Speed of sound in three-dimensional solids (shear waves)

Description

The speed of sound is the distance travelled per unit of time by a sound wave propagating through an elastic medium. Sound travels faster in liquids and non-porous solids than it does in air.
Sound waves in solids are composed of compression waves, but there is also a different type of sound wave called a shear wave, which occurs only in solids.
The speed of a compression sound wave in solids is determined by the medium’s compressibility, shear modulus and density. The speed of shear waves is determined only by the solid material’s shear modulus and density.
In a solid, there is a non-zero stiffness both for volumetric deformations and shear deformations. Hence, it is possible to generate sound waves with different velocities dependent on the deformation mode. Sound waves generating volumetric deformations (compression) and shear deformations (shearing) are called pressure waves (longitudinal waves) and shear waves (transverse waves), respectively. The speed of shear waves depends on the shear properties only.

Related formulas

Variables

csolidshearSpeed of sound (m/s)
GThe bulk modulus (Pa)
ρDensity (kg/m3)