensity reflected if this medium met air (Z of air taken as 415 rayl), showing how strong the impedance mismatch is. Estimate only.
How it works
The characteristic acoustic impedance is the density of the medium multiplied by the speed of sound in it: Z equals rho times c. Denser materials and faster sound speeds both push the impedance up, which is why solids and liquids have impedances thousands of times larger than gases. The result is shown in rayl, the SI unit equal to one pascal second per metre, and again in MRayl for readability. The reflection figure uses the standard intensity reflection coefficient at a boundary, the squared ratio of the impedance difference to the impedance sum, comparing this medium against air taken at 415 rayl. That single number captures why sound struggles to cross a large impedance gap: when the two impedances are far apart the reflected fraction climbs towards 100 percent.
Worked example
Take water at room temperature, with a density of 1000 kilograms per cubic metre and a speed of sound of 1480 metres per second. The acoustic impedance is 1000 multiplied by 1480, which is 1,480,000 rayl, or 1.48 MRayl, a textbook value for water. Against air at 415 rayl the reflection coefficient is the square of (1,480,000 minus 415) divided by (1,480,000 plus 415), which rounds to 99.9 percent, so almost all the sound reflects at a water to air surface. Swap in soft tissue at about 1.63 MRayl and the water to tissue mismatch is tiny, so sound passes through easily, the principle behind ultrasound coupling gel.
Related calculators
- Density Calculator: density from mass and volume.
- Sound Intensity Calculator: intensity and sound level.
- Decibel Calculator: sound levels in decibels.
- Wavelength Calculator: wavelength from speed and frequency.
- Frequency Calculator: frequency, period and wavelength.