The acoustic impedance calculator above does two related jobs. First it gives the specific acoustic impedance of a medium, which is simply its density multiplied by the speed of sound in it. Then it takes a second medium and works out what happens when a sound wave travelling in the first one hits the boundary: how much of the pressure bounces back, how much of the power crosses over, and what that loss is in decibels.
Arb Digital builds free physics calculators that each own one job properly. The speed of sound calculator gives you one of the two inputs this page needs, and the density calculator gives you the other, but neither combines them into an impedance or says anything about what happens at a boundary. This page starts where those two leave off.
What This Acoustic Impedance Calculator Does
Specific acoustic impedance is the ratio of sound pressure to particle velocity in a travelling plane wave. It has units of pascal-seconds per metre, usually written as the rayl, and for a plane wave in a uniform medium it collapses to the product of density and wave speed. That is the whole definition: z = ρc. It tells you how hard a medium pushes back for a given amount of motion.
What makes impedance the central quantity in acoustics is that boundaries care about it. When a wave reaches an interface between two media, the fraction that reflects is fixed entirely by the ratio of the two impedances. Density alone does not decide it. Sound speed alone does not decide it. Only the product does.
So the tool reports both impedances, the pressure reflection coefficient, the fraction of incident power that gets through, and the transmission loss in decibels. It also converts the specific impedance into an acoustic impedance for a duct of the area you enter, which is the version you need when you are working with tubes, horns and enclosures rather than open space.
How to Use It
- Enter the density and sound speed of the medium the wave is in. That is medium 1, the incident side. The defaults describe air at about twenty degrees Celsius.
- Enter the same two figures for the medium on the other side. The defaults describe fresh water. Swapping the two media changes the sign of the pressure reflection coefficient but not the transmitted power.
- Set the area if you care about a duct. Acoustic impedance in a tube is the specific impedance divided by the cross-sectional area, and it is what you compare against a source impedance.
- Enter an incident power if you want absolute figures. The note under the grid then splits it into the reflected and transmitted shares in watts.
- Read the transmission loss last. It is the single most useful number on the page, because it tells you directly how many decibels you lose crossing the boundary.
The Formula: How Acoustic Impedance Is Calculated
The specific acoustic impedance of a medium is z = ρc, where ρ is density in kilograms per cubic metre and c is the speed of sound in metres per second. The result is in rayl. Georgia State University's HyperPhysics page on acoustic impedance derives this from the relationship between pressure, particle displacement and the bulk modulus, and notes that the product form is convenient precisely because it is what reflection and transmission coefficients are built from.
At a boundary between medium 1 and medium 2, the pressure reflection coefficient for normal incidence is R = (z2 − z1) ÷ (z2 + z1). The fraction of incident intensity that reflects is R², and by conservation the fraction transmitted is 1 − R², which can also be written directly as 4z1z2 ÷ (z1 + z2)². The HyperPhysics page on reflection and transmission of plane waves sets out both coefficients and works the steel-and-water case, including the phase reversal that appears when the wave meets a lower impedance.
Transmission loss in decibels is 10 log10 of the reciprocal of the transmitted power fraction, following the ordinary power-ratio definition of the decibel used throughout acoustics and described on the HyperPhysics decibels page.
Work the defaults by hand. Air at 1.204 kg/m³ and 343 m/s gives z1 = 412.97 rayl. Fresh water at 998 kg/m³ and 1,481 m/s gives z2 = 1,478,038 rayl. Then R = (1,478,038 − 413) ÷ (1,478,038 + 413) = 0.99944. Squaring that gives 0.99888 reflected, so only 0.001117 of the power — about one part in nine hundred — crosses into the water. In decibels that is a transmission loss of 29.5 dB. The direct formula agrees: 4 × 412.97 × 1,478,038 ÷ (1,478,451)² = 0.001117.
Why Sound Barely Crosses from Air into Water
That 0.1 per cent figure is one of the most consequential numbers in physical acoustics, and it explains a great deal of everyday experience. Shouting at a swimmer underwater achieves almost nothing, not because water absorbs the sound but because the boundary refuses to let it in. The impedance ratio is about 3,600 to one, and a ratio that extreme reflects nearly everything.
The same mismatch runs the other way, which is why a diver hears little of what happens above the surface. It is also why the middle ear exists: the inner ear is fluid-filled, and the lever system and area ratio between the eardrum and the oval window together supply roughly the impedance transformation the boundary would otherwise deny.
Medical ultrasound faces the identical difficulty at a much smaller scale. Soft tissue has an impedance near 1.6 million rayl and air has 413, so a film of air between the transducer and the skin would reflect essentially the entire beam. That is the only reason coupling gel exists: it fills the gap with something whose impedance is close to tissue, and the boundary becomes almost invisible.
Sign, Phase and Why the Direction Matters
The pressure reflection coefficient carries a sign, and the sign is physically real. Going from a low impedance to a high one — air into water, water into steel — gives a positive R, and the reflected pressure wave returns in phase with the incident one. Going the other way gives a negative R, and the reflected wave comes back inverted.
Swap medium 1 and medium 2 in the calculator and you will see the magnitude of R stay identical while the sign flips. The transmitted power fraction does not change at all, because the expression 4z1z2 ÷ (z1 + z2)² is symmetric in the two impedances. Reciprocity is not an accident here; it falls out of the algebra.
