Acoustic Impedance Calculator

The acoustic impedance calculator will help you determine a material's specific acoustic impedance and the intensity reflection and transmission coefficients of a sound wave at the boundary of two materials.

Acoustic impedance3.962e+7 Pa·s/mρc — enormously higher than air's 413, which is why almost all sound reflects at a solid-air boundary rather than crossing it

Speed of sound in the rod5,047.54 m/s√(E/ρ) — 14.72× the speed in air, which is why sound carries so far along a rail

Reflected at an air boundary99.9958%((z₂ − z₁)/(z₂ + z₁))² against air's 413 Pa·s/m — it is the MISMATCH that decides this, not the absolute impedance

Transmitted into the air0.00417%-43.8 dB — a fraction of a percent, which is why a solid wall is such a good sound barrier and why ultrasound scanning needs coupling gel

Impedance ratio to air9.587e+4:1matching two media means matching these; a mismatch this large reflects almost everything

This is the thin-rod speednot the bulk speeda rod free to expand sideways uses E alone; in bulk material the constraint raises the speed, so seismic and ultrasonic figures are higher

Travel time over 340 m67.3595 ms

Wavelength of a 440 Hz tone11.4717 mconcert A — wavelength scales with the medium's speed, which is why instruments must be retuned as a hall warms

The formula

gas c = √(γRT/M); solid rod c = √(E/ρ)

Temperature, not pressure

The speed of sound in a gas is √(γRT/M), which contains temperature but not pressure. Pressure and density appear in the underlying relation as a ratio and cancel exactly, so taking a gas up a mountain does not slow its sound — only cooling it does. This is why the speed of sound falls through the troposphere and then holds steady through the isothermal stratosphere while the pressure keeps dropping.

Molar mass is the other lever. Helium's 4 g/mol against air's 29 makes sound nearly three times faster in it, which is what changes a voice. The vocal folds still vibrate at the same rate — the pitch is unchanged — but the vocal tract's resonances scale with the speed of sound and all shift upward, altering the timbre. Describing it as raising the pitch is wrong.

In solids the relevant relation is √(E/ρ), giving speeds of several kilometres per second. The huge acoustic impedance mismatch with air means almost all sound reflects at the boundary rather than crossing it — which is simultaneously why sound travels so far along a rail and why so little of it reaches your ear through the air.