Speed of Sound vs. Temperature

## Question:

Mr. Jones,

I have a question regarding the speed of sound in air. Why is the speed of sound in air faster in warmer temperatures than in colder temperatures? Does it have to do with the air's density?

## Answer:

Hi Laurie,
As a very general proposition the speed of a traveling wave is proportional to the square root of an (elastic property divided by an inertial property). In the case of air and other media where the elastic property or springiness is described by a bulk modulus (change in volume per unit volume for a given stress) and the inertial property is the density (mass per unit volume) the velocity is proportional to the square root of the bulk modulus over the density. As the temperature of air increases the density decreases so the denominator of the expression for the velocity decreases, causing an increase in velocity.

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JDJ