How this instrument works
Drive a plane sound wave through any material and two quantities oscillate in lockstep: acoustic pressure, and the velocity of particles carrying it along. Their ratio depends on that material alone, and that ratio is acoustic impedance — pressure divided by particle velocity, measured in rayl. Density supplies inertia, sound speed encodes stiffness, and their product states how firmly a medium resists being set into motion by a given push.
Lord Rayleigh laid out this machinery in The Theory of Sound (1877), and acousticians later hung his name on its unit. One MKS rayl equals one pascal-second per metre; an older CGS rayl, still lurking in mid-century papers, runs ten times larger, so any figure quoted without naming its system deserves scrutiny. Magnitudes span an enormous range. Air near room temperature sits around 420 rayl, water at 1.5 MRayl, soft tissue 1.63, cortical bone close to 7.8, aluminium near 17, steel about 46, and PZT ceramic inside an ultrasound probe roughly 33.
What ρc assumes is a plane progressive wave in a lossless, non-dispersive medium, far enough from any source that pressure and particle velocity stay in phase. Close to any small radiator, wavefront curvature throws them out of step and impedance turns complex, gaining a reactive part that merely stores energy rather than passing it on — which is why a bare loudspeaker cone moves plenty of air yet radiates so feebly down low. Strongly absorbing or dispersive materials likewise carry an imaginary component this product cannot see. One more boundary on its authority: impedance never predicts absorption. It governs what happens where two media meet, not what a wave surrenders in transit.
- Put your figure into Medium density — 1000 for water, 1.225 for sea-level air, 7850 for steel. Its unit menu also takes g/cm3.
- Enter Speed of sound in the medium: longitudinal bulk value for that same material at that same temperature, never a shear or surface figure.
- Read Acoustic impedance (rayl). Divide by one million to quote MRayl, which is how ultrasound and weld-inspection literature writes tissue and metal.
- Studying a boundary? Run this twice, then feed both answers into R = ((Z₂ − Z₁) ⁄ (Z₂ + Z₁))² for reflected power fraction.
- Designing a matching layer? Aim at the geometric mean √(Z₁·Z₂) of whatever material sits on either side.
Worked example — water, and why gel exists
Fresh water at its textbook round numbers: Medium density 1000 kg/m3, Speed of sound in the medium 1500 m/s. Acoustic impedance (rayl) hands back 1000 × 1500 = 1500000 rayl, or 1.5 MRayl. That single figure anchors medical ultrasound, because soft tissue lands within roughly 10% of it — a probe designed against water therefore works on a patient at all.
Now stand air on one side of that boundary: 1.225 × 343 = 420 rayl, some 3,500 times smaller. Feed both into R and you get ((1500000 − 420) ⁄ (1500000 + 420))² = 0.9989, meaning 99.9% of your wave turns straight around while barely one part per thousand crosses. A film of air mere micrometres thick under a transducer thus behaves as an acoustic wall. Gel exists to replace it with something near 1.5 MRayl — and identical arithmetic explains why fish ignore shouting from a riverbank.
Questions
What exactly is a rayl, and is it an SI unit?
One rayl is one pascal-second per metre, equivalently one kilogram per square metre per second. Strictly it is a named convenience honouring Lord Rayleigh rather than an SI unit; SI itself would write kg·m⁻²·s⁻¹. Mind which system a source uses: a CGS rayl equals 1 dyn·s/cm³, ten times larger, so water reads 1.5 MRayl here yet 150,000 rayl in some older acoustics papers. This instrument works purely in MKS.
Does acoustic impedance tell me how much sound a material absorbs?
No — those are independent properties, and conflating them causes real design mistakes. Impedance governs boundaries: how a wave divides into reflected and transmitted portions where two media meet. Absorption is a bulk property, quoted in dB per centimetre (often per megahertz too), driven by viscosity, thermal conduction and molecular relaxation. Water and silicone rubber can share nearly identical impedance while differing tenfold in loss. Any good acoustic window needs matched impedance and low attenuation together, which is most of the engineering.
Is this the same quantity as acoustic impedance in Pa·s/m³?
No, and overlapping names trip people constantly. This sheet returns specific or characteristic acoustic impedance — pressure over particle velocity, in rayl. Acoustic impedance proper divides pressure by volume velocity, carries units of Pa·s/m³, and depends on radiating area: ρc/S for a piston driving a tube. Mechanical impedance, force over velocity, is yet another relative, in N·s/m. Check what sits underneath before trusting anyone's number.
Which speed of sound should I enter for a solid?
Longitudinal bulk wave speed, since these expressions describe a normal-incidence pressure wave. Solids also carry shear waves at roughly half that pace, while thin rods and plates have their own lower bar and plate velocities. Steel makes a useful warning: bulk longitudinal 5900 m/s yields about 46 MRayl, whereas a rod velocity of 5100 m/s would hand you 40 instead. Pick whichever mode your measurement genuinely uses.
How do I choose a quarter-wave matching layer?
Target the geometric mean of impedances either side, √(Z₁ Z₂), at a thickness of one quarter wavelength measured inside that layer. A PZT element near 33 MRayl coupled into tissue at 1.63 wants √(33 × 1.63) ≈ 7.3 MRayl, which is broadly what metal-loaded epoxies are formulated to deliver. A single layer only performs across a narrow band, so broadband probes stack two or three in a graded sequence.
Do temperature and frequency shift the answer?
Temperature does, through both terms at once. Warm water gains sound speed while losing density, and those trends partly cancel: impedance peaks near 1.52 MRayl somewhere in a 50–60 °C band, worth a percent or two when precision matters. Frequency barely registers in ordinary media, since ρ and c hold near enough constant from audio through low megahertz. Only strongly dispersive or resonant materials — bubbly liquids, porous foams, some composites — break that comfort.