text: In isotropic and homogeneous solids, a P wave travels in a straight line longitudinally; thus, the particles in the solid vibrate along the axis of propagation (the direction of motion) of the wave energy. The velocity of P waves in that kind of medium is given by
  where  is the bulk modulus (the modulus of incompressibility),  is the shear modulus (modulus of rigidity, sometimes denoted as  and also called the second Lamé parameter),  is the density of the material through which the wave propagates, and  is the first Lamé parameter.
  In typical situations in the interior of the Earth, the density  usually varies much less than  or , so the velocity is mostly "controlled" by these two parameters.
  The elastic moduli P-wave modulus, , is defined so that  and thereby
  Typical values for P wave velocity in earthquakes are in the range 5 to 8 km/s. The precise speed varies according to the region of the Earths interior, from less than 6 km/s in the Earths crust to 13.5 km/s in the lower mantle, and 11 km/s through the inner core.
  Geologist Francis Birch discovered a relationship between the velocity of P waves and the density of the material the waves are traveling in:
  which later became known as Birch's law. (The symbol  is an empirically tabulated function, and  is a constant.)