The vectorial wave equation (from which the scalar wave equation can be directly derived) can be obtained by applying a force equilibrium to an infinitesimal volume element. In a homogeneous continuum (cartesian coordinate x ) with a constant modulus of elasticity E a vectorial, elastic deflection u ( x , t ) causes the stress tensor T = E ∇ ∇ u . The local equilibrium of a) the tension force div ⁡ ⁡ T = ∇ ∇ ⋅ ⋅ ( E ∇ ∇ u ) = E Δ Δ u due to deflection u and b) the inertial force ρ ρ ∂ ∂ 2 u / ∂ ∂ t 2 caused by the local acceleration ∂ ∂ 2 u / ∂ ∂ t 2 can be written as ρ ρ ∂ ∂ 2 u ∂ ∂ t 2 − − E Δ Δ u = 0 . By merging density ρ ρ and elasticity module E , the sound velocity c = E / ρ ρ results (material law). After insertion, follows the well-known governing wave equation for a homogeneous medium: ∂ ∂ 2 u ∂ ∂ t 2 − − c 2 Δ Δ u = 0 . (Note: Instead of vectorial u ( x , t ) , only scalar u ( x , t ) can be used, i.e. waves are travelling only along the x axis, and the scalar wave equation follows as ∂ ∂ 2 u ∂ ∂ t 2 − − c 2 ∂ ∂ 2 u ∂ ∂ x 2 = 0 .)