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Speed of Sound in Liquid or Fluid Formula
Fluids Flow Design and Engineering
Heat Transfer Engineering
Thermodynamics
Speed of Sound in a Liquid or Fluid Formula Equations and Calculator
The speed of sound (acoustic velocity or sonic velocity), in a fluid is a function of its bulk modulus (or, equivalently, of its compressibility). Equation 1 gives the speed of sound through a liquid.
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Eq. 1a, SI Units
a = ( E / ρ )^{0.5}
Eq. 1b, U.S.
a = ( E g_{c} / ρ )^{0.5}
Eq. 2a, SI Units
a = ( 1 / ( β ρ ) ) ^{0.5}
Eq. 2b U.S.
a = ( g_{c} / ( β ρ ) ) ^{0.5}
Equation 3 gives the speed of sound in an ideal gas. The temperature, T, must be in degrees absolute (i.e., °R or °K). For air, the ratio of specific heats is k = 1.4, and the molecular weight is 28.967. The universal gas constant is R^{*} 1545.35 ftlbf/lbmol°R (8314.47 J/kmol·K). a = ( E / ρ )^{1/2} = ( k p / ρ )^{1/2}
a = ( E / ρ )^{1/2} = ( k p / ρ )^{1/2}
Eq. 3a, SI
a = ( k R T )^{1/2} = ( k R^{*} T / MW )^{1/2}
a = ( E g_{c} / ρ )^{1/2} = ( k g_{c} p / ρ )^{1/2}
Eq. 3b, US
a = ( k g_{c} RT )^{1/2} = ( k g_{c} R^{*} T / MW )^{1/2}
Since k and R are constant for an ideal gas, the speed of sound is a function of temperature only. Equation 4 can be used to calculate the new speed of sound when temperature is varied.
Eq. 4
a_{1} / a_{2} = ( T_{1} / T_{2} )
Where:
a = speed of sound ft/sec, (m/s)
E = bulk modulus lbf/ft^{2}, (Pa)
β = compressibility ft^{2}/lbf, (Pa^{1})
ρ = density lbm/ft^{3}, (kg/m^{3})
g_{c} = gravitational acceleration, 32.2 ft/sec^{2}, (9.81 m/s^{2})
MW = Molecular weight, lbm/lbmol, (kg/kmol)
R = specific gas constant ftlbf/lbmol°R, (J/kmol·K)
R^{*} = universal gas constant, 1545.35 (8314.47) ftlbf/lbmol!R J/kmol·K
k = ratio of specific heats
The symbol c is also used for the speed of sound.
Approximate Speeds of Sound (at one atmospheric pressure)
Material 
Speed of sound


(ft/sec)

(m/s)


air 
1130 at 70° F

330 at 0° C

aluminum 
16,400

4990

carbon dioxide 
870 at 70° F

260 at 0° C

hydrogen 
3310 at 70° F

3310 at 70° C

steel 
16,900

5150

water 
4880 at 70° F

1490 at 20° C

(Multiply ft/sec by 0.3048 to obtain m/s.)
Reference:
Civil Engineering Reference Manual, Fifteenth Edition, Michael R. Lindeburg, PE
Related:
 Speed of Sound Table Chart
 Speed of Sound in Various Liquids and Solids
 Bulk Modulus for Materials Metals and Liquids
 Density of Common Engineering Materials
 Air Density Table and Specific Weight Table, Equations and Calculator
 Densities of Metals and Elements Table
 Water Vapor Density
 Density Equation and Review