Tube wave speed
= Tube wave speed
{title2=$c^2=(A/\rho)\,dp/dA$}
Linearizing area conservation and the axial momentum equation of a <collapsible tube flow> gives waves travelling relative to the fluid at speeds $\pm c$, where the displayed relation uses the area derivative at fixed external pressure. For $p=P_0+\rho c_0^2(A/A_0)^2/2$, it gives $c=c_0A/A_0$.