v = √(γRT/M)

where:

* v is the velocity of sound (in meters per second, m/s)

* γ is the adiabatic index (for air, γ ≈ 1.4)

* R is the ideal gas constant (8.314 J/mol·K)

* T is the temperature in Kelvin (K)

* M is the molar mass of air (approximately 0.029 kg/mol)

Explanation:

* Adiabatic Index (γ): This represents the ratio of specific heats at constant pressure and constant volume. For air, it's approximately 1.4.

* Ideal Gas Constant (R): This constant relates pressure, volume, temperature, and the number of moles of a gas.

* Temperature (T): The velocity of sound increases with temperature.

* Molar Mass (M): This is the mass of one mole of air molecules.

Simplified Formula:

For practical purposes, a simplified formula can be used:

v ≈ 331.5 + 0.6T

where:

* v is the velocity of sound (in meters per second, m/s)

* T is the temperature in Celsius (°C)

Note: This simplified formula is valid for temperatures near room temperature.

Example:

To calculate the velocity of sound in air at 20°C:

Using the simplified formula:

v ≈ 331.5 + 0.6(20)

v ≈ 343.5 m/s