Calculating an accurate speed of sound in humid air

Understanding how sound travels through humid air is integral for measurement standards. Beyond meteorological applications, like characterizing temperature distributions of the atmospheric boundary layer, it can also be used to estimate temperature-dependent corrections in optical distance measurements.

The last comprehensive predictive model for the speed of sound in humid air, however, was published in 2002.

By revising input data and modifying the formulas of the previous model, Gavioso et al. reduced the standard uncertainty by more than an order of magnitude. The dominant contribution was recent improvements in theoretical calculations for the heat capacities of nitrogen and oxygen as a function of temperature.

The team also developed a novel experimental setup to validate the model at near-ambient temperature and pressure conditions. They determined the acoustic wavelength by measuring the phase delay between a speaker and a microphone at varying distances in a hemi-anechoic chamber, an experimental room that absorbs sound in most directions. An acoustic resonator continuously measured the speed of sound to verify uncertainty budgets and ensure experimental consistency.

“The experiment represents a practical application of our work. Laser interferometry uses a speed of sound measurement to determine the temperature of the air along the optical path to correct for the temperature dependence of the refractive index,” said author Roberto Gavioso. “Because we now have an accurate model of the speed of sound in air, the determination of the air temperature, and therefore the refractive index correction, will also be accurate.”

Future, precisely controlled laboratory experiments will test the model’s accuracy in a wider range of pressure, temperature, and humidity conditions. Gavioso hopes the model will become routinely used by other communities, particularly in acoustic metrology.

Source: “Speed of sound in humid air: Accurate thermodynamic model and experimental validation,” by R.M. Gavioso, M. Astrua, M. Zucco, and M. Pisani, Journal of Physical and Chemical Reference Data (2025). The article can be accessed at https://doi.org/10.1063/5.0294663 .