ThermodynamicsFluid Flow Speed of sound in a gas CaM kRT Vi

Thermodynamics/Fluid Flow Speed of sound in a gas CaM - kRT Vibrations Natural frequency (normal modes of vibration of a string fixed at each end Fn? 4 n 2

Solution

SOLUTION:

Speed of Sound - Sonic Velocity - in Ideal Gases

For an isentropic process the ideal gas law can be used and the speed of sound can be expressed as

c = (k p / )^1/2

= (k R T)^1/2

where

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)

where

k = 1.4

and

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)