Sound speed is defined as the wavespeed of an isentropic transformation: a s ( ρ ρ , p ) ≡ ≡ ( ∂ ∂ p ∂ ∂ ρ ρ ) s by the definition of the isoentropic compressibility: K s ( ρ ρ , p ) ≡ ≡ ρ ρ ( ∂ ∂ p ∂ ∂ ρ ρ ) s the soundspeed results always the square root of ratio between the isentropic compressibility and the density: a s ≡ ≡ K s ρ ρ