# How to relate speed of sound with relative humidity?

I am exploring the idea of measuring the humidity of a space using sound waves, however I am having trouble finding a mathematical relationship between the speed of sound and the humidity level.

$c_{air} = 331.3 \sqrt{1 + \frac{T}{273.15}}$ but this is for dry air (0%RH)

How can I factor the effects of humidity into this relationship?

Speed of sound in a gas is given by the equation: $$c = \sqrt{\gamma R T}$$

where $\gamma = c_p/c_v$ ( $c_p$ and $c_v$ are specific heats), $R$ is the gas constant, and $T$ is temperature. The specific heat of a gas changes with humidity, so varying these will vary your calculated speed of sound.

This page has a calculator as well as a great explanation of how their formula works.

Hope this helps!

The speed of sound in a gas is:

$$c = \sqrt{\gamma R T}$$

where $\gamma = c_p/c_v$ is the ratio of specific heats, $R$ is the specific gas constant and $T$ is temperature. Both $\gamma$ and $R$ depend on the composition of the gas, which includes humidity in air.

The specific heats are $c_p = 1.005+1.82H$ (see this answer) where $H$ is the absolute humidty and $c_v = c_p - R$. Finally, $R = R_{univ}/M_{gas}$ where $M_{gas}$ is the molecular weight of the gas (which depends on humidity).

To get it all in terms of relative humidity is just an exercise in unit conversion.

you can simply use the formula as

Velocity = 331.4 + 0.6*Temperature + 0.0124*Relative_Humidity

Temperature is in Celsius Degrees Relative Humidity can be measured by sensors in %age

• What units of velocity? – Whit3rd Jul 2 '18 at 20:48
• Where did you get your formula from? – sammy gerbil Aug 13 '18 at 7:41