The inversion matters whenever a reflected wave meets the incident one, which is to say in every pipe, duct, string and tube. An open pipe end is close to a low-impedance termination and inverts the pressure wave; a closed end is a high-impedance termination and does not. That single distinction is what makes a pipe closed at one end sound an octave lower than an open one of the same length, and it is a difference of sign, not of magnitude.
Specific Impedance Versus Acoustic Impedance
Three different quantities in acoustics are all called impedance, and mixing them up is the most common error on this topic. Specific acoustic impedance is pressure divided by particle velocity, measured in rayl, and it is a property of the medium alone. Acoustic impedance is pressure divided by volume velocity, measured in acoustic ohms, and it depends on the cross-sectional area as well as the medium. Mechanical impedance is force divided by velocity and belongs to the structure rather than the fluid.
The calculator gives you the first two, because they are the pair that matter for waves in fluids. For a duct of area A, the acoustic impedance is simply z ÷ A, so a narrow tube presents a much higher acoustic impedance than a wide one filled with the same air. This is why a loudspeaker in a horn is louder than the same driver in free air: the horn raises the acoustic impedance the cone sees, and the driver couples more of its motion into the medium instead of flapping uselessly.
Electrical intuition transfers cleanly. Pressure behaves like voltage and volume velocity like current, so matching two acoustic impedances buys the same maximum power transfer that matching two electrical ones does. The RLC impedance calculator handles the reactive circuit case with the same algebra.
Where This Sits Next to the Other Sound Tools
This page owns the boundary calculation, and the neighbouring tools own the steps either side of it. The speed of sound calculator produces the wave speed you enter here, across gases, liquids and solids. The sound attenuation calculator handles what happens as a wave travels through a medium rather than across a boundary, which is a completely separate loss mechanism. The decibel calculator and the sound level converter do the level arithmetic once you have a ratio.
On the geometry side, the wavelength calculator decides whether a boundary is acoustically large or small in the first place, and the bulk modulus calculator covers the stiffness that sets the sound speed in a fluid.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Comparing densities instead of impedances — a wave does not care which material is heavier. It cares about the product of density and speed, and the two comparisons can point in different directions.
- Squaring the reflection coefficient when you wanted pressure — R is a pressure ratio and R² is an intensity ratio. A boundary that reflects 90 per cent of the pressure reflects 81 per cent of the power.
- Assuming normal incidence always applies — every formula here is for a wave arriving perpendicular to the boundary. At an angle you need the full expressions with the incidence and refraction angles, and beyond a critical angle you get total internal reflection.
- Ignoring layer thickness — these results describe a single interface between two half-spaces. A thin layer between two media behaves quite differently and can be made almost transparent at one frequency.
- Using specific impedance where acoustic impedance is meant — the rayl and the acoustic ohm differ by a factor of area, and dropping that factor is a silent error of orders of magnitude in duct work.
Related Free Tools From Arb Digital
Get the wave speed from the speed of sound calculator and the density from the density calculator. For travel through a medium rather than across a boundary, use the sound attenuation calculator. For level arithmetic, use the decibel calculator and the sound level converter. The wavelength calculator covers wave geometry, the bulk modulus calculator covers fluid stiffness, and the RLC impedance calculator handles the electrical analogue. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
It is how hard a medium resists being set into motion by a sound wave, expressed as the ratio of pressure to particle velocity. For a plane wave it equals density times the speed of sound, so a stiff dense material has a high acoustic impedance and a light gas has a very low one.
The rayl is the unit of specific acoustic impedance, equal to one pascal-second per metre in SI. Air at room temperature is about 413 rayl, fresh water is about 1.48 million rayl, and steel is around 46 million rayl. The megarayl is used for the larger values.
Because the impedance ratio is roughly 3,600 to one, and reflection is set by that ratio. Only about one part in nine hundred of the incident power crosses the surface, which is a transmission loss of about 29.5 decibels. The rest bounces straight back into the air.
The amount of power reflected does not, because the transmission expression is symmetric in the two impedances. The phase does: going from low impedance to high gives a reflection in phase with the incident wave, and going from high to low inverts it.
Specific acoustic impedance is pressure over particle velocity and is a property of the medium, measured in rayl. Acoustic impedance is pressure over volume velocity and depends on cross-sectional area as well, measured in acoustic ohms. Divide the specific value by the area to get the second one.
Because a film of air between the transducer and the skin would reflect almost the entire beam. Tissue has an impedance near 1.6 million rayl and air has 413, so the gel replaces the air with something close to tissue and makes the boundary nearly transparent.
No. Everything on this page assumes the wave arrives perpendicular to the boundary. Oblique incidence needs the fuller expressions involving both the incidence and refraction angles, and above a critical angle the wave is totally reflected rather than partly transmitted.
Yes, if the products of density and sound speed happen to be similar. Materials with very different densities can still match well when their sound speeds compensate, which is exactly what matching layers in transducers are designed to exploit.
This tool is provided for educational and study use. It models plane waves at normal incidence between two lossless half-spaces, and does not account for oblique incidence, absorption, layered structures, anisotropy or near-field effects, so treat its output as a physics result rather than a measured or design-grade value.
