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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 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 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
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)
g_c = 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

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