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. In earthquakes, the corresponding seismic waves are called P-waves (primary waves) and S-waves (secondary waves), respectively. The sound velocities of these two types of waves propagating in a homogeneous 3-dimensional solid are respectively given by
where
* K is the bulk modulus of the elastic materials;
* G is the shear modulus of the elastic materials;
* E is the Young's modulus;
* ρ is the density;
* ν is Poisson's ratio.
The last quantity is not an independent one, as . Note that the speed of pressure waves depends both on the pressure and shear resistance properties of the material, while the speed of shear waves depends on the shear properties only.
Typically, pressure waves travel faster in materials than do shear waves, and in earthquakes this is the reason that the onset of an earthquake is often preceded by a quick upward-downward shock, before arrival of waves that produce a side-to-side motion. For example, for a typical steel alloy, ,  and , yielding a compressional speed c of . This is in reasonable agreement with c measured experimentally at  for a (possibly different) type of steel. The shear speed c is estimated at  using the same numbers.
Speed of sound in semiconductor solids can be very sensitive to the amount of electronic dopant in them.