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Efficiently compute the speed of sound in air.
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Speed of Sound

CircleCI Coverage Status

Speed of Sound is a library to efficiently compute the speed of sound in air. It is intended for use in embedded systems that require a high-precision computation of the speed of sound in air based a variety of ambient conditions.


Quick facts

  • Computes the speed of sound in air based on temperature, relative humidity, pressure, and carbon dioxide mole fraction.
  • Runtime of subsequent speed of sound computations reduced by 67.7% through the use of calculus linear approximations.
  • Approximation maintains precision of at least 0.05% with environmental factors varying up to 20%.

Environmental parameters

The speed of sound computation takes on the following parameters and is only valid in within the following range.

Variable (units) Minimum Default Maximum
temperature (°C) 0.0 20.0 30.0
relative humidity (dimensionless) 0.0 0.5 1.0
pressure (Pa) 75000.0 101325.0 102000.0
Carbon dioxide mole fraction (dimensionless) 0.0 0.000314 0.01

Note: This library is intended for use with embedded systems and therefore does not throw an exception if passed an invalid quantity. Instead, methods are provided to validate that values are within the given constraints (see Usage).


#include "speed_of_sound.h"

Create Environment object to hold ambient conditions (initializes values to default).

speedofsound::Environment ambient_conditions;

Access Environment object members.


Adjust environment variables.

ambient_conditions.temperature_ = 25.0;

Check if environmental parameters are within specified constraints (see Constraints for details).

// Validate individual parameters
bool is_valid = ambient_conditions.ValidateTemperature();
is_valid = ambient_conditions.ValidateHumidity();
is_valid = ambient_conditions.ValidatePressure();
is_valid = ambient_conditions.ValidateCO2MoleFraction();

// Validate all parameters
is_valid = ambient_conditions.ValidateEnvironment();

Create SpeedOfSound object and set initial conditions.

speedofsound::SpeedOfSound speed_of_sound(ambient_conditions);

speedofsound::SpeedOfSound speed_of_sound(); // Default Environment values

Compute speed of sound.

// Full computation, reset initial conditions
double sound_speed = speed_of_sound.Compute(ambient_conditions);

// Full computation, do not reset initial conditions
sound_speed = speed_of_sound.QuickCompute(ambient_conditions);

// Linear approximation, do not reset initial conditions
sound_speed = speed_of_sound.Approximate(ambient_conditions);


#include <iostream>
#include "some_sensor.h"
#include "speed_of_sound.h"

int main() {
  speedofsound::Environment ambient_conditions;
  ambient_conditions.temperature_ = sensor::MeasureTemperature();

  // Initial "full" computation
  speedofsound::SpeedOfSound speed_of_sound(ambient_conditions);

  const auto distance = 100.0; // meters
  while (true) {
    ambient_conditions.temperature_ = sensor::MeasureTemperature();
    if (!ambient_conditions.ValidateTemperature()) break;
    const auto sound_speed = speed_of_sound.Approximate(ambient_conditions);
    std::cout << "It would take a sound wave approximately " <<
                 distance / sound_speed << " seconds to travel " <<
                 distance << " meters." << std::endl;

Notes on notation

The following abbreviations are used in theory-related computations.

Lower-case variables (t, h, etc.) represent measured environmental parameters. Variables starting with an uppercase character (C, Psv, etc.) represent computed values.

Variable Meaning Units
C speed of sound meters per second (m/s)
t temperature Celsius (°C)
T thermodynamic temperature Kelvin (K)
h relative humidity fraction (dimensionless)
xc Carbon dioxide mole fraction fraction (dimensionless)
p pressure Pascals (Pa)
Xw mole fraction of water in air fraction (dimensionless)
Psv saturation vapor pressure Pascals (Pa)
F Enhancement factor for moist air dimensionless
k00, k01, ... experimental constants various

dy_dx denotes the partial derivative of y with respect to x.


Tests are written using Google Test.

Run all tests:

$ test/test


The equation for computing the speed of sound in air uses Owen Cramer's research.

J. Acoust. Soc. Am. 93, 2510 (1993);

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