Seismic Wave Speed

This formula says that an elastic wave travels faster in a material that is stiffer and slower in a material that is denser. The elastic modulus E measures how strongly the rock resists deformation, while density ρ represents how much mass must be accelerated as the wave passes through. In the simplest wave models, the balance between restoring stiffness and inertia leads to a speed proportional to the square root of E/ρ.

Use this when estimating how quickly seismic energy can move through a homogeneous rock or simplified Earth layer, especially in problems involving P-waves or other elastic wave speeds. It is also useful for comparing wave speeds between materials when you know their stiffness and density.

• Using shear modulus when the problem specifically gives a bulk or Young's modulus without checking which wave type the formula applies to
• Forgetting to keep units consistent, especially mixing GPa with kg/m^3 without converting to SI units
• Assuming the speed depends linearly on E/ρ instead of on the square root of that ratio