text: For an ideal gas, K (the bulk modulus in equations above, equivalent to C, the coefficient of stiffness in solids) is given by
  Thus, from the Newton–Laplace equation above, the speed of sound in an ideal gas is given by
  where
  * γ is the adiabatic index also known as the isentropic expansion factor. It is the ratio of the specific heat of a gas at constant pressure to that of a gas at constant volume () and arises because a classical sound wave induces an adiabatic compression, in which the heat of the compression does not have enough time to escape the pressure pulse, and thus contributes to the pressure induced by the compression;
  * p is the pressure;
  * ρ is the density.
  Using the ideal gas law to replace p with nRT/V, and replacing ρ with nM/V, the equation for an ideal gas becomes
  where
  * c is the speed of sound in an ideal gas;
  * R is the molar gas constant;
  * k is the Boltzmann constant;
  * γ (gamma) is the adiabatic index. At room temperature, where thermal energy is fully partitioned into rotation (rotations are fully excited) but quantum effects prevent excitation of vibrational modes, the value is  for diatomic gases (such as oxygen and nitrogen), according to kinetic theory. Gamma is actually experimentally measured over a range from 1.3991 to 1.403 at , for air. Gamma is exactly  for monatomic gases (such as argon) and it is  for triatomic molecule gases that, like , are not co-linear (a co-linear triatomic gas such as  is equivalent to a diatomic gas for our purposes here);
  * T is the absolute temperature;
  * M is the molar mass of the gas. The mean molar mass for dry air is about ;
  * n is the number of moles;
  * m is the mass of a single molecule.
  This equation applies only when the sound wave is a small perturbation on the ambient condition, and the certain other noted conditions are fulfilled, as noted below. Calculated values for c have been found to vary slightly from experimentally determined values.
  Newton famously considered the speed of sound before most of the development of thermodynamics and so incorrectly used isothermal calculations instead of adiabatic. His result was missing the factor of γ but was otherwise correct.
  Numerical substitution of the above values gives the ideal gas approximation of sound velocity for gases, which is accurate at relatively low gas pressures and densities (for air, this includes standard Earth sea-level conditions). Also, for diatomic gases the use of  requires that the gas exists in a temperature range high enough that rotational heat capacity is fully excited (i.e., molecular rotation is fully used as a heat energy "partition" or reservoir); but at the same time the temperature must be low enough that molecular vibrational modes contribute no heat capacity (i.e., insignificant heat goes into vibration, as all vibrational quantum modes above the minimum-energy-mode have energies that are too high to be populated by a significant number of molecules at this temperature). For air, these conditions are fulfilled at room temperature, and also temperatures considerably below room temperature (see tables below). See the section on gases in specific heat capacity for a more complete discussion of this phenomenon.
  For air, we introduce the shorthand
  In addition, we switch to the Celsius temperature , which is useful to calculate air speed in the region near 0 °C (273 K). Then, for dry air,
  Substituting numerical values
  and using the ideal diatomic gas value of , we have
  Finally, Taylor expansion of the remaining square root in  yields
  A graph comparing results of the two equations is to the right, using the slightly more accurate value of  for the speed of sound at .