The speed of sound is the sum of two
nonadiabatic terms

Thus, even for a nonzero *∂p/∂**r** *the speed of sound may vanish if the second term on the right-hand
side cancels the first one. This
cancellation will take place if in the course of an adiabatic expansion, the perturbation *δφ** *grows with *a* in the same
way as *δ**r**
. *In this case,
it is only a matter of adjusting the initial conditions of *δφ* with *δ**r** *to get *c*s=0.