Speed of Sound

Calculation formulas for the speed of sound in gases, fluids and solids.

Acoustic Velocity and Speed of Sound

The velocity at which these small disturbances will propagate through the medium is called the Acoustic Velocity or the Speed of Sound.

Acoustic velocity can be expressed as:

speed of sound

In equation (1) the speed of sound is related to changes in pressure and density of the fluid.

In equation (2) the speed of sound is in terms of the Bulk Modulus for Elasticity and density of the medium. This equation is valid for liquids, solids and gases. The sound will travel faster through media with higher elasticity and lower density. If the medium is not compressible at all - incompressible - the speed of sound is infinite (c ≈ ∞).

Medium Properties at 1 bar and 0 ^oC	Bulk Modulus for Elasticity E_v (N/m²)	Density ρ (kg/m³)
Water	2,06 10⁹	999,8
Oil	1,35 10⁹	920
Ethyl Alcohol	0,94 10⁹	810
Mercury	28,5 10⁹	13.595

Since the disturbances introduced in some 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 (3) and (4).

For an ideal gas the speed of sound is proportional to the square root of absolute temperature.

Example - Speed of Sound in Air

If we have air at 0 ^oC and the absolute pressure is 1 bar - the speed of sound can be calculated:

c = (1,4 287 273)^1/2 = 331,2 (m/s)

where

k=1,4 and R=287 (J/K kg)

If we have air at 20 ^oC and the absolute pressure is 1 bar - the speed of sound can be calculated:

c = (1,4 287 293)^1/2 = 343,1 (m/s)

Example - Speed of Sound in Water

If we have water at 0 ^oC - the speed of sound can be calculated:

c = (2,06 10⁹/999,8)^1/2 = 1435,4 (m/s)

where

E_v= 2,06 10⁹ (N/m²) and ρ = 999,8 (kg/m³)

Speed of Sound in Water - Speed of sound in water at different temperatures - imperial and SI units.

Speed of Sound in Solids

Speed of Sound in some common Solids

Subsonic and Supersonic speed

If the Mach Number is below 1, the flow velocity is lower than the speed of sound - and the speed is subsonic.
If the Mach Number is above 1, the flow velocity is higher than the speed of sound - and the speed is supersonic.

The Mach Number An introduction to and a definition of the Mach Number

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