Longitudinal Wave Speed Calculator

Calculate the longitudinal wave speed in a material from its elastic modulus and density. Shows the equation, variables and result.

Ballistics & Penetration2 min read

calculatorwave speedlongitudinalelastic modulusdensity

Calculator

1D (thin rod):
  c = sqrt(E / rho)

3D (infinite medium):
  c_d = sqrt(E*(1-nu) / (rho*(1+nu)*(1-2*nu)))

where:
  c, c_d = wave speed [m/s]
  E = elastic modulus [Pa]
  rho = density [kg/m^3]
  nu = Poisson's ratio

Enter E, rho and (for 3D) nu to compute the wave speed.

Assumptions

Material is homogeneous, isotropic and linear-elastic
1D wave speed applies to thin rods; 3D applies to bulk material

Limitations

This calculator computes the elastic wave speed. The actual wave speed in a real impact may differ due to plasticity, damage, anisotropy (composites) or temperature dependence. The wave speed is used to assess stress-wave effects and to estimate the structural response time — it does not predict the structural response.