Tube wave speed ($c^2=(A/\rho )dp/dA$)

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 $c=c_{0}A/A_0$.