Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Speed of Sound Formulas

Calculation formulas for velocity of sound - sonic velocity - in gases, fluids or solids

Sponsored Links

A disturbance introduced in some point of a substance - solid or fluid - will propagate through the substance as a wave with a finite velocity.

sound velocity

Acoustic Velocity and Speed of Sound

The velocity at which a small disturbance will propagate through the medium is called Acoustic Velocity or 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)


c = speed of sound (m/s, ft/s)

dp = change in pressure (Pa, psi)

dρ = change in density (kg/m3, lb/ft3)

Speed of Sound in Gases, Fluids and Solids

The acoustic velocity can alternatively be expressed with Hook's Law as

c = (K / ρ)1/2                                 (2)


K = Bulk Modulus of Elasticity (Pa, psi)

ρ = density (kg/m3, lb/ft3)

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 ≈ ∞).

SubstanceBulk Modulus Elasticity
- K
(109 N/m2)
- ρ
Water 2.15 999.8
Oil 1.35 920
Ethyl Alcohol 1.06 810
Mercury 28.5 13595
  • properties at 1 bar and 0 oC

Speed of Sound - Sonic Velocity - in Ideal Gases

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)


k = ratio of specific heats (adiabatic index)

p = pressure (Pa, psi)

R = individual gas constant (J/kg K, ft lb/slug oR)

T = absolute temperature (oK, oR)

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

Example - Speed of Sound in Air

The speed of sound in air at 0 oC (273.15 K) and absolute pressure 1 bar can be calculated as

c = (1.4 (286.9 J/K kg) (273.15 K))1/2

    = 331.2 (m/s)


k = 1.4


R = 286.9 (J/K kg)

The speed of sound in air at 20 oC (293.15 K) and absolute pressure 1 bar can be calculated as

c = (1.4 (286.9  J/K kg) (293.15 K))1/2

    = 343.1 (m/s)

Example - Speed of Sound in Water

The speed of sound in water at 0 oC can be calculated as

c = ((2.06 109 N/m2) / (999.8 kg/m3))1/2

    = 1435.4 (m/s)


Ev= 2.06 109 (N/m2)


ρ = 999.8 (kg/m3)

Speed of Sound in 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 1 - the speed is transonic.
  • If the Mach Number is above 1, the flow velocity is higher than the speed of sound - and the speed is supersonic.
Sponsored Links

Related Topics

Related Documents

Tag Search

  • en: sound speed materials air
Sponsored Links

Search the Engineering ToolBox

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse!

Translate this page to
About the Engineering ToolBox!


This page can be cited as

  • Engineering ToolBox, (2003). Speed of Sound Formulas. [online] Available at: [Accessed Day Mo. Year].

Modify access date.

Customize Ads in the ToolBox

Make ads more useful in Google Ad Settings .

. .


3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Scientific Online Calculator

Scientific Calculator

4 20

Sponsored Links