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Engineering ToolBox > Speed of Sound Formulas
As a consequence of the compressibility of gases, fluids or solids, a disturbance introduced in some point of a substance will propagate through the substance with a finite velocity.
The velocity at which these small disturbances will propagate through the medium is called the Acoustic Velocity or the Speed of Sound.
The acoustic velocity is related to the change in pressure and density of the substance and can be expressed as
c = (dp / dρ)1/2 (1)
where
c = sound velocity (m/s, ft/s)
dp = change in pressure (Pa, psi)
dρ = change in density (kg/m3, lb/ft3)
The acoustic velocity can alternatively be expressed as
c = (E / ρ)1/2 (2)
where
E = bulk modulus elasticity (Pa, psi)
This equation is valid for liquids, solids and gases. The sound travels faster through media with higher elasticity and/or lower density. If a medium is not compressible at all - incompressible - the speed of sound is infinite (c ≈ ∞).
| Medium Properties at 1 bar and 0 oC | ||
| Substance | Bulk Modulus Elasticity - E - 109 (N/m2) | Density - ρ - (kg/m3) |
| Water | 2.15 | 999.8 |
| Oil | 1.35 | 920 |
| Ethyl Alcohol | 1.06 | 810 |
| Mercury | 28.5 | 13595 |
Since the acoustic disturbance introduced in a point is very small, the heat transfer can be neglected and for gases assumed isentropic. For an isentropic process the ideal gas law can be used and the speed of sound can be expressed as
c = (k p / ρ)1/2
= (k R T)1/2 (3)
where
k = ratio of specific heats (adiabatic index)
p = pressure (Pa, psi)
R = gas constant
T = absolute temperature (oK, oR)
For an ideal gas the speed of sound is proportional to the square root of the absolute temperature.
The speed of sound in air at 0 oC and absolute pressure 1 bar can be calculated as
c = (1.4 287 273)1/2 = 331.2 (m/s)
where
k = 1.4
and
R = 287 (J/K kg)
The speed of sound in air at 20 oC and absolute pressure 1 bar can be calculated as
c = (1.4 287 293)1/2
= 343.1 (m/s)
The speed of sound in water at 0 oC can be calculated as
c = (2.06 109/999.8)1/2
= 1435.4 (m/s)
where
Ev= 2.06 109 (N/m2)
and
ρ = 999.8 (kg/m3)