# What causes an increase in sound speed in a medium?

Its an established fact that increase in the temperature causes increase in speed of sound waves but what is the property which is changed by changing temperature ? Does frequency and wavelength get affected by temperature?

The speed of sound is given by the Newton-Laplace equation:

$$v = \sqrt{\frac{K}{\rho}}$$

where $K$ is the bulk modulus (i.e. a measure of stiffness) and $\rho$ is the density. The physical interpretation of this is fairly obvious. Stiffer substances recoil faster from a displacement so increasing the stiffness increases the speed of sound. Heavier substances recoil more slowly from a displacement so increasing the density decreases the speed of sound.

The effect of temperature lies in how it changes $K$ and $\rho$, but the effect will vary for different materials. For an ideal gas the the bulk modulus P is simply the gas pressure multiplied by the adiabatic index, $\gamma$, so the speed is given by:

$$v = \sqrt{\frac{\gamma P}{\rho}} \tag{1}$$

We can manipulate this equation using the ideal gas formula:

$$PV = nRT$$

For example the density is $nM/V$, where $M$ is the molar mass of the gas, so:

$$\rho = \frac{nM}{V} = \frac{PM}{RT}$$

If we make this substitution in equation (1) we get:

$$v = \sqrt{\frac{\gamma RT}{M}}$$

giving us the result that the speed of sound increases with temperature as you said in your question.

• But does increasing temperature increases its wavelength and frequency? Oct 10, 2014 at 14:42
• @user60180: that depends on what you're asking. The frequency of a sound wave depends on what is generating it. If I play a 1kHz tone on my HiFi then the frequency doesn't change with temperature. However because the speed of sound changes the wavelength will also change in proportion. Oct 10, 2014 at 15:24