# Speed of Sound

Does anyone have an equation that gives the speed of sound in respect to the density and temperature of the medium in which the sound wave is propagating? I know the speed of sound in average temperature air molecules is like 700mph (I think).

Janus
Staff Emeritus
Gold Member
The speed of sound is equal to

s= [squ](E/D)

where E is the elasticity(Young's modulus) and D is the density.

For air, E = 1.41P (approx.)

Since pressure and density go hand in hand, barometric pressure does not effect the speed of sound.

Density varies inversely by temp(Kelvin), so the speed of sound varies by the squareroot of temp.

thus : S1/S2 = [squ](T1/T2)

Sound travels through air at 332 m/s (741mph) at 0°C (273°K) so at room temp 22°C (295°K), it would travel at

S2 = 741/[squ](273/295) = 770 mph

Etc.

russ_watters
Mentor
Originally posted by Janus
Since pressure and density go hand in hand, barometric pressure does not effect the speed of sound.
This one always confused me, so let me expand. Hell, my understanding may even be wrong, but it makes sense to me . Sound waves propagate by air molecules bouncing off of each other. Since the speed an air molecule travels is determined by temperature (and its mass of course), thats what determines the speed of sound. In air less dense, each individual molecule will travel further than in more dense air, but the speed it travels before hitting the next molecule is unchanged.