Isentropic speed of sound

Derived by Laplace, the formula for the speed of sound in fluids uses the pressure-density dependence and the fact that the oscillations in a sound wave happen so fast, and the thermal conductivity of air is so small, that there is no heat transfer in the sound wave, i.e. it is an adiabatic, and therefore isentropic, process. This is in contrast with the Newton’s formula, who thought that the sound propagation is an isothermal process in the assumption that the temperature differences between different parts of the sound wave immediately level out, which eventually turned out to be inconsistent with experimental data.

Links:

1. Wikipedia, last equation in paragraph.

speed_of_sound

speed of sound in the fluid.

Symbol:

v_s

Latex:

\(v_\text{s}\)

Dimension:

velocity

density

density of the fluid.

Symbol:

rho

Latex:

\(\rho\)

Dimension:

mass/volume

entropy

entropy of the fluid.

Symbol:

S

Latex:

\(S\)

Dimension:

energy/temperature

pressure

pressure inside the fluid as a function of density and entropy.

Symbol:

p(rho, S)

Latex:

\(p{\left(\rho,S \right)}\)

Dimension:

pressure

law

v_s = sqrt(Derivative(p(rho, S), rho))

Latex:

\[v_\text{s} = \sqrt{\frac{\partial}{\partial \rho} p{\left(\rho,S \right)}}\]