= Speed of sound
{wiki}
= Sound speed
{synonym}
The <speed of sound> is the propagation speed of a small mechanical pressure disturbance through a medium. Compression creates a restoring <pressure gradient>, while the medium's <mass density> supplies inertia. For an inviscid fluid undergoing locally isentropic disturbances,
$$
c_s^2=\left(\frac{\partial p}{\partial\rho}\right)_s.
$$
A stiffer pressure response increases the speed. For a <perfect gas>, this becomes $c_s^2=\gamma p/\rho$, with $\gamma$ the <heat capacity ratio>.
The disturbance travels while individual fluid parcels undergo much smaller oscillatory motions; <acoustic particle velocity> and propagation speed are different quantities. Timing a short sound pulse between two sensors a known distance apart gives a direct measurement after accounting for electronic delays. If heat exchange maintains a different thermodynamic response during compression, the relevant derivative changes, as in the <isothermal sound speed>. The formula also presumes a wavelength and timescale for which the continuum model is appropriate.
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