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### Speed of Sound in Liquid or Fluid Formula

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 gc / ρ )0.5

Eq. 2a, SI Units
a =
( 1 / ( β ρ ) ) 0.5

Eq. 2b U.S.
a = ( gc / ( 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 ft-lbf/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 gc / ρ )1/2 = ( k gc p / ρ )1/2

Eq. 3b, US
a = ( k gc RT )1/2 = ( k gc 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
a1 / a2 = ( T1 / T2 )

Where:

a = speed of sound ft/sec, (m/s)
E = bulk modulus lbf/ft2, (Pa)
β = compressibility ft2/lbf, (Pa-1)
ρ = density lbm/ft3, (kg/m3)
gc = gravitational acceleration, 32.2 ft/sec2, (9.81 m/s2)
MW = Molecular weight, lbm/lbmol, (kg/kmol)
R = specific gas constant ft-lbf/lbmol-°R, (J/kmol·K)
R* = universal gas constant, 1545.35 (8314.47) ft-lbf/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

